# All Publications

# Preprints

Nail Kashaev, Martin Plávala, Victor H. Aguiar
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Entangled vs. Separable Choice
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arXiv:2403.09045

We study joint probabilistic choice rules that describe the behavior of two decision makers, each facing a possibly different menu. These choice rules are separable when they can be factored into autonomous choices from each individual solely correlated through their individual probabilistic choice rules. Despite recent interest in studying such rules, a complete characterization of the restrictions on them remains an open question. A reasonable conjecture is that such restrictions on separable joint choice can be factored into individual choice restrictions. We name these restrictions separable and show that this conjecture is true if and only if the probabilistic choice rule of at least one decision maker uniquely identifies the distribution over deterministic choice rules. Otherwise, entangled choice rules exist that satisfy separable restrictions yet are not separable. The possibility of entangled choice complicates the characterization of separable choice since one needs to augment the separable restrictions with the new emerging ones.

Michael Gaida, Stefan Nimmrichter
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Otto cycles with a quantum planar rotor
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arXiv:2403.00684

We present two realizations of an Otto cycle with a quantum planar rotor as the working medium controlled by means of external fields. By comparing the quantum and the classical description of the working medium, we single out genuine quantum effects with regards to the performance and the engine and refrigerator modes of the Otto cycle. The first example is a rotating electric dipole subjected to a controlled electric field, equivalent to a quantum pendulum. Here we find a systematic disadvantage of the quantum rotor compared to its classical counterpart. In contrast, a genuine quantum advantage can be observed with a charged rotor generating a magnetic moment that is subjected to a controlled magnetic field. Here, we prove that the classical rotor is inoperable as a working medium for any choice of parameters, whereas the quantum rotor supports an engine and a refrigerator mode, exploiting the quantum statistics during the cold strokes of the cycle.

Leonardo Santos, Zhen-Peng Xu, Jyrki Piilo, Otfried Gühne
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Quantifying information flow in quantum processes
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arXiv:2402.04213

We present a framework for quantifying information flow within general quantum processes. For this purpose, we introduce the signaling power of quantum channels and discuss its relevant operational properties. This function supports extensions to higher order maps, enabling the evaluation of information flow in general quantum causal networks and also processes with indefinite causal order. Furthermore, our results offer a rigorous approach to information dynamics in open systems that applies also in the presence of initial system-environment correlations, and allows for the distinction between classical and quantum information backflow.

Konrad Szymański, Lina Vandré, Otfried Gühne
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Useful entanglement can be extracted from noisy graph states
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arXiv:2402.00937

Cluster states and graph states in general offer a useful model of the stabilizer formalism and a path toward the development of measurement-based quantum computation. Their defining structure -- the stabilizer group -- encodes all possible correlations which can be observed during measurement. Those outcomes which are compatible with the stabilizer structure make error correction possible. Here, we leverage both properties to design feasible families of states that can be used as robust building blocks of quantum computation. This procedure reduces the effect of experimentally relevant noise models on the extraction of smaller entangled states from the larger noisy graph state. In particular, we study the extraction of Bell pairs from linearly extended graph states -- this has the immediate consequence for state teleportation across the graph. We show that robust entanglement can be extracted by proper design of the linear graph with only a minimal overhead of the physical qubits. This scenario is relevant to systems in which the entanglement can be created between neighboring sites. The results shown in this work may provide a mathematical framework for noise reduction in measurement-based quantum computation. With proper connectivity structures, the effect of noise can be minimized for a large class of realistic noise processes.

Marta Maria Marchese, Martin Plávala, Matthias Kleinmann, Stefan Nimmrichter
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Newton's laws of motion can generate gravity-mediated entanglement
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arXiv:2401.07832

The interface between quantum theory and gravity represents still uncharted territory. Recently, some works suggested promising alternative approaches aimed at witnessing quantum features to test the fundamental nature of gravity in tabletop experiments: Two masses in an initial superposition of spatially localized states are allowed to interact only through gravity and it is measured whether the final state is entangled. Here we show that one can generate the same amount of entanglement in this setup by using classical time evolution given by Newton's laws of motion. We argue that theories of quantum gravity that can be approximated by the Newtonian potential and classical time evolution given by Newton's laws of motion will generate gravity-mediated entanglement.

Philipp Haslinger, Stefan Nimmrichter, Dennis Rätzel
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Spin Resonance Spectroscopy with an Electron Microscope
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arXiv:2401.06496

Coherent spin resonance methods, such as nuclear magnetic resonance and electron spin resonance spectroscopy, have led to spectrally highly sensitive, non-invasive quantum imaging techniques. Here, we propose a pump-probe spin resonance spectroscopy approach, designed for electron microscopy, based on microwave pump fields and electron probes. We investigate how quantum spin systems couple to electron matter waves through their magnetic moments and how the resulting phase shifts can be utilized to gain information about the states and dynamics of these systems. Notably, state-of-the-art transmission electron microscopy provides the means to detect phase shifts almost as small as that due to a single electron spin. This could enable state-selective observation of spin dynamics on the nanoscale and indirect measurement of the environment of the examined spin systems, providing information, for example, on the atomic structure, local chemical composition and neighboring spins.

Ye-Chao Liu, Otfried Gühne, Stefan Nimmrichter
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Entanglement Buffers
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arXiv:2312.05099

Quantum entanglement is the essential resource for quantum communication and distributed information processing in a quantum network. However, the remote generation over a network suffers from inevitable transmission loss and other technical difficulties. This paper introduces the concept of entanglement buffers as a potential primitive for preparing long-distance entanglement. We investigate the filling of entanglement buffers with either one Bell state or a stream of Bell states. We illustrate their resilience to non-ideal interactions and transmission loss, making them sometimes more advantageous than other entanglement generation approaches in the quantum network scenario. Additionally, larger entanglement buffers can always enhance these benefits.

Jan Lennart Bönsel, Satoya Imai, Ye-Chao Liu, Otfried Gühne
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Error estimation of different schemes to measure spin-squeezing inequalities
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arXiv:2311.17845

How can we analyze quantum correlations in large and noisy systems without quantum state tomography? An established method is to measure total angular momenta and employ the so-called spin-squeezing inequalities based on their expectations and variances. This allows to detect metrologically useful entanglement, but efficient strategies for estimating such non-linear quantities have yet to be determined. In this paper, we focus on the measurement of spin-squeezing inequalities in multi-qubit systems. We show that spin-squeezing inequalities can not only be evaluated by measurements of the total angular momentum but also by two-qubit correlations, either involving all pair correlations or randomly chosen pair correlations. Then we analyze the estimation errors of our approaches in terms of a hypothesis test. For this purpose, we discuss how error bounds can be derived for non-linear estimators with the help of their variances, characterizing the probability of falsely detecting a separable state as entangled. Our methods can be applied for the statistical treatment of other non-linear parameters of quantum states.

Teiko Heinosaari, Leevi Leppäjärvi, Martin Plávala
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Encoding and decoding of information in general probabilistic theories
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arXiv:2311.17522

Encoding and decoding are the two key steps in information processing. In this work we study the encoding and decoding capabilities of operational theories in the context of information-storability game, where the task is to freely choose a set of states from which one state is chosen at random and by measuring the state it must be identified; a correct guess results in as many utiles as the number of states in the chosen set and an incorrect guess means a penalty of a fixed number of utiles. We connect the optimal winning strategy of the game to the amount of information that can be stored in a given theory, called the information storability of the theory, and show that one must use so-called nondegradable sets of states and nondegradable measurements whose encoding and decoding properties cannot be reduced. We demonstrate that there are theories where the perfect discrimination strategy is not the optimal one so that the introduced game can be used as an operational test for super information storability. We further develop the concept of information storability by giving new useful conditions for calculating it in specific theories.

Mei Yu, H. Chau Nguyen, Stefan Nimmrichter
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Criticality-Enhanced Precision in Phase Thermometry
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arXiv:2311.14578

Temperature estimation of interacting quantum many-body systems is both a challenging task and topic of interest in quantum metrology, given that critical behavior at phase transitions can boost the metrological sensitivity. Here we study non-invasive quantum thermometry of a finite, two-dimensional Ising spin lattice based on measuring the non-Markovian dephasing dynamics of a spin probe coupled to the lattice. We demonstrate a strong critical enhancement of the achievable precision in terms of the quantum Fisher information, which depends on the coupling range and the interrogation time. Our numerical simulations are compared to instructive analytic results for the critical scaling of the sensitivity in the Curie-Weiss model of a fully connected lattice and to the mean-field description in the thermodynamic limit, both of which fail to describe the critical spin fluctuations on the lattice the spin probe is sensitive to. Phase metrology could thus help to investigate the critical behaviour of finite many-body systems beyond the validity of mean-field models.

Gereon Koßmann, René Schwonnek, Jonathan Steinberg
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Hierarchies for Semidefinite Optimization in C*-Algebras
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arXiv:2309.13966

Semidefinite Optimization has become a standard technique in the landscape of Mathematical Programming that has many applications in finite dimensional Quantum Information Theory. This paper presents a way for finite-dimensional relaxations of general cone programs on $\mathcal{C}^\star$-algebras which have structurally similar properties to ordinary cone programs, only putting the notion of positivity at the core of optimization. We show that well-known hierarchies for generalized problems like NPA but also Lasserre's hierarchy and to some extend symmetry reductions of generic SDPs by de-Klerk et al. can be considered from a general point of view of $\mathcal{C}^\star$-algebras in combination to optimization problems.

Lisa T. Weinbrenner, Nidhin Prasannan, Kiara Hansenne, Sophia Denker, Jan Sperling, Benjamin Brecht, Christine Silberhorn, Otfried Gühne
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Certifying the topology of quantum networks: theory and experiment
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arXiv:2309.12907

Distributed quantum information in networks is paramount for global secure quantum communication. Moreover, it finds applications as a resource for relevant tasks, such as clock synchronization, magnetic field sensing, and blind quantum computation. For quantum network analysis and benchmarking of implementations, however, it is crucial to characterize the topology of networks in a way that reveals the nodes between which entanglement can be reliably distributed. Here, we demonstrate an efficient scheme for this topology certification. Our scheme allows for distinguishing, in a scalable manner, different networks consisting of bipartite and multipartite entanglement sources, for different levels of trust in the measurement devices and network nodes. We experimentally demonstrate our approach by certifying the topology of different six-qubit networks generated with polarized photons, employing active feed-forward and time multiplexing. Our methods can be used for general simultaneous tests of multiple hypotheses with few measurements, being useful for other certification scenarios in quantum technologies.

Satoya Imai, Géza Tóth, Otfried Gühne
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Collective randomized measurements in quantum information processing
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arXiv:2309.10745

The concept of randomized measurements on individual particles has proven to be useful for analyzing quantum systems and is central for methods like shadow tomography of quantum states. We introduce $\textit{collective}$ randomized measurements as a tool in quantum information processing. Our idea is to perform measurements of collective angular momentum on a quantum system and actively rotate the directions using simultaneous multilateral unitaries. Based on the moments of the resulting probability distribution, we propose systematic approaches to characterize quantum entanglement in a collective-reference-frame-independent manner. First, we show that existing spin-squeezing inequalities can be accessible in this scenario. Next, we present an entanglement criterion based on three-body correlations, going beyond spin-squeezing inequalities with two-body correlations. Finally, we apply our method to characterize entanglement between spatially-separated two ensembles.

Shravan Shravan, Simon Morelli, Otfried Gühne, Satoya Imai
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Geometry of two-body correlations in three-qubit states
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arXiv:2309.09549

We study restrictions of two-body correlations in three-qubit states, using three local-unitarily invariant coordinates based on the Bloch vector lengths of the marginal states. First, we find tight nonlinear bounds satisfied by all pure states and extend this result by including the three-body correlations. Second, we consider mixed states and conjecture a tight non-linear bound for all three-qubit states. Finally, within the created framework we give criteria to detect different types of multipartite entanglement as well as characterize the rank of the quantum state.

Martin Plávala, Teiko Heinosaari, Stefan Nimmrichter, Otfried Gühne
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Tsirelson Inequalities: Detecting Cheating and Quantumness in One Fell Swoop
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arXiv:2309.00021

Quantumness refers to the peculiar and counterintuitive characteristics exhibited by quantum systems. Tsirelson inequalities have emerged as a powerful tool in quantum theory to detect quantumness and entanglement of harmonic oscillators, spins undergoing uniform precession, and anharmonic systems. In this paper, we harness the versatility of Tsirelson inequalities to address two distinct problems: detecting cheating in classic shell games and probing quantumness in harmonic oscillators. By adopting a black-box approach and a geometric characterization of the space of conditional probabilities, we demonstrate that Tsirelson inequalities can be used in both scenarios, enabling us to uncover quantum signatures and identify cheaters in a single unified framework. This connection provides an intuitive new perspective on quantumness of mechanical systems.

Teiko Heinosaari, Oskari Kerppo, Leevi Leppäjärvi, Martin Plávala
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Simple Information Processing Tasks with Unbounded Quantum Advantage
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arXiv:2308.07727

Communication scenarios between two parties can be implemented by first encoding messages into some states of a physical system which acts as the physical medium of the communication and then decoding the messages by measuring the state of the system. We show that already in the simplest possible scenarios it is possible to detect a definite, unbounded advantage of quantum systems over classical systems. We do this by constructing a family of operationally meaningful communication tasks each of which on one hand can be implemented by using just a single qubit but which on the other hand require unboundedly larger classical system for classical implementation. Furthemore, we show that even though with the additional resource of shared randomness the proposed communication tasks can be implemented by both quantum and classical systems of the same size, the number of coordinated actions needed for the classical implementation also grows unboundedly. In particular, no finite storage can be used to store all the coordinated actions needed to implement all the possible quantum communication tasks with classical systems. As a consequence, shared randomness cannot be viewed as a free resource.

Carlos de Gois, Matthias Kleinmann
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User-friendly confidence regions for quantum state tomography
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arXiv:2308.01851

Quantum state tomography is the standard technique for reconstructing a quantum state from experimental data. In the regime of finite statistics, experimental data cannot give perfect information about the quantum state. A common way to express this limited knowledge is by providing confidence regions in the state space. Though other confidence regions were previously proposed, they are either too wasteful to be of practical interest, cannot easily be applied to general measurement schemes, or are too difficult to report. Here we construct confidence regions that solve these issues, as they have an asymptotically optimal sample cost and good performance for realistic parameters, are applicable to any measurement scheme, and can be described by an ellipsoid in the space of Hermitian operators. Our construction relies on a vector Bernstein inequality and bounds with high probability the Hilbert-Schmidt norm error of sums of multinomial samples transformed by linear maps.

Isadora Veeren, Martin Plávala, Leevi Leppäjärvi, Roope Uola
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Semi-device-independent certification of number of measurements
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arXiv:2307.13737

We develop a method for semi-device-independent certification of number of measurements. We achieve this by testing whether Bob's steering equivalent observables (SEO) can be simulated by k measurements, which we do by testing whether they are k-compatible with separable joint observable. This test can be performed with the aid of hierarchy of semidefinite programs, and whenever it fails one can conclude that Alice must have access to at least k + 1 incompatible measurements.

Kiara Hansenne, Otfried Gühne
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Covariance matrix-based criteria for network entanglement
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arXiv:2307.13480

Quantum networks offer a realistic and practical scheme for generating multiparticle entanglement and implementing multiparticle quantum communication protocols. However, the correlations that can be generated in networks with quantum sources and local operations are not yet well understood. Covariance matrices, which are powerful tools in entanglement theory, have been also applied to the network scenario. We present simple proofs for the decomposition of such matrices into the sum of positive semidefinite block matrices and, based on that, develop analytical and computable necessary criteria for preparing states in quantum networks. These criteria can be applied to networks in which any two nodes share at most one source, such as all bipartite networks.

Benjamin Yadin, Satoya Imai, Otfried Gühne
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Quantum speed limit for perturbed open systems
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arXiv:2307.09118

Quantum speed limits provide upper bounds on the rate with which a quantum system can move away from its initial state. Here, we provide a different kind of speed limit, describing the divergence of a perturbed open system from its unperturbed trajectory. In the case of weak coupling, we show that the divergence speed is bounded by the quantum Fisher information under a perturbing Hamiltonian, up to an error which can be estimated from system and bath timescales. We give two applications of our speed limit. Firstly, it enables experimental estimation of quantum Fisher information in the presence of decoherence that is not fully characterised. Secondly, it implies that large quantum work fluctuations are necessary for a thermal system to be driven quickly out of equilibrium under a quench.

Yuxiang Yang, Benjamin Yadin, Zhen-Peng Xu
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Quantum-enhanced metrology with network states
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arXiv:2307.07758

Armed with quantum correlations, quantum sensors in a network have shown the potential to outclass their classical counterparts in distributed sensing tasks such as clock synchronization and reference frame alignment. On the other hand, this analysis was done for simple and idealized networks, whereas the correlation shared within a practical quantum network, captured by the notion of network states, is much more complex. Here, we prove a general bound that limits the performance of using quantum network states to estimate a global parameter, establishing the necessity of genuine multipartite entanglement for achieving a quantum advantage. The bound can also serve as an entanglement witness in networks and can be generalized to states generated by shallow circuits. Moreover, while our bound prohibits local network states from achieving the Heisenberg limit, we design a probabilistic protocol that, once successful, attains this ultimate limit of quantum metrology. Our work establishes both the limitation and the possibility of quantum metrology within quantum networks.

Jun Gao, Leonardo Santos, Govind Krishna, Ze-Sheng Xu, Adrian Iovan, Stephan Steinhauer, Otfried Gühne, Philip J. Poole, Dan Dalacu, Val Zwiller, Ali W. Elshaari
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Scalable generation and detection of on-demand W states in nanophotonic circuits
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arXiv:2307.06116

Quantum physics phenomena, entanglement and coherence, are crucial for quantum information protocols, but understanding these in systems with more than two parts is challenging due to increasing complexity. The W state, a multipartite entangled state, is notable for its robustness and benefits in quantum communication. Here, we generate an 8-mode on-demand single photon W states, using nanowire quantum dots and a silicon nitride photonic chip. We demonstrate a reliable, scalable technique for reconstructing W-state in photonic circuits using Fourier and real-space imaging, supported by the Gerchberg-Saxton phase retrieval algorithm. Additionally, we utilize an entanglement witness to distinguish between mixed and entangled states, thereby affirming the entangled nature of our generated state. The study provides a new imaging approach of assessing multipartite entanglement in W-states, paving the way for further progress in image processing and Fourier-space analysis techniques for complex quantum systems.

Chao Zhang, Yuan-Yuan Zhao, Nikolai Wyderka, Satoya Imai, Andreas Ketterer, Ning-Ning Wang, Kai Xu, Keren Li, Bi-Heng Liu, Yun-Feng Huang, Chuan-Feng Li, Guang-Can Guo, Otfried Gühne
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Experimental verification of bound and multiparticle entanglement with the randomized measurement toolbox
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arXiv:2307.04382

In recent years, analysis methods for quantum states based on randomized measurements have been investigated extensively. Still, in the experimental implementations these methods were typically used for characterizing strongly entangled states and not to analyze the different families of multiparticle or weakly entangled states. In this work, we experimentally prepare various entangled states with path-polarization hyper-entangled photon pairs, and study their entanglement properties using the full toolbox of randomized measurements. First, we successfully characterize the correlations of a series of GHZ-W mixed states using the second moments of the random outcomes, and demonstrate the advantages of this method by comparing it with the well-known three-tangle and squared concurrence. Second, we generate bound entangled chessboard states of two three-dimensional systems and verify their weak entanglement with a criterion derived from moments of randomized measurements.

Adán Cabello, Marco Túlio Quintino, Matthias Kleinmann
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Logical possibilities for physics after MIP*=RE
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arXiv:2307.02920

MIP*=RE implies that C_{qa} (the closure of the set of tensor product correlations) and C_{qc} (the set of commuting correlations) can be separated by a hyperplane (i.e., a Bell-like inequality) and that there are correlations produced by commuting measurements (a finite number of them and with a finite number of outcomes) on an infinite-dimensional quantum system which cannot be approximated by sequences of finite-dimensional tensor product correlations. We point out that there are four logically possible universes after this result. Each possibility is interesting because it reveals either limitations in accepted physical theories or opportunities to test crucial aspects of nature. We list some open problems that may help us to design a road map to learn in which of these universes we are.

Lukas Kienesberger, Thomas Juffmann, Stefan Nimmrichter
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Quantum Limits of Position and Polarizability Estimation in the Optical Near Field
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arXiv:2307.02348

Optical near fields are at the heart of various applications in sensing and imaging. We investigate dipole scattering as a parameter estimation problem and show that optical near-fields carry more information about the location and the polarizability of the scatterer than the respective far fields. This increase in information originates from and occurs simultaneously with the scattering process itself. Our calculations also yield the far-field localization limit for dipoles in free space.

Paweł Cieśliński, Satoya Imai, Jan Dziewior, Otfried Gühne, Lukas Knips, Wiesław Laskowski, Jasmin Meinecke, Tomasz Paterek, Tamás Vértesi
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Analysing quantum systems with randomised measurements
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arXiv:2307.01251

Randomised measurements provide a way of determining physical quantities without the need for a shared reference frame nor calibration of measurement devices. Therefore, they naturally emerge in situations such as benchmarking of quantum properties in the context of quantum communication and computation where it is difficult to keep local reference frames aligned. In this review, we present the advancements made in utilising such measurements in various quantum information problems focusing on quantum entanglement and Bell inequalities. We describe how to detect and characterise various forms of entanglement, including genuine multipartite entanglement and bound entanglement. Bell inequalities are discussed to be typically violated even with randomised measurements, especially for a growing number of particles and settings. Additionally, we provide an overview of estimating other relevant nonlinear functions of a quantum state or performing shadow tomography from randomised measurements. Throughout the review, we complement the description of theoretical ideas by explaining key experiments.

Ties-A. Ohst, Martin Plávala
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Symmetries and Wigner representations of operational theories
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arXiv:2306.11519

We develop the theory of Wigner representations for a large class of operational theories that include both classical and quantum theory. The Wigner representations that we introduce are a natural way to describe the theory in terms of some fixed observables; these observables are often picked to be position and momentum or spin observables. This allows us to introduce symmetries which transform the outcomes of the observables used to construct the Wigner representation; we obtain several results for when these symmetries are well defined or when they uniquely specify the Wigner representation.

Lisa T. Weinbrenner, Lina Vandré, Tim Coopmans, Otfried Gühne
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Aging and Reliability of Quantum Networks
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arXiv:2305.19976

Quantum information science may lead to technological breakthroughs in computing, cryptography and sensing. For the implementation of these tasks, however, complex devices with many components are needed and the quantum advantage may easily be spoiled by failure of few parts only. A paradigmatic example are quantum networks. There, not only noise sources like photon absorption or imperfect quantum memories lead to long waiting times and low fidelity, but also hardware components may break, leading to a dysfunctionality of the entire network. For the successful long-term deployment of quantum networks in the future, it is important to take such deterioration effects into consideration during the design phase. Using methods from reliability theory and the theory of aging we develop an analytical approach for characterizing the functionality of networks under aging and repair mechanisms, also for non-trivial topologies. Combined with numerical simulations, our results allow to optimize long-distance entanglement distribution under aging effects.

Hamza Jnane, Jonathan Steinberg, Zhenyu Cai, H. Chau Nguyen, Bálint Koczor
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Quantum Error Mitigated Classical Shadows
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arXiv:2305.04956

Classical shadows enable us to learn many properties of a quantum state $ρ$ with very few measurements. However, near-term and early fault-tolerant quantum computers will only be able to prepare noisy quantum states $ρ$ and it is thus a considerable challenge to efficiently learn properties of an ideal, noise free state $ρ_{id}$. We consider error mitigation techniques, such as Probabilistic Error Cancellation (PEC), Zero Noise Extrapolation (ZNE) and Symmetry Verification (SV) which have been developed for mitigating errors in single expected value measurements and generalise them for mitigating errors in classical shadows. We find that PEC is the most natural candidate and thus develop a thorough theoretical framework for PEC shadows with the following rigorous theoretical guarantees: PEC shadows are an unbiased estimator for the ideal quantum state $ρ_{id}$; the sample complexity for simultaneously predicting many linear properties of $ρ_{id}$ is identical to that of the conventional shadows approach up to a multiplicative factor which is the sample overhead due to error mitigation. Due to efficient post-processing of shadows, this overhead does not depend directly on the number of qubits but rather grows exponentially with the number of noisy gates. The broad set of tools introduced in this work may be instrumental in exploiting near-term and early fault-tolerant quantum computers: We demonstrate in detailed numerical simulations a range of practical applications of quantum computers that will significantly benefit from our techniques.

Jonathan Steinberg, H. Chau Nguyen, Matthias Kleinmann
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Certifying activation of quantum correlations with finite data
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arXiv:2305.03748

Quantum theory allows for different classes of correlations, such as entanglement, steerability or Bell-nonlocality. Experimental demonstrations of the preparation of quantum states within specific classes and their subsequent interconversion have been carried out; however, rigorous statements on the statistical significance are not available. Behind this are two difficulties: the lack of a method to derive a suitable confidence region from the measured data and an efficient technique to classify the quantum correlations for every state in the confidence region. In this work, we show how both of these problems can be addressed. Specifically, we introduce a confidence polytope in the form of a hyperoctahedron and provide a computationally efficient method to verify whether a quantum state admits a local hidden state model, thus being unsteerable and, consequently, Bell-local. We illustrate how our methods can be used to analyse the activation of quantum correlations by local filtering, specifically for Bell-nonlocality and quantum steerability.

Michael Gaida, Stefan Nimmrichter
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Quantum measurement feedback models of friction beyond the diffusive limit and their connection to collapse models
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arXiv:2304.05940

We present and discuss a master equation blueprint for a generic class of quantum measurement feedback based models of friction. A desired velocity-dependent friction force is realized on average by random repeated applications of unsharp momentum measurements followed by immediate outcome-dependent momentum displacements. The master equations can describe arbitrarily strong measurement-feedback processes as well as the weak continuous limit resembling diffusion master equations of Caldeira-Leggett type. We show that the special case of linear friction can be equivalently represented by an average over random position measurements with squeezing and position displacements as feedback. In fact, the dissipative continuous spontaneous localization model of objective wavefunction collapse realizes this representation for a single quantum particle. We reformulate a consistent many-particle generalization of this model and highlight the possibility of feedback-induced correlations between otherwise non-interacting particles.

Chengjie Zhang, Sophia Denker, Ali Asadian, Otfried Gühne
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Analyzing quantum entanglement with the Schmidt decomposition in operator space
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arXiv:2304.02447

Characterizing entanglement is central for quantum information science. Special observables which indicate entanglement, so-called entanglement witnesses, are a widely used tool for this task. The construction of these witnesses typically relies on the observation that quantum states with a high fidelity to some entangled target state are entangled, too. We introduce a general method to construct entanglement witnesses based on the Schmidt decomposition of observables. The method works for two- and, more importantly, many-body systems and is strictly stronger than fidelity-based constructions. The resulting witnesses can also be used to quantify entanglement as well as to characterize the dimensionality of it. Finally, we present experimentally relevant examples, where our approach improves entanglement detection significantly.

Nail Kashaev, Victor H. Aguiar, Martin Plávala, Charles Gauthier
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Dynamic and Stochastic Rational Behavior
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arXiv:2302.04417

We analyze choice behavior using Dynamic Random Utility Model (DRUM). Under DRUM, each consumer or decision-maker draws a utility function from a stochastic utility process in each period and maximizes it subject to a menu. DRUM allows for unrestricted time correlation and cross-section heterogeneity in preferences. We fully characterize DRUM when panel data on choices and menus are available. Our results cover consumer demand with a continuum of choices and finite discrete choice setups. DRUM is linked to a finite mixture of deterministic behaviors that can be represented as the Kronecker product of static rationalizable behaviors. We exploit a generalization of the Weyl-Minkowski theorem that uses this link and enables conversion of the characterizations of the static Random Utility Model (RUM) of McFadden-Richter (1990) to its dynamic form. DRUM is more flexible than Afriat's (1967) framework and more informative than RUM. In an application, we find that static utility maximization fails to explain population behavior, but DRUM can explain it.

Jan Nöller, Otfried Gühne, Mariami Gachechiladze
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Symmetric hypergraph states: Entanglement quantification and robust Bell nonlocality
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arXiv:2302.01695

Quantum hypergraph states are the natural generalization of graph states. Here we investigate and analytically quantify entanglement and nonlocality for large classes of quantum hypergraph states. More specifically, we connect the geometric measure of entanglement of symmetric hypergraphs to their local Pauli stabilizers. As a result we recognize the resemblance between symmetric graph states and symmetric hypergraph states, which explains both, exponentially increasing violation of local realism for infinitely many classes of hypergraph states and its robustness towards particle loss.

Xiao-Dong Yu, Isadora Veeren, Otfried Gühne
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Characterizing finite-dimensional quantum contextuality
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arXiv:2212.11559

As a phenomenon encompassing measurement incompatibility and Bell nonlocality, quantum contextuality is not only central to our understanding of quantum mechanics, but also an essential resource in many quantum information processing tasks. The dimension-dependent feature of quantum contextuality is known ever since its discovery, but systematic methods for characterizing the quantum contextuality in systems with fixed dimension are still lacking. In this work, we solve this problem. We provide systematic and reliable methods for verifying whether or not an obtained probability distribution can result from a $d$-dimensional quantum system, as well as calculating finite-dimensional violation of a general noncontextuality inequality. As an application, our methods reveal the non-convex structure of finite-dimensional quantum contextuality.

Michael Gaida, Matthias Kleinmann
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Seven definitions of bipartite bound entanglement
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arXiv:2212.11015

An entangled state is bound entangled, if one cannot combine any number of copies of the state to a maximally entangled state, by using only local operations and classical communication. If one formalizes this notion of bound entanglement, one arrives immediately at four different definitions. In addition, at least three more definitions are commonly used in the literature, in particular so in the very first paper on bound entanglement. Here we review critical distillation protocols and we examine how different results from quantum information theory interact in order to prove that all seven definitions are eventually equivalent. Our self-contained analysis unifies and extends previous results scattered in the literature and reveals details of the structure of bound entanglement.

Mei Yu, Otfried Gühne, Stefan Nimmrichter
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Exact Entanglement Dynamics of Two Spins in Finite Baths
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arXiv:2212.09151

We consider the buildup and decay of two-spin entanglement through phase interactions in a finite environment of surrounding spins, as realized in quantum computing platforms based on arrays of atoms, molecules, or nitrogen vacancy centers. The non-Markovian dephasing caused by the spin environment through Ising-type phase interactions can be solved exactly and compared to an effective Markovian treatment based on collision models. In a first case study on a dynamic lattice of randomly hopping spins, we find that non-Markovianity boosts the dephasing rate caused by nearest neighbour interactions with the surroundings, degrading the maximum achievable entanglement. However, we also demonstrate that additional three-body interactions can mitigate this degradation, and that randomly timed reset operations performed on the two-spin system can help sustain a finite average amount of steady-state entanglement. In a second case study based on a model nuclear magnetic resonance system, we elucidate the role of bath correlations at finite temperature on non-Markovian dephasing. They speed up the dephasing at low temperatures while slowing it down at high temperatures, compared to an uncorrelated bath, which is related to the number of thermally accessible spin configurations with and without interactions.

Jonathan Steinberg, Otfried Gühne
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Maximizing the geometric measure of entanglement
*

arXiv:2210.13475

The characterization of the maximally achievable entanglement in a given physical system is relevant, as entanglement is known to be a resource for various quantum information tasks. This holds especially for pure multiparticle quantum states, where the problem of maximal entanglement is not only of physical interest, but also closely related to fundamental mathematical problems in multilinear algebra and tensor analysis. We propose an algorithmic method to find maximally entangled states of several particles in terms of the geometric measure of entanglement. Besides identifying physically interesting states our results deliver insights to the problem of absolutely maximally entangled states; moreover, our methods can be generalized to identify maximally entangled subspaces.

Martin Plávala, Otfried Gühne
*
Contextuality as a precondition for entanglement
*

arXiv:2209.09942

Quantum theory features several phenomena which can be considered as resources for information processing tasks. Some of these effects, such as entanglement, arise in a non-local scenario, where a quantum state is distributed between different parties. Other phenomena, such as contextuality can be observed, if quantum states are prepared and then subjected to sequences of measurements. Here we provide an intimate connection between different resources by proving that entanglement in a non-local scenario can only arise if there is preparation & measurement contextuality in a sequential scenario derived from the non-local one by remote state preparation. Moreover, the robust absence of entanglement implies the absence of contextuality. As a direct consequence, our result allows to translate any inequality for testing preparation & measurement contextuality into an entanglement test; in addition, entanglement witnesses can be used to obtain novel contextuality inequalities.

Yi-Xuan Wang, Zhen-Peng Xu, Otfried Gühne
*
Quantum networks cannot generate graph states with high fidelity
*

arXiv:2208.12100

Quantum networks lead to novel notions of locality and correlations which are not well understood. An important problem concerns the question which states can be experimentally prepared with a given network structure and which not. By exploiting the inflation technique and symmetry analysis, we prove that all multi-qubit graph states arising from a connected graph cannot originate from any bipartite network. Moreover, the fidelity of a multi-qubit graph state and any network state cannot exceed $9/10$. Similar results can also be established for a large class of multi-qudit graph states. More specifically, the fidelity of any prime-dimensional graph state and states prepared in a bipartite network cannot exceed $0.95495$.

Pascal Höhn, Zhen-Peng Xu, Matthias Kleinmann
*
Systematic construction of quantum contextuality scenarios with rank advantage
*

arXiv:2207.11183

A set of quantum measurements exhibits quantum contextuality when any consistent value assignment to the measurement outcomes leads to a contradiction with quantum theory. In the original Kochen-Specker-type of argument the measurement projectors are assumed to be rays, that is, of unit rank. Only recently a contextuality scenario has been identified where state-independent contextuality requires measurements with projectors of rank two. Using the disjunctive graph product, we provide a systematic method to construct contextuality scenarios which require non-unit rank. We construct explicit examples requiring ranks greater than rank one up to rank five.

Guillaume Aubrun, Alexander Müller-Hermes, Martin Plávala
*
Monogamy of entanglement between cones
*

arXiv:2206.11805

A separable quantum state shared between parties A and B can be symmetrically extended to a quantum state shared between party A and parties B1,…,Bk for every k∈N. Quantum states that are not separable, i.e., entangled, do not have this property. This phenomenon is known as "monogamy of entanglement". We show that monogamy is not only a feature of quantum theory, but that it characterizes the minimal tensor product of general pairs of convex cones 𝖢A and 𝖢B: The elements of the minimal tensor product 𝖢A⊗min𝖢B are precisely the tensors that can be symmetrically extended to elements in the maximal tensor product 𝖢A⊗max𝖢⊗maxkB for every k∈N. Equivalently, the minimal tensor product of two cones is the intersection of the nested sets of k-extendible tensors. It is a natural question when the minimal tensor product 𝖢A⊗min𝖢B coincides with the set of k-extendible tensors for some finite k. We show that this is universally the case for every cone 𝖢A if and only if 𝖢B is a polyhedral cone with a base given by a product of simplices. Our proof makes use of a new characterization of products of simplices up to affine equivalence that we believe is of independent interest.

Carlos Vieira, Carlos de Gois, Lucas Pollyceno, Rafael Rabelo
*
Interplays between classical and quantum entanglement-assisted communication scenarios
*

arXiv:2205.05171

Prepare and measure scenarios, in their many forms, can be seen as basic building blocks of communication tasks. As such, they can be used to analyze a diversity of classical and quantum protocols -- of which dense coding and random access codes are key examples -- in a unified manner. In particular, the use of entanglement as a resource in prepare and measure scenarios have only recently started to be systematically investigated, and many crucial questions remain open. In this work, we explore such scenarios and provide answers to some seminal questions. More specifically, we show that, in scenarios where entanglement is a free resource, quantum messages are equivalent to classical ones with twice the capacity. We also prove that, in such scenarios, it is always advantageous for the parties to share entangled states of dimension greater than the transmitted message. Finally, we show that unsteerable states cannot provide advantages in classical communication tasks -- tasks where classical messages are transmitted --, thus proving that not all entangled states are useful resources in these scenarios and establishing an interesting link between quantum steering and nonclassicality in prepare and measure scenarios.

Adam Czaplinski, Thorsten Raasch, Jonathan Steinberg
*
Real eigenstructure of regular simplex tensors
*

arXiv:2203.01865

We are concerned with the eigenstructure of supersymmetric tensors. Like in the matrix case, normalized tensor eigenvectors are fixed points of the tensor power iteration map. However, unless the given tensor is orthogonally decomposable, some of these fixed points may be repelling and therefore be undetectable by any numerical scheme. In this paper, we consider the case of regular simplex tensors whose symmetric decomposition is induced by an overcomplete, equiangular set of $n+1$ vectors from $\mathbb R^n$. We discuss the full real eigenstructure of such tensors, including the robustness analysis of all normalized eigenvectors. As it turns out, regular simplex tensors exhibit robust as well as non-robust eigenvectors which, moreover, only partly coincide with the generators from the symmetric tensor decomposition.

Kishor Bharti, Maharshi Ray, Zhen-Peng Xu, Masahito Hayashi, Leong-Chuan Kwek, Adán Cabello
*
Graph-Theoretic Framework for Self-Testing in Bell Scenarios
*

arXiv:2104.13035

Quantum self-testing is the task of certifying quantum states and measurements using the output statistics solely, with minimal assumptions about the underlying quantum system. It is based on the observation that some extremal points in the set of quantum correlations can only be achieved, up to isometries, with specific states and measurements. Here, we present a new approach for quantum self-testing in Bell non-locality scenarios, motivated by the following observation: the quantum maximum of a given Bell inequality is, in general, difficult to characterize. However, it is strictly contained in an easy-to-characterize set: the \emph{theta body} of a vertex-weighted induced subgraph $(G,w)$ of the graph in which vertices represent the events and edges join mutually exclusive events. This implies that, for the cases where the quantum maximum and the maximum within the theta body (known as the Lovász theta number) of $(G,w)$ coincide, self-testing can be demonstrated by just proving self-testability with the theta body of $G$. This graph-theoretic framework allows us to (i) recover the self-testability of several quantum correlations that are known to permit self-testing (like those violating the Clauser-Horne-Shimony-Holt (CHSH) and three-party Mermin Bell inequalities for projective measurements of arbitrary rank, and chained Bell inequalities for rank-one projective measurements), (ii) prove the self-testability of quantum correlations that were not known using existing self-testing techniques (e.g., those violating the Abner Shimony Bell inequality for rank-one projective measurements). Additionally, the analysis of the chained Bell inequalities gives us a closed-form expression of the Lovász theta number for a family of well-studied graphs known as the Möbius ladders, which might be of independent interest in the community of discrete mathematics.

Tristan Kraft and Marco Piani
*
Monogamy relations of quantum coherence between multiple subspaces
*

arXiv:1911.10026

Quantum coherence plays an important role in quantum information protocols that provide an advantage over classical information processing. The amount of coherence that can exist between two orthogonal subspaces is limited by the positivity constraint on the density matrix. On the level of multipartite systems, this gives rise to what is known as monogamy of entanglement. On the level of single systems this leads to a bound, and hence, a trade-off in coherence that can exist between different orthogonal subspaces. In this work we derive trade-off relations for the amount of coherence that can be shared between a given subspace and all other subspaces based on trace norm, Hilbert-Schmidt norm and von Neumann relative entropy. From this we derive criteria detecting genuine multisubspace coherence.

Jiangwei Shang, Yi-Lin Seah, Boyu Wang, Hui Khoon Ng, David John Nott and Berthold-Georg Englert
*
Random samples of quantum states: Online resources
*

arXiv:1612.05180

This is the documentation for generating random samples from the quantum state space in accordance with a specified distribution, associated with this webpage: http://tinyurl.com/QSampling . Ready-made samples (each with at least a million points) from various distributions are available for download, or one can generate one's own samples from a chosen distribution using the provided source codes. The sampling relies on the Hamiltonian Monte Carlo algorithm as described in New J. Phys. 17, 043018 (2015). The random samples are reposited in the hope that they would be useful for a variety of tasks in quantum information and quantum computation. Constructing credible regions for tomographic data, optimizing a function over the quantum state space with a complicated landscape, testing the typicality of entanglement among states from a multipartite quantum system, or computing the average of some quantity of interest over a subset of quantum states are but some exemplary applications among many.

# Publications

## 2023

Julia Boeyens, Björn Annby-Andersson, Pharnam Bakhshinezhad, Géraldine Haack, Martí Perarnau-Llobet, Stefan Nimmrichter, Patrick P. Potts, Mohammad Mehboudi
*
Probe thermometry with continuous measurements
*

New J. Phys. 25, 123009 (2023) ,
(2023),
arXiv:2307.13407

Temperature estimation plays a vital role across natural sciences. A standard approach is provided by probe thermometry, where a probe is brought into contact with the sample and examined after a certain amount of time has passed. In many situations however, continuously monitoring the probe may be preferred. Here, we consider a minimal model, where the probe is provided by a two-level system coupled to a thermal reservoir. Monitoring thermally activated transitions enables real-time estimation of temperature with increasing accuracy over time. Within this framework we comprehensively investigate thermometry in both bosonic and fermionic environments employing a Bayesian approach. Furthermore, we explore adaptive strategies and find a significant improvement on the precision. Additionally, we examine the impact of noise and find that adaptive strategies may suffer more than non-adaptive ones for short observation times. While our main focus is on thermometry, our results are easily extended to the estimation of other environmental parameters, such as chemical potentials and transition rates.

Yi Li, Yu Xiang, Xiao-Dong Yu, H. Chau Nguyen, Otfried Gühne, Qiongyi He
*
Randomness Certification from Multipartite Quantum Steering for Arbitrary Dimensional Systems
*

Phys. Rev. Lett. 132, 080201 (2024) ,
(2023),
arXiv:2307.02061

Entanglement in bipartite systems has been applied for the generation of secure random numbers, which are playing an important role in cryptography or scientific numerical simulations. Here, we propose to use multipartite entanglement distributed between trusted and untrusted parties for generating randomness of arbitrary dimensional systems. We show that the distributed structure of several parties leads to additional protection against possible attacks by an eavesdropper, resulting in more secure randomness generated than in the corresponding bipartite scenario. Especially, randomness can be certified in the group of untrusted parties, even there is no randomness exists in either of them individually. We prove that the necessary and sufficient resource for quantum randomness in this scenario is multipartite quantum steering when two measurement settings are performed on the untrusted parties. However, the sufficiency no longer holds with more measurement settings. Finally, we apply our analysis to some experimentally realized states and show that more randomness can be extracted in comparison to the existing analysis.

Jessica O. de Almeida, Matthias Kleinmann, Gael Sentís
*
Comparison of confidence regions for quantum state tomography
*

New J. Phys. 25 113018 (2023) ,
(2023),
arXiv:2303.07136

The quantum state associated to an unknown experimental preparation procedure can be determined by performing quantum state tomography. If the statistical uncertainty in the data dominates over other experimental errors, then a tomographic reconstruction procedure must express this uncertainty. A rigorous way to accomplish this is via statistical confidence regions in state space. Naturally, the size of this region decreases when increasing the number of samples, but it also depends critically on the construction method of the region. We compare recent methods for constructing confidence regions as well as a reference method based on a Gaussian approximation. For the comparison, we propose an operational measure with the finding, that there is a significant difference between methods, but which method is preferable can depend on the details of the state preparation scenario.

Xue Yang, Yan-Han Yang, Mir Alimuddin, Raffaele Salvia, Shao-Ming Fei, Li-Ming Zhao, Stefan Nimmrichter, Ming-Xing Luo
*
The battery capacity of energy-storing quantum systems
*

Phys. Rev. Lett. 131 030402 ,
(2023),
arXiv:2302.09905

The quantum battery capacity is introduced in this letter as a figure of merit that expresses the potential of a quantum system to store and supply energy. It is defined as the difference between the highest and the lowest energy that can be reached by means of the unitary evolution of the system. This function is closely connected to the ergotropy, but it does not depend on the temporary level of energy of the system. The capacity of a quantum battery can be directly linked with the entropy of the battery state, as well as with measures of coherence and entanglement.

Lina Vandré, Otfried Gühne
*
Entanglement Purification of Hypergraph States
*

Phys. Rev. A 108, 062417 14 December 2023 ,
(2023),
arXiv:2301.11341

Entanglement purification describes a primitive in quantum information processing, where several copies of noisy quantum states are distilled into few copies of nearly-pure states of high quality via local operations and classical communication. Especially in the multiparticle case, the task of entanglement purification is complicated, as many inequivalent forms of pure state entanglement exist and purification protocols need to be tailored for different target states. In this paper we present optimized protocols for the purification of hypergraph states, which form a family of multi-qubit states that are relevant from several perspectives. We start by reformulating an existing purification protocol in a graphical language. This allows for systematical optimization and we present improvements in three directions. First, one can optimize the sequences of the protocol with respect to the ordering of the parties. Second, one can use adaptive schemes, where the measurement results obtained within the protocol are used to modify the protocols. Finally, one can improve the protocol with respect to the efficiency, requiring fewer copies of noisy states to reach a certain target state.

Carlos de Gois, Martin Plávala, René Schwonnek, Otfried Gühne
*
Complete hierarchy for high-dimensional steering certification
*

Phys. Rev. Lett. 131, 010201 ,
(2023),
arXiv:2212.12544

High-dimensional quantum steering can be seen as a test for the dimensionality of entanglement, where the devices at one side are not characterized. As such, it is an important component in quantum informational protocols that make use of high-dimensional entanglement. Although it has been recently observed experimentally, the phenomenon of high-dimensional steering is lacking a general certification procedure. We provide necessary and sufficient conditions to certify the entanglement dimension in a steering scenario. These conditions are stated in terms of a hierarchy of semidefinite programs, which can also be used to quantify the phenomenon using the steering dimension robustness. To demonstrate the practical viability of our method, we characterize the dimensionality of entanglement in steering scenarios prepared with maximally entangled states measured in mutually unbiased bases. Our methods give significantly stronger bounds on the noise robustness necessary to experimentally certify high-dimensional entanglement.

Shuheng Liu, Qiongyi He, Marcus Huber, Otfried Gühne, Giuseppe Vitagliano
*
Characterizing entanglement dimensionality from randomized measurements
*

PRX Quantum 4, 020324 ,
(2023),
arXiv:2211.09614

We consider the problem of detecting the dimensionality of entanglement with the use of correlations between measurements in randomized directions. First, exploiting the recently derived covariance matrix criterion for the entanglement dimensionality [S. Liu et al., arXiv:2208.04909], we derive an inequality that resembles well-known entanglement criteria, but contains different bounds for the different dimensionalities of entanglement. This criterion is invariant under local changes of $su(d)$ bases and can be used to find regions in the space of moments of randomized correlations, generalizing the results of [S. Imai et al., Phys. Rev. Lett. 126, 150501 (2021)] to the case of entanglement-dimensionality detection. In particular, we find analytical boundary curves for the different entanglement dimensionalities in the space of second- and fourth-order moments of randomized correlations for all dimensions $d_a = d_b = d$ of a bipartite system. We then show how our method works in practice, also considering a finite statistical sample of correlations, and we also show that it can detect more states than other entanglement-dimensionality criteria available in the literature, thus providing a method that is both very powerful and potentially simpler in practical scenarios. We conclude by discussing the partly open problem of the implementation of our method in the multipartite scenario.

Björn Schrinski, Yu Yang, Uwe von Lüpke, Marius Bild, Yiwen Chu, Klaus Hornberger, Stefan Nimmrichter, Matteo Fadel
*
Macroscopic quantum test with bulk acoustic wave resonators
*

Phys. Rev. Lett. 130, 133604 ,
(2023),
arXiv:2209.06635

Recently, solid-state mechanical resonators have become a platform for demonstrating non-classical behavior of systems involving a truly macroscopic number of particles. Here, we perform the most macroscopic quantum test in a mechanical resonator to date, which probes the validity of quantum mechanics at the microgram mass scale. This is done by a direct measurement of the Wigner function of a high-overtone bulk acoustic wave resonator mode, monitoring the gradual decay of negativities over tens of microseconds. While the obtained macroscopicity of $μ= 11.3$ is on par with state-of-the-art atom interferometers, future improvements of mode geometry and coherence times could confirm the quantum superposition principle at unprecedented scales.

Teiko Heinosaari, Anna Jenčová, Martin Plávala
*
Dispensing of quantum information beyond no-broadcasting theorem -- is it possible to broadcast anything genuinely quantum?
*

J. Phys. A: Math. Theor. 56 135301 ,
(2023),
arXiv:2208.10341

No-broadcasting theorem is one of the most fundamental results in quantum information theory; it guarantees that the simplest attacks on any quantum protocol, based on eavesdropping and copying of quantum information, are impossible. Due to the fundamental importance of the no-broadcasting theorem, it is essential to understand the exact boundaries of this limitation. We generalize the standard definition of broadcasting by restricting the set of states which we want to broadcast and restricting the sets of measurements which we use to test the broadcasting. We show that in some of the investigated cases broadcasting is equivalent to commutativity, while in other cases commutativity is not necessary.

Carlos de Gois, Kiara Hansenne, Otfried Gühne
*
Uncertainty relations from graph theory
*

Phys. Rev. A 107, 062211 ,
(2023),
arXiv:2207.02197

Quantum measurements are inherently probabilistic. Further defying our classical intuition, quantum theory often forbids us to precisely determine the outcomes of simultaneous measurements. This phenomenon is captured and quantified through uncertainty relations. Although studied since the inception of quantum theory, this problem of determining the possible expectation values of a collection of quantum measurements remains, in general, unsolved. By constructing a close connection between observables and graph theory, we derive uncertainty relations valid for any set of dichotomic observables. These relations are, in many cases, tight, and related to the size of the maximum clique of the associated graph. As applications, they can be straightforwardly used to build entropic uncertainty relations, separability criteria and entanglement witnesses.

Zhen-Peng Xu, Satoya Imai, Otfried Gühne
*
Fate of multiparticle entanglement when one particle becomes classical
*

Phys. Rev. A 107, L040401 ,
(2023),
arXiv:2206.12834

We study the change of multiparticle entanglement if one particle becomes classical, in the sense that this particle is destructed by a measurement, but the gained information is encoded into a new register. We present an estimation of this change for different entanglement measures and ways of encoding. We first simplify the numerical calculation to analyze the change of entanglement under classicalization in special cases. Second, we provide general upper and lower bounds on the entanglement change. Third, we show that the entanglement change caused by classicalization of one qubit only can still be arbitrarily large. Finally, we discuss cases where no entanglement is left under classicalization for any possible measurement. Our results shed light on the storage of quantum resources and help to develop a novel direction in the field of quantum resource theories.

Benjamin Yadin, Benjamin Morris, Kay Brandner
*
Thermodynamics of Permutation-Invariant Quantum Many-Body Systems: A Group-Theoretical Framework
*

Phys. Rev. Research 5, 033018 ,
(2023),
arXiv:2206.12639

Quantum systems of indistinguishable particles are commonly described using the formalism of second quantisation, which relies on the assumption that any admissible quantum state must be either symmetric or anti-symmetric under particle permutations. Coherence-induced many-body effects such as superradiance, however, can arise even in systems whose constituents are not fundamentally indistinguishable as long as all relevant dynamical observables are permutation-invariant. Such systems are not confined to symmetric or anti-symmetric states and therefore require a different theoretical approach. Focusing on non-interacting systems, here we combine tools from representation theory and thermodynamically consistent master equations to develop such a framework. We characterise the structure and properties of the steady states emerging in permutation-invariant ensembles of arbitrary multi-level systems that are collectively weakly coupled to a thermal environment. As an application of our general theory, we further explore how these states can in principle be used to enhance the performance of quantum thermal machines. Our group-theoretical framework thereby makes it possible to analyse various limiting cases that would not be accessible otherwise. In addition, it allows us to show that the properties of multi-level ensembles differ qualitatively from those of spin ensembles, which have been investigated earlier using the standard Clebsch-Gordan theory. Our results have a large scope for future generalisations and pave the way for systematic investigations of collective effects arising from permutation-invariance in quantum thermodynamics.

Satoya Imai, Otfried Gühne, Stefan Nimmrichter
*
Work fluctuations and entanglement in quantum batteries
*

Phys. Rev. A 107, 022215 ,
(2023),
arXiv:2205.08447

We consider quantum batteries given by composite interacting quantum systems in terms of the thermodynamic work cost of local random unitary processes. We characterize quantum correlations by monitoring the average energy change and its fluctuations in the high-dimensional bipartite systems. We derive a hierarchy of bounds on high-dimensional entanglement (the so-called Schmidt number) from the work fluctuations and thereby show that larger work fluctuations can verify the presence of stronger entanglement in the system. Finally, we develop two-point measurement protocols with noisy detectors that can estimate work fluctuations, showing that the dimensionality of entanglement can be probed in this manner.

Zhen-Peng Xu, Jonathan Steinberg, Jaskaran Singh, Antonio J. López-Tarrida, José R. Portillo, Adán Cabello
*
Graph-theoretic approach to Bell experiments with low detection efficiency
*

Quantum 7, 922 ,
(2023),
arXiv:2205.05098

Bell inequality tests where the detection efficiency is below a certain threshold $η_{\rm{crit}}$ can be simulated with local hidden-variable models. Here, we introduce a method to identify Bell tests requiring low $η_{\rm{crit}}$ and relatively low dimension $d$ of the local quantum systems. The method has two steps. First, we show a family of bipartite Bell inequalities for which, for correlations produced by maximally entangled states, $η_{\rm{crit}}$ can be upper bounded by a function of some invariants of graphs, and use it to identify correlations that require small $η_{\rm{crit}}$. We present examples in which, for maximally entangled states, $η_{\rm{crit}} \le 0.516$ for $d=16$, $η_{\rm{crit}} \le 0.407$ for $d=28$, and $η_{\rm{crit}} \le 0.326$ for $d=32$. We also show evidence that the upper bound for $η_{\rm{crit}}$ can be lowered down to $0.415$ for $d=16$ and present a method to make the upper bound of $η_{\rm{crit}}$ arbitrarily small by increasing the dimension and the number of settings. All these upper bounds for $η_{\rm{crit}}$ are valid (as it is the case in the literature) assuming no noise. The second step is based on the observation that, using the initial state and measurement settings identified in the first step, we can construct Bell inequalities with smaller $η_{\rm{crit}}$ and better noise robustness. For that, we use a modified version of Gilbert's algorithm that takes advantage of the automorphisms of the graphs used in the first step. We illustrate its power by explicitly developing an example in which $η_{\rm{crit}}$ is $12.38\%$ lower and the required visibility is $14.62\%$ lower than the upper bounds obtained in the first step. The tools presented here may allow for developing high-dimensional loophole-free Bell tests and loophole-free Bell nonlocality over long distances.

Fabian Bernards, Otfried Gühne
*
Bell inequalities for nonlocality depth
*

Phys. Rev. A 107, 022412 ,
(2023),
arXiv:2205.04250

When three or more particles are considered, quantum correlations can be stronger than the correlations generated by so-called hybrid local hidden variable models, where some of the particles are considered as a single block inside which communication and signaling is allowed. We provide an exhaustive classification of Bell inequalities to characterize various hybrid scenarios in four- and five-particle systems. In quantum mechanics, these inequalities provide device-independent witnesses for the entanglement depth. In addition, we construct a family of inequalities to detect a non-locality depth of (n-1) in n-particle systems. Moreover, we present two generalizations of the original Svetlichny inequality, which was the first Bell inequality designed for hybrid models. Our results are based on the cone-projection technique, which can be used to completely characterize Bell inequalities under affine constraints; even for many parties, measurements, and outcomes.

Shashank Gupta, Debashis Saha, Zhen-Peng Xu, Adán Cabello, A. S. Majumdar
*
Quantum contextuality provides communication complexity advantage
*

Phys. Rev. Lett. 130, 080802 ,
(2023),
arXiv:2205.03308

Despite the conceptual importance of contextuality in quantum mechanics, there is a hitherto limited number of applications requiring contextuality but not entanglement. Here, we show that for any quantum state and observables of sufficiently small dimension producing contextuality, there exists a communication task with quantum advantage. Conversely, any quantum advantage in this task admits a proof of contextuality whenever an additional condition holds. We further show that given any set of observables allowing for quantum state-independent contextuality, there exists a class of communication tasks wherein the difference between classical and quantum communication complexities increases as the number of inputs grows. Finally, we show how to convert each of these communication tasks into a semi-device independent protocol for quantum key distribution.

Matteo Fadel, Benjamin Yadin, Yuping Mao, Tim Byrnes, Manuel Gessner
*
Multiparameter quantum metrology and mode entanglement with spatially split nonclassical spin states
*

New J. Phys. 25 073006 ,
(2023),
arXiv:2201.11081

We identify the multiparameter sensitivity of split nonclassical spin states, such as spin-squeezed and Dicke states spatially distributed into several addressable modes. Analytical expressions for the spin-squeezing matrix of a family of states that are accessible by current atomic experiments reveal the quantum gain in multiparameter metrology, as well as the optimal strategies to maximize the sensitivity. We further study the mode entanglement of these states by deriving a witness for genuine $k$-partite mode entanglement from the spin-squeezing matrix. Our results highlight the advantage of mode entanglement for distributed sensing, and outline optimal protocols for multiparameter estimation with nonclassical spatially-distributed spin ensembles.

Otfried Gühne, Erkka Haapasalo, Tristan Kraft, Juha-Pekka Pellonpää, Roope Uola
*
Incompatible measurements in quantum information science
*

Rev. Mod. Phys. 95, 011003 ,
(2023),
arXiv:2112.06784

Some measurements in quantum mechanics disturb each other. This has puzzled physicists since the formulation of the theory, but only in recent decades has the incompatibility of measurements been analyzed in depth and detail, using the notion of joint measurability of generalized measurements. In this Colloquium joint measurability and incompatibility are reviewed from the perspective of quantum information science. The Colloquium starts by discussing the basic definitions and concepts. An overview on applications of incompatibility, such as in measurement uncertainty relations, the characterization of quantum correlations, or information processing tasks like quantum state discrimination, is then presented. Finally, emerging directions of research, such as a resource theory of incompatibility as well as other concepts to grasp the nature of measurements in quantum mechanics, are discussed.

Zhen-Peng Xu, Jonathan Steinberg, H. Chau Nguyen, Otfried Gühne
*
No-go theorem based on incomplete information of Wigner about his friend
*

Phys. Rev. A 107, 022424 ,
(2023),
arXiv:2111.15010

The notion of measurements is central for many debates in quantum mechanics. One critical point is whether a measurement can be regarded as an absolute event, giving the same result for any observer in an irreversible manner. Using ideas from the gedankenexperiment of Wigner's friend it has been argued that, when combined with the assumptions of locality and no-superdeterminism, regarding a measurement as an absolute event is incompatible with the universal validity of quantum mechanics. We consider a weaker assumption: is the measurement event realised relatively to the observer when he only partially observed the outcome. We proposed a protocol to show that this assumption putting in conjunction with the natural assumptions of no-superdeterminism and locality is also not compatible with the universal validity of quantum mechanics.

Giuseppe Vitagliano, Matteo Fadel, Iagoba Apellaniz, Matthias Kleinmann, Bernd Lücke, Carsten Klempt, Géza Tóth
*
Number-phase uncertainty relations and bipartite entanglement detection in spin ensembles
*

Quantum 7, 914 ,
(2023),
arXiv:2104.05663

We present a method to detect bipartite entanglement based on number-phase-like uncertainty relations in split spin ensembles. First, we derive an uncertainty relation that plays the role of a number-phase uncertainty for spin systems. It is important that the relation is given with well-defined and easily measurable quantities, and that it does not need assuming infinite dimensional systems. Based on this uncertainty relation, we show how to detect bipartite entanglement in an unpolarized Dicke state of many spin-1/2 particles. The particles are split into two subensembles, then collective angular momentum measurements are carried out locally on the two parts. First, we present a bipartite Einstein-Podolsky-Rosen (EPR) steering criterion. Then, we present an entanglement condition that can detect bipartite entanglement in such systems. We demonstrate the utility of the criteria by applying them to a recent experiment given in K. Lange et al. [Science 360, 416 (2018)] realizing a Dicke state in a Bose-Einstein condensate of cold atoms, in which the two subensembles were spatially separated from each other. Our methods also work well if split spin-squeezed states are considered. We show in a comprehensive way how to handle experimental imperfections, such as the nonzero particle number variance including the partition noise, and the fact that, while ideally BECs occupy a single spatial mode, in practice the population of other spatial modes cannot be fully suppressed.

## 2022

Martin Plávala, Matthias Kleinmann
*
Generalized dynamical theories in phase space and the hydrogen atom
*

Phys. Rev. A 108, 052212 (2023) ,
(2022),
arXiv:2212.12267

We show that the phase-space formulation of general probabilistic theories can be extended to include a generalized time-evolution and that it can describe a nonquantum hydrogen-like system which is stable, has discrete energy levels, and includes the Zeeman effect. This allows us to study dynamical effects such as excitations of the hydrogen-like system by a resonant laser and Rutherford scattering. Our construction demonstrates that classical theory and quantum theory can be seen as specific choices of general probabilistic theory in phase space and that other probabilistic theories also lead to measurable predictions.

Nikolai Wyderka, Andreas Ketterer, Satoya Imai, Jan Lennart Bönsel, Daniel E. Jones, Brian T. Kirby, Xiao-Dong Yu, Otfried Gühne
*
Complete characterization of quantum correlations by randomized measurements
*

Phys. Rev. Lett. 131, 090201 (2023) ,
(2022),
arXiv:2212.07894

The fact that quantum mechanics predicts stronger correlations than classical physics is an essential cornerstone of quantum information processing. Indeed, these quantum correlations are a valuable resource for various tasks, such as quantum key distribution or quantum teleportation, but characterizing these correlations in an experimental setting is a formidable task, especially in scenarios where no shared reference frames are available. By definition, quantum correlations are reference-frame independent, i.e., invariant under local transformations; this physically motivated invariance implies, however, a dedicated mathematical structure and, therefore, constitutes a roadblock for an efficient analysis of these correlations in experiments. Here we provide a method to directly measure any locally invariant property of quantum states using locally randomized measurements, and we present a detailed toolbox to analyze these correlations for two quantum bits. We implement these methods experimentally using pairs of entangled photons, characterizing their usefulness for quantum teleportation and their potential to display quantum nonlocality in its simplest form. Our results can be applied to various quantum computing platforms, allowing simple analysis of correlations between arbitrary distant qubits in the architecture.

Fabian Bernards, Otfried Gühne
*
Multiparticle singlet states cannot be maximally entangled for the bipartitions
*

J. Math. Phys. 65, 012201 (2024) ,
(2022),
arXiv:2211.03813

One way to explore multiparticle entanglement is to ask for maximal entanglement with respect to different bipartitions, leading to the notion of absolutely maximally entangled states or perfect tensors. A different path uses unitary invariance and symmetries, resulting in the concept of multiparticle singlet states. We show that these two concepts are incompatible in the sense that the space of pure multiparticle singlet states does not contain any state for which all partitions of two particles versus the rest are maximally entangled. This puts restrictions on the construction of quantum codes and contributes to discussions in the context of the AdS/CFT correspondence and quantum gravity.

Ties-A. Ohst, Xiao-Dong Yu, Otfried Gühne, H. Chau Nguyen
*
Certifying Quantum Separability with Adaptive Polytopes
*

SciPost Phys. 16, 063 (2024) ,
(2022),
arXiv:2210.10054

The concept of entanglement and separability of quantum states is relevant for several fields in physics. Still, there is a lack of effective operational methods to characterise these features. We propose a method to certify quantum separability of two- and multiparticle quantum systems based on an adaptive polytope approximation. This leads to an algorithm which, for practical purposes, conclusively recognises two-particle separability for small and medium-size dimensions. For multiparticle systems, the approach allows to characterise full separability for up to five qubits or three qutrits; in addition, different classes of entanglement can be distinguished. Finally, our methods allow to identify systematically quantum states with interesting entanglement properties, such as maximally robust states which are separable for all bipartitions, but not fully separable.

H. Chau Nguyen, Jan Lennart Bönsel, Jonathan Steinberg, Otfried Gühne
*
Optimising shadow tomography with generalised measurements
*

Phys. Rev. Lett. 129, 220502 ,
(2022),
arXiv:2205.08990

Advances in quantum technology require scalable techniques to efficiently extract information from a quantum system, such as expectation values of observables or its entropy. Traditional tomography is limited to a handful of qubits and shadow tomography has been suggested as a scalable replacement for larger systems. Shadow tomography is conventionally analysed based on outcomes of ideal projective measurements on the system upon application of randomised unitaries. Here, we suggest that shadow tomography can be much more straightforwardly formulated for generalised measurements, or positive operator valued measures. Based on the idea of the least-square estimator, shadow tomography with generalised measurements is both more general and simpler than the traditional formulation with randomisation of unitaries. In particular, this formulation allows us to analyse theoretical aspects of shadow tomography in detail. For example, we provide a detailed study of the implication of symmetries in shadow tomography. Shadow tomography with generalised measurements is also indispensable in realistic implementation of quantum mechanical measurements, when noise is unavoidable. Moreover, we also demonstrate how the optimisation of measurements for shadow tomography tailored toward a particular set of observables can be carried out.

Raffaele Salvia, Martí Perarnau-Llobet, Géraldine Haack, Nicolas Brunner, Stefan Nimmrichter
*
Quantum advantage in charging cavity and spin batteries by repeated interactions
*

Phys. Rev. Research 5, 013155 (2023) ,
(2022),
arXiv:2205.00026

Recently, an unconditional advantage has been demonstrated for the process of charging of a quantum battery in a collisional model. Motivated by the question of whether such an advantage could be observed experimentally, we consider a model where the battery is modeled by a quantum harmonic oscillator or a large spin, charged via repeated interactions with a stream of non-equilibrium qubit units. For both setups, we show that a quantum protocol can significantly outperform the most general adaptive classical schemes, leading to 90\% and 38\% higher charging power for the cavity and large spin batteries respectively. Towards an experimental realization, we also characterise the robustness of this quantum advantage to imperfections (noise and decoherence) considering implementations with state-of-the-art micromasers and hybrid superconducting devices.

Marius Constantin Chirita Mihaila, Philipp Weber, Matthias Schneller, Lucas Grandits, Stefan Nimmrichter, Thomas Juffmann
*
Transverse Electron Beam Shaping with Light
*

Phys. Rev. X 12, 031043, (2022) ,
(2022),
arXiv:2203.07925

Interfacing electrons and light enables ultrafast electron microscopy, quantum control of electrons, as well as new optical elements for high sensitivity imaging. Here we demonstrate for the first time programmable transverse electron beam shaping in free space based on ponderomotive potentials from short intense laser pulses. We can realize both convex and concave electron lenses with a focal length of a few millimeters, comparable to those in state-of-the-art electron microscopes. We further show that we can realize almost arbitrary deflection patterns by shaping the ponderomotive potentials using a spatial light modulator. Our modulator is lossless, programmable, has unity fill factor, and could pave the way to electron wavefront shaping with hundreds of individually addressable pixels.

Marcel Seelbach Benkner, Jens Siewert, Otfried Gühne, Gael Sentís
*
Characterizing generalized axisymmetric quantum states in $d\times d$ systems
*

Phys. Rev. A 106, 022415 ,
(2022),
arXiv:2202.11033

We introduce a family of highly symmetric bipartite quantum states in arbitrary dimensions. It consists of all states that are invariant under local phase rotations and local cyclic permutations of the basis. We solve the separability problem for a subspace of these states and show that a sizeable part of the family is bound entangled. We also calculate some of the Schmidt numbers for the family in $d = 3$, thereby characterizing the dimensionality of entanglement. Our results allow to estimate entanglement properties of arbitrary states, as general states can be symmetrized to the considered family by local operations.

Martin Plávala
*
Incompatibility in restricted operational theories: connecting contextuality and steering
*

J. Phys. A: Math. Theor. 55, 174001 ,
(2022),
arXiv:2112.10596

We investigate the connection between steering and contextuality in general probabilistic theories. We show that for a class of bipartite states the steerability of the state by given set of measurements is equivalent to non-existence of preparation noncontextual hidden variable model for certain restricted theory constructed from the given state and measurements. The connection between steering and contextuality is provided by the concept of incompatibility in restricted theories, which we also investigate.

Benjamin Yadin, Hyejung H. Jee, Carlo Sparaciari, Gerardo Adesso, Alessio Serafini
*
Catalytic Gaussian thermal operations
*

J. Phys. A: Math. Theor. 55 325301 ,
(2022),
arXiv:2112.05540

We examine the problem of state transformations in the framework of Gaussian thermal resource theory in the presence of catalysts. To this end, we introduce an expedient parametrisation of covariance matrices in terms of principal mode temperatures and asymmetries, and consider both weak and strong catalytic scenarios. We show that strong catalysts (where final correlations with the system are forbidden) are useless for the single mode case, in that they do not expand the set of states reachable from a given initial state through Gaussian thermal operations. We then go on to prove that weak catalysts (where final correlations with the system are allowed) are instead capable of reaching more final system states, and determine exact conditions for state transformations of a single-mode in their presence. Next, we derive necessary conditions for Gaussian thermal state transformations holding for any number of modes, for strong catalysts and approximate transformations, and for weak catalysts with and without the addition of a thermal bath. We discuss the implications of these results for devices operating with Gaussian elements.

Wei Zhang, Tim van Leent, Kai Redeker, Robert Garthoff, Rene Schwonnek, Florian Fertig, Sebastian Eppelt, Valerio Scarani, Charles C.-W. Lim, Harald Weinfurter
*
Experimental device-independent quantum key distribution between distant users
*

Nature 609, 687 ,
(2022),
arXiv:2110.00575

Device-independent quantum key distribution (DIQKD) is the art of using untrusted devices to establish secret keys over an untrusted channel. So far, the real-world implementation of DIQKD remains a major challenge, as it requires the demonstration of a loophole-free Bell test across two remote locations with very high quality entanglement to ensure secure key exchange. Here, we demonstrate for the first time the distribution of a secure key -- based on asymptotic security estimates -- in a fully device-independent way between two users separated by 400 metres. The experiment is based on heralded entanglement between two independently trapped single Rubidium 87 atoms. The implementation of a robust DIQKD protocol indicates an expected secret key rate of r=0.07 per entanglement generation event and r>0 with a probability error of 3%. Furthermore, we analyse the experiment's capability to distribute a secret key with finite-size security against collective attacks.

Xiao-Dong Yu, Jiangwei Shang, Otfried Gühne
*
Statistical Methods for Quantum State Verification and Fidelity Estimation
*

Adv. Quantum Technol. 5, 2100126 ,
(2022),
arXiv:2109.10805

The efficient and reliable certification of quantum states is essential for various quantum information processing tasks as well as for the general progress on the implementation of quantum technologies. In the last few years several methods have been introduced which use advanced statistical methods to certify quantum states in a resource-efficient manner. In this article we present a review of the recent progress in this field. We first explain how the verification and fidelity estimation of a quantum state can be discussed in the language of hypothesis testing. Then, we explain in detail various strategies for the verification of entangled states with local measurements or measurements assisted by local operations and classical communication. Finally, we discuss several extensions of the problem, such as the certification of quantum channels and the verification of entanglement.

Guillaume Aubrun, Ludovico Lami, Carlos Palazuelos, Martin Plávala
*
Entanglement and superposition are equivalent concepts in any physical theory
*

Phys. Rev. Lett. 128, 160402 ,
(2022),
arXiv:2109.04446

We prove that any two general probabilistic theories (GPTs) are entangleable, in the sense that their composite exhibits either entangled states or entangled measurements, if and only if they are both non-classical, meaning that neither of the state spaces is a simplex. This establishes the universal equivalence of the (local) superposition principle and the existence of global entanglement, valid in a fully theory-independent way. As an application of our techniques, we show that all non-classical GPTs exhibit a strong form of incompatibility of states and measurements, and use this to construct a version of the BB84 protocol that works in any non-classical GPT.

Kiara Hansenne, Zhen-Peng Xu, Tristan Kraft, Otfried Gühne
*
Symmetries in quantum networks lead to no-go theorems for entanglement distribution and to verification techniques
*

Nature Communications 13, 496 ,
(2022),
arXiv:2108.02732

Quantum networks are promising tools for the implementation of long-range quantum communication. The characterization of quantum correlations in networks and their usefulness for information processing is therefore central for the progress of the field, but so far only results for small basic network structures or pure quantum states are known. Here we show that symmetries provide a versatile tool for the analysis of correlations in quantum networks. We provide an analytical approach to characterize correlations in large network structures with arbitrary topologies. As examples, we show that entangled quantum states with a bosonic or fermionic symmetry can not be generated in networks; moreover, cluster and graph states are not accessible. Our methods can be used to design certification methods for the functionality of specific links in a network and have implications for the design of future network structures.

Lina Vandré, Marcelo Terra Cunha
*
On quantum sets of the multicoloured-graph approach to contextuality
*

Phys. Rev. A 106, 062210 ,
(2022),
arXiv:2105.08561

The CHSH bipartite Bell scenario [...] is the most famous Bell scenario and leads to the best known and most used CHSH-Bell inequalities. In 2010 Cabello, Severini, and Winter (CSW) came up with a graph approach on non-contextuality inequalities, which connects some graph-theoretical concepts to quantum and classical correlations. For example, a convex set defined by the exclusivity graph can be associated to the set of correlations achieved by quantum theory, while a polytope corresponds to the set of classically achieved ones. [...] To deal with the extra structure related to the presence of different players in a Bell scenario like CHSH, the coloured graph approach was introduced in 2014. An interesting question is: Does it make any difference to think about CHSH as a Bell scenario or a more general NC scenario? The Bell CHSH inequality is represented by a bi-coloured graph and the NC CHSH inequality by a simple graph, which is the shadow of the coloured one. In general, we have that the theta body of coloured graph is a subset of the theta body of its shadow graph in the same way as the Lovász number, which corresponds to the quantum bound, of the simple graph is greater than or equal to the Lovász number of the coloured graph. In the case of CHSH we have that the equality of these two invariants, which brings the question: Does this accident also hold for the corresponding quantum sets? This would mean that every correlation reached by quantum theory applied to the CHSH NC scenario could also be obtained at the (in principle) more restrictive CHSH Bell scenario? In this paper we answer negatively such question in a constructive way. We show that the coloured version is a proper subset of the shadow one and therefore that there are quantum correlations which can not be obtained under Bell restrictions. [...]

Costantino Budroni, Adán Cabello, Otfried Gühne, Matthias Kleinmann and Jan-Åke Larsson
*
Kochen-Specker Contextuality
*

Rev. Mod. Phys. 94, 045007 ,
(2022),
arXiv:2102.13036

A central result in the foundations of quantum mechanics is the Kochen-Specker theorem. In short, it states that quantum mechanics is in conflict with classical models in which the result of a measurement does not depend on which other compatible measurements are jointly performed. Here, compatible measurements are those that can be performed simultaneously or in any order without disturbance. This conflict is generically called quantum contextuality. In this article, we present an introduction to this subject and its current status. We review several proofs of the Kochen-Specker theorem and different notions of contextuality. We explain how to experimentally test some of these notions and discuss connections between contextuality and nonlocality or graph theory. Finally, we review some applications of contextuality in quantum information processing.

Martin Plávala, Matthias Kleinmann
*
Operational Theories in Phase Space: Toy Model for the Harmonic Oscillator
*

Phys. Rev. Lett. 128, 040405 ,
(2022),
arXiv:2101.08323

We show how to construct general probabilistic theories that contain an energy observable dependent on position and momentum. The construction is in accordance with classical and quantum theory and allows for physical predictions, such as the probability distribution for position, momentum and energy. We demonstrate the construction by formulating a toy model for the harmonic oscillator that is neither classical nor quantum. The model features a discrete energy spectrum, a ground state with sharp position and momentum, an eigenstate with non-positive Wigner function as well as a state that has tunneling properties. The toy model demonstrates that operational theories can be a viable alternative approach for formulating physical theories.

Andreas Ketterer, Satoya Imai, Nikolai Wyderka and Otfried Gühne
*
Statistically significant tests of multiparticle quantum correlations based on randomized measurements
*

Phys. Rev. A 106, L010402 ,
(2022),
arXiv:2012.12176

The presence of multiparticle entanglement is an important benchmark for the performance of intermediate-scale quantum technologies. In this work we consider statistical methods based on locally randomized measurements in order to characterize different degrees of multiparticle entanglement in qubit systems. We introduce hierarchies of criteria, satisfied by states which are separable with respect to partitions of different size, involving only second moments of the underlying probability distribution. Furthermore, we study in detail the resources required for a statistical estimation of the respective moments if only a finite number of samples is available, and discuss their scaling with the system size.

Ernest Y.-Z. Tan, Pavel Sekatski, Jean-Daniel Bancal, René Schwonnek, Renato Renner, Nicolas Sangouard, Charles C.-W. Lim
*
Improved DIQKD protocols with finite-size analysis
*

Quantum 6, 880 ,
(2022),
arXiv:2012.08714

The security of finite-length keys is essential for the implementation of device-independent quantum key distribution (DIQKD). Presently, there are several finite-size DIQKD security proofs, but they are mostly focused on standard DIQKD protocols and do not directly apply to the recent improved DIQKD protocols based on noisy preprocessing, random key measurements, and modified CHSH inequalities. Here, we provide a general finite-size security proof that can simultaneously encompass these approaches, using tighter finite-size bounds than previous analyses. In doing so, we develop a method to compute tight lower bounds on the asymptotic keyrate for any such DIQKD protocol with binary inputs and outputs. With this, we show that positive asymptotic keyrates are achievable up to depolarizing noise values of 9.33%, exceeding all previously known noise thresholds. We also develop a modification to random-key-measurement protocols, using a pre-shared seed followed by a "seed recovery" step, which yields substantially higher net key generation rates by essentially removing the sifting factor. Some of our results may also improve the keyrates of device-independent randomness expansion.

Xiao-Dong Yu, Timo Simnacher, H. Chau Nguyen and Otfried Gühne
*
Quantum-inspired hierarchy for rank-constrained optimization
*

PRX Quantum 3, 010340 ,
(2022),
arXiv:2012.00554

Many problems in information theory can be reduced to optimizations over matrices, where the rank of the matrices is constrained. We establish a link between rank-constrained optimization and the theory of quantum entanglement. More precisely, we prove that a large class of rank-constrained semidefinite programs can be written as a convex optimization over separable quantum states, and consequently, we construct a complete hierarchy of semidefinite programs for solving the original problem. This hierarchy not only provides a sequence of certified bounds for the rank-constrained optimization problem, but also gives pretty good and often exact values in practice when the lowest level of the hierarchy is considered. We demonstrate that our approach can be used for relevant problems in quantum information processing, such as the optimization over pure states, the characterization of mixed unitary channels and faithful entanglement, and quantum contextuality, as well as in classical information theory including the maximum cut problem, pseudo-Boolean optimization, and the orthonormal representation of graphs. Finally, we show that our ideas can be extended to rank-constrained quadratic and higher-order programming.

## 2021

Julia Boeyens, Stella Seah, Stefan Nimmrichter
*
Uninformed Bayesian Quantum Thermometry
*

Phys. Rev. A 104, 052214 ,
(2021),
arXiv:2108.07025

We study the Bayesian approach to thermometry with no prior knowledge about the expected temperature scale, through the example of energy measurements on fully or partially thermalized qubit probes. We show that the most common Bayesian estimators, namely the mean and the median, lead to high-temperature divergences when used for uninformed thermometry. To circumvent this and achieve better overall accuracy, we propose two new estimators based on an optimization of relative deviations. Their global temperature-averaged behavior matches a modified van Trees bound, which complements the Cramér-Rao bound for smaller probe numbers and unrestricted temperature ranges. Furthermore, we show that, using partially thermalized probes, one can increase the range of temperatures to which the thermometer is sensitive at the cost of the local accuracy.

Jonathan Steinberg, H. Chau Nguyen, Matthias Kleinmann
*
Minimal scheme for certifying three-outcome qubit measurements in the prepare-and-measure scenario
*

Phys. Rev. A 104, 062431 ,
(2021),
arXiv:2105.09925

The number of outcomes is a defining property of a quantum measurement, in particular, if the measurement cannot be decomposed into simpler measurements with fewer outcomes. Importantly, the number of outcomes of a quantum measurement can be irreducibly higher than the dimension of the system. The certification of this property is possible in a semi-device-independent way either based on a Bell-like scenario or by utilizing the simpler prepare-and-measure scenario. Here we show that in the latter scenario the minimal scheme for a certifying an irreducible three-outcome qubit measurement requires three state preparations and only two measurements and we provide experimentally feasible examples for this minimal certification scheme. We also discuss the dimension assumption characteristic to the semi-device-independent approach and to which extend it can be mitigated.

Stella Seah, Martí Perarnau-Llobet, Géraldine Haack, Nicolas Brunner, Stefan Nimmrichter
*
Quantum speed-up in collisional battery charging
*

Phys. Rev. Lett. 127, 100601 ,
(2021),
arXiv:2105.01863

We present a collision model for the charging of a quantum battery by identical nonequilibrium qubit units. When the units are prepared in a mixture of energy eigenstates, the energy gain in the battery can be described by a classical random walk, where both average energy and variance grow linearly with time. Conversely, when the qubits contain quantum coherence, interference effects buildup in the battery and lead to a faster spreading of the energy distribution, reminiscent of a quantum random walk. This can be exploited for faster and more efficient charging of a battery initialized in the ground state. Specifically, we show that coherent protocols can yield higher charging power than any possible incoherent strategy, demonstrating a quantum speed-up at the level of a single battery. Finally, we characterize the amount of extractable work from the battery through the notion of ergotropy.

Fabian Bernards and Otfried Gühne
*
Finding optimal Bell inequalities using the cone-projection technique
*

Phys. Rev. A 104, 012206 ,
(2021),
arXiv:2103.17247

Bell inequalities are relevant for many problems in quantum information science, but finding them for many particles is computationally hard. Recently, a computationally feasible method called cone-projection technique has been developed to find all optimal Bell inequalities under some constraints, which may be given by some symmetry or other linear conditions. In this paper we extend this work in several directions. We use the method to generalize the I4422 inequality to three particles and a so-called GYNI inequality to four particles. Additionally, we find Bell inequalities for three particles that generalize the I3322 inequality and the CHSH inequality at the same time. We discuss the obtained inequalities in some detail and characterize their violation in quantum mechanics.

Xiao-Dong Yu, Satoya Imai and Otfried Gühne
*
Optimal entanglement certification from moments of the partial transpose
*

Phys. Rev. Lett. 127, 060504 *127*,
060504
(2021),
arXiv:2103.06897

For the certification and benchmarking of medium-size quantum devices efficient methods to characterize entanglement are needed. In this context, it has been shown that locally randomized measurements on a multiparticle quantum system can be used to obtain valuable information on the so-called moments of the partially transposed quantum state. This allows to infer some separability properties of a state, but it is open how to use the given information in an optimal and systematic manner. We propose two general entanglement detection methods based on the moments of the partially transposed density matrix. The first method is based on the Hankel matrices and provides a family of entanglement criteria, of which the lowest order reduces to the known p3-PPT criterion proposed in [A. Elben et al., Phys. Rev. Lett. 125, 200501 (2020)]. The second method is optimal and gives necessary and sufficient conditions for entanglement based on some moments of the partially transposed density matrix.

Gabriele Riccardi, Daniel E. Jones, Xiao-Dong Yu, Otfried Gühne and Brian T. Kirby
*
Exploring the relationship between the faithfulness and entanglement of two qubits
*

Phys. Rev. A 103, 042417 ,
(2021),
arXiv:2102.10121

A conceptually simple and experimentally prevalent class of entanglement witnesses, known as fidelity witnesses, detect entanglement via a state's fidelity with a pure reference state. While existence proofs guarantee that a suitable witness can be constructed for every entangled state, such assurances do not apply to fidelity witnesses. Recent results have found that entangled states that cannot be detected by a fidelity witness, known as unfaithful states, are exceedingly common among bipartite states. In this paper, we show that even among two-qubit states, the simplest of all entangled states, unfaithful states can be created through a suitable application of decoherence and filtering to a Bell state. We also show that the faithfulness is not monotonic to entanglement, as measured by the concurrence. Finally, we experimentally verify our predictions using polarization-entangled photons and specifically demonstrate a situation where an unfaithful state is brought to faithfulness at the expense of further reducing the entanglement of the state.

Simon Milz, Cornelia Spee, Zhen-Peng Xu, Felix A. Pollock, Kavan Modi and Otfried Gühne
*
Genuine Multipartite Entanglement in Time
*

SciPost Phys. 10, 141 ,
(2021),
arXiv:2011.09340

While spatial quantum correlations have been studied in great detail, much less is known about the genuine quantum correlations that can be exhibited by temporal processes. Employing the quantum comb formalism, processes in time can be mapped onto quantum states, with the crucial difference that temporal correlations have to satisfy causal ordering, while their spatial counterpart is not constrained in the same way. Here, we exploit this equivalence and use the tools of multipartite entanglement theory to provide a comprehensive picture of the structure of correlations that (causally ordered) temporal quantum processes can display. First, focusing on the case of a process that is probed at two points in time -- which can equivalently be described by a tripartite quantum state -- we provide necessary as well as sufficient conditions for the presence of bipartite entanglement in different splittings. Next, we connect these scenarios to the previously studied concepts of quantum memory, entanglement breaking superchannels, and quantum steering, thus providing both a physical interpretation for entanglement in temporal quantum processes, and a determination of the resources required for its creation. Additionally, we construct explicit examples of W-type and GHZ-type genuinely multipartite entangled two-time processes and prove that genuine multipartite entanglement in temporal processes can be an emergent phenomenon. Finally, we show that genuinely entangled processes across multiple times exist for any number of probing times.

Satoya Imai, Nikolai Wyderka, Andreas Ketterer, and Otfried Gühne
*
Bound Entanglement from Randomized Measurements
*

Phys. Rev. Lett. *126*,
150501
(2021),
arXiv:2010.08372

If only limited control over a multiparticle quantum system is available, a viable method to characterize correlations is to perform random measurements and consider the moments of the resulting probability distribution. We present systematic methods to analyze the different forms of entanglement with these moments in an optimized manner. First, we find the optimal criteria for different forms of multiparticle entanglement in three-qubit systems using the second moments of randomized measurements. Second, we present the optimal inequalities if entanglement in a bipartition of a multiqubit system shall be analyzed in terms of these moments. Finally, for higher-dimensional two-particle systems and higher moments, we provide criteria that are able to characterize various examples of bound entangled states, showing that detection of such states is possible in this framework.

Erkka Haapasalo, Tristan Kraft, Nikolai Miklin and Roope Uola
*
Quantum marginal problem and incompatibility
*

Quantum 5, 476 ,
(2021),
arXiv:1909.02941

One of the basic distinctions between classical and quantum mechanics is the existence of fundamentally incompatible quantities. Such quantities are present on all levels of quantum objects: states, measurements, quantum channels, and even higher order dynamics. In this manuscript we show that two seemingly different aspects of quantum incompatibility: the quantum marginal problem of states and the incompatibility on the level of quantum channels are in one-to-one correspondence with each other. Importantly, as incompatibility of measurements is a special case of channel incompatibility, it also forms an instance of the quantum marginal problem. The connection enables the translation of various results between the fields. As examples we solve the marginal problem for pairs of two-qubit Bell diagonal states, derive entropic criteria for channel incompatibility and give a task-oriented characterisation for a well-known semi-definite programming hierarchy of symmetric extendability of quantum states.

Tristan Kraft, Sébastien Designolle, Christina Ritz, Nicolas Brunner, Otfried Gühne and Marcus Huber
*
Quantum entanglement in the triangle network
*

Phys. Rev. A 103, L060401 ,
(2021),
arXiv:2002.03970

Beyond future applications, quantum networks open interesting fundamental perspectives, notably novel forms of quantum correlations. In this work we discuss quantum correlations in networks from the perspective of the underlying quantum states and their entanglement. We address the questions of which states can be prepared in the so-called triangle network, consisting of three nodes connected pairwise by three sources. We derive necessary criteria for a state to be preparable in such a network, considering both the cases where the sources are statistically independent and classically correlated. This shows that the network structure imposes strong and non-trivial constraints on the set of preparable states, fundamentally different from the standard characterisation of multipartite quantum entanglement.

Xiao-Dong Yu, Timo Simnacher, Nikolai Wyderka, H. Chau Nguyen and Otfried Gühne
*
Complete hierarchy for the quantum marginal problem
*

Nat. Commun. *12*,
1012
(2021),
arXiv:2008.02124

Clarifying the relation between the whole and its parts is crucial for many problems in science. In quantum mechanics, this question manifests itself in the quantum marginal problem, which asks whether there is a global pure quantum state for some given marginals. This problem arises in many contexts, ranging from quantum chemistry to entanglement theory and quantum error correcting codes. In this paper, we prove a correspondence of the marginal problem to the separability problem. Based on this, we describe a sequence of semidefinite programs which can decide whether some given marginals are compatible with some pure global quantum state. As an application, we prove that the existence of multiparticle absolutely maximally entangled states for a given dimension is equivalent to the separability of an explicitly given two-party quantum state. Finally, we show that the existence of quantum codes with given parameters can also be interpreted as a marginal problem, hence, our complete hierarchy can also be used.

## 2020

F. E. S. Steinhoff and M. C. de Oliveira
*
Limitations imposed by complementarity
*

Quantum Inf Process 19, 358 ,
(2020),
arXiv:1406.1710

We consider the consequences of hypothetical violations of the principle of complementarity. For two-level systems, it is shown that any preparation violating complementarity enables the preparation of a non-signalling box violating Tsirelson s bound. Moreover, these superquantum objects could be used to distinguish a plethora of non-orthogonal quantum states and hence enable improved cloning protocols. For higher-dimensional systems the main ideas are briefly sketched.

H. Chau Nguyen and Fabian Bernards
*
Entanglement dynamics of two mesoscopic objects with gravitational
interaction
*

The European Physical Journal D volume 74, 69 ,
(2020),
arXiv:1906.11184

We analyse the entanglement dynamics of the two particles interacting through gravity in the recently proposed experiments aiming at testing quantum signatures for gravity (Phy. Rev. Lett 119, 240401 & 240402 (2017)). We consider the open dynamics of the system under decoherence due to the environmental interaction. We show that as long as the coupling between the particles is strong, the system does indeed develop entanglement, confirming the qualitative analysis in the original proposals. We show that the entanglement is also robust against stochastic fluctuations in setting up the system. The optimal interaction duration for the experiment is computed. A condition under which one can prove the entanglement in a device-independent manner is also derived.

Cornelia Spee
*
Certifying the purity of quantum states with temporal correlations
*

Phys. Rev. A 102, 012420 ,
(2020),
arXiv:1909.06233

Correlations obtained from sequences of measurements have been employed to distinguish among different physical theories or to witness the dimension of a system. In this work we show that they can also be used to establish semi-device independent lower bounds on the purity of the initial quantum state or even on one of the post-measurement states. For single systems this provides information on the quality of the preparation procedures of pure states or the implementation of measurements with anticipated pure post-measurement states. For joint systems one can combine our bound with results from entanglement theory to infer an upper bound on the concurrence based on the temporal correlations observed on a subsystem.

Roope Uola, Tom Bullock, Tristan Kraft, Juha-Pekka Pellonpää and Nicolas Brunner
*
All quantum resources provide an advantage in exclusion tasks
*

Phys. Rev. Lett. 125, 110402 ,
(2020),
arXiv:1909.10484

A key ingredient in quantum resource theories is a notion of measure. Such as a measure should have a number of fundamental properties, and desirably also a clear operational meaning. Here we show that a natural measure known as the convex weight, which quantifies the resource cost of a quantum device, has all the desired properties. In particular, the convex weight of any quantum resource corresponds exactly to the relative advantage it offers in an exclusion task. After presenting the general result, we show how the construction works for state assemblages, sets of measurements and sets of transformations. Moreover, in order to bound the convex weight analytically, we give a complete characterisation of the convex components and corresponding weights of such devices.

Andreas Ketterer and Otfried Gühne
*
Entropic uncertainty relations from quantum designs
*

Phys. Rev. Research 2, 023130 ,
(2020),
arXiv:1911.07533

In the course of the last decades entropic uncertainty relations have attracted much attention not only due to their fundamental role as manifestation of non-classicality of quantum mechanics, but also as major tools for applications of quantum information theory. Amongst the latter are protocols for the detection of quantum correlations or for the secure distribution of secret keys. In this work we show how to derive entropic uncertainty relations for sets of measurements whose effects form quantum designs. The key property of quantum designs is their indistinguishability from truly random quantum processes as long as one is concerned with moments up to some finite order. Exploiting this characteristic enables us to evaluate polynomial functions of measurement probabilities which leads to lower bounds on sums of generalized entropies. As an application we use the derived uncertainty relations to investigate the incompatibility of sets of binary observables.

Zhen-Peng Xu, Jing-Ling Chen, and Otfried Gühne
*
Proof of the Peres Conjecture for Contextuality
*

Phys. Rev. Lett. *122*,
230401
(2020),
arXiv:2001.07656

A central result in the foundations of quantum mechanics is the Kochen-Specker theorem. In short, it states that quantum mechanics cannot be reconciled with classical models that are noncontextual for ideal measurements. The first explicit derivation by Kochen and Specker was rather complex, but considerable simplifications have been achieved thereafter. We propose a systematic approach to find minimal Hardy-type and Greenberger-Horne-Zeilinger-type (GHZ-type) proofs of the Kochen-Specker theorem, these are characterized by the fact that the predictions of classical models are opposite to the predictions of quantum mechanics. Based on our results, we show that the Kochen-Specker set with 18 vectors from Cabello et al. [A. Cabello et al., Phys. Lett. A 212, 183 (1996)] is the minimal set for any dimension, verifying a longstanding conjecture by Peres. Our results allow to identify minimal contextuality scenarios and to study their usefulness for information processing.

Fabian Bernards and Otfried Gühne
*
Generalizing Optimal Bell Inequalities
*

Phys. Rev. Lett. *125*,
200401
(2020),
arXiv:2005.08687

Bell inequalities are central tools for studying nonlocal correlations and their applications in quantum information processing. Identifying inequalities for many particles or measurements is, however, difficult due to the computational complexity of characterizing the set of local correlations. We develop a method to characterize Bell inequalities under constraints, which may be given by symmetry or other linear conditions. This allows to search systematically for generalizations of given Bell inequalities to more parties. As an example, we find all possible generalizations of the two-particle inequality by Froissart [Il Nuovo Cimento B64, 241 (1981)], also known as I3322 inequality, to three particles. For the simplest of these inequalities, we study their quantum mechanical properties and demonstrate that they are relevant, in the sense that they detect nonlocality of quantum states, for which all two-setting inequalities fail to do so.

H. Chau Nguyen and Otfried Gühne
*
Quantum steering of Bell-diagonal states with generalized measurements
*

Phys. Rev. A *101*,
042125
(2020),
arXiv:1909.03963

The phenomenon of quantum steering in bipartite quantum systems can be reduced to the question whether or not the first party can perform measurements such that the conditional states on the second party can be explained by a local hidden state model. Clearly, the answer to this depends on the measurements which the first party is able to perform. We introduce a local hidden state model explaining the conditional states for all generalized measurements on Bell-diagonal states of two qubits. More precisely, it is known for the restricted case of projective measurements and Bell-diagonal states characterised by the correlation matrix T that a local hidden state model exists if and only if RT=2πNT|det(T)|≥1, where NT is defined by an integral over the Bloch sphere. For generalized measurements described by positive operator valued measures we construct a model if RT≥6/5. Our work paves the way for a systematic study of steerability of quantum states with generalized measurements beyond the highly-symmetric Werner states.

H. Chau Nguyen and Otfried Gühne
*
Some Quantum Measurements with Three Outcomes Can Reveal Nonclassicality where All Two-Outcome Measurements Fail to Do So
*

Phys. Rev. Lett. *125*,
230402
(2020),
arXiv:2001.03514

Measurements serve as the intermediate communication layer between the quantum world and our classical perception. So, the question which measurements efficiently extract information from quantum systems is of central interest. Using quantum steering as a nonclassical phenomenon, we show that there are instances, where the results of all two-outcome measurements can be explained in a classical manner, while the results of some three-outcome measurements cannot. This points at the important role of the number of outcomes in revealing the nonclassicality hidden in a quantum system. Moreover, our methods allow to improve the understanding of quantum correlations by delivering novel criteria for quantum steering and improved ways to construct local hidden variable models.

Giulio Chiribella, Adán Cabello, Matthias Kleinmann, Markus P. Müller*General Bayesian theories and the emergence of the exclusivity principle*

Phys. Rev. Res. *2*,
042001(R)
(2020),
arXiv:1901.11412

We address the problem of reconstructing quantum theory from the perspective of an agent who makes bets about the outcomes of possible experiments. We build a general Bayesian framework that can be used to organize the agent's beliefs and update them when new information becomes available. Our framework includes as special cases classical and quantum probability theory, as well as other forms of probabilistic reasoning that may arise in future physical theories. Building on this framework, we develop a notion of an ideal experiment, which in quantum theory coincides with the notion of projective measurement. We then prove that, in every general Bayesian theory, ideal experiments must satisfy the exclusivity principle, a property of projective measurements that plays a central role in the characterization of quantum correlations. Our result suggests that the set of quantum correlations may be completely characterized in terms of Bayesian consistency conditions.

Jonathan Steinberg, H. Chau Nguyen, Matthias Kleinmann*Quaternionic quantum theory admits universal dynamics only for two-level systems*

J. Phys. A: Math. Theor. *53*,
375304
(2020),
arXiv:2001.05482

We revisit the formulation of quantum mechanics over the quaternions and investigate the dynamical structure within this framework. Similar to standard complex quantum mechanics, time evolution is then mediated by a unitary operator which can be written as the exponential of the generator of time shifts. By imposing physical assumptions on the correspondence between the energy observable and the generator of time shifts, we prove that quaternionic quantum theory admits a time evolution only for systems with a quaternionic dimension of at most two. Applying the same strategy to standard complex quantum theory, we reproduce that the correspondence dictated by the Schrödinger equation is the only possible choice, up to a shift of the global phase.

Fabian Pokorny, Chi Zhang, Gerard Higgins, Adán Cabello, Matthias Kleinmann, Markus Hennrich*Tracking the Dynamics of an Ideal Quantum Measurement*

Phys. Rev. Lett. *124*,
080401
(2020),
arXiv:1903.10398

The existence of ideal quantum measurements is one of the fundamental predictions of quantum mechanics. In theory, an ideal measurement projects a quantum state onto the eigenbasis of the measurement observable, while preserving coherences between eigenstates that have the same eigenvalue. The question arises whether there are processes in nature that correspond to such ideal quantum measurements and how such processes are dynamically implemented in nature. Here we address this question and present experimental results monitoring the dynamics of a naturally occurring measurement process: the coupling of a trapped ion qutrit to the photon environment. By taking tomographic snapshots during the detection process, we show that the process develops in agreement with the model of an ideal quantum measurement with an average fidelity of 94%.

Cornelia Spee, Hendrik Siebeneich, Timm Florian Gloger, Peter Kaufmann, Michael Johanning, Matthias Kleinmann, Christof Wunderlich, Otfried Gühne*Genuine temporal correlations can certify the quantum dimension*

New J. Phys. *22*,
023028
(2020),
arXiv:1811.12259

Temporal correlations in quantum mechanics are the origin of several non-classical phenomena, but they depend on the dimension of the underlying quantum system. This allows one to use such correlations for the certification of a minimal Hilbert space dimension. Here we provide a theoretical proposal and an experimental implementation of a device-independent dimension test, using temporal correlations observed on a single trapped ¹⁷¹Yb⁺ ion. Our test goes beyond the prepare-and-measure scheme of previous approaches, demonstrating the advantage of genuine temporal correlations.

Roope Uola, Tristan Kraft, and Alastair A. Abbott
*
Quantification of quantum dynamics with input-output games
*

Phys. Rev. A *101*,
052306
(2020),
arXiv:1906.09206

Recent developments surrounding resource theories have shown that any quantum state or measurement resource, with respect to a convex (and compact) set of resourceless objects, provides an advantage in a tailored subchannel or state discrimination task, respectively. Here we show that an analogous, more general result is also true in the case of dynamical quantum resources, i.e., channels and instruments. In the scenario we consider, the tasks associated to a resource are input-output games. The advantage a resource provides in these games is naturally quantified by a generalized robustness measure. We illustrate our approach by applying it to a broad collection of examples, including classical and measure-and-prepare channels, measurement and channel incompatibility, LOCC operations, and steering, as well as discussing its applicability to other resources in, e.g., quantum thermodynamics. We finish by showing that our approach generalizes to higher-order dynamics where it can be used, for example, to witness causal properties of supermaps.

Roope Uola, Ana C. S. Costa, H. Chau Nguyen, and Otfried Gühne
*
Quantum steering
*

Rev. Mod. Phys.. *92*,
015001
(2020),
arXiv:1903.06663

Quantum correlations between two parties are essential for the argument of Einstein, Podolsky, and Rosen in favour of the incompleteness of quantum mechanics. Schrödinger noted that an essential point is the fact that one party can influence the wave function of the other party by performing suitable measurements. He called this phenomenon quantum steering and studied its properties, but only in the last years this kind of quantum correlation attracted significant interest in quantum information theory. In this paper the theory of quantum steering is reviewed. First, the basic concepts of steering and local hidden state models are presented and their relation to entanglement and Bell nonlocality is explained. Then various criteria for characterizing steerability and structural results on the phenomenon are described. A detailed discussion is given on the connections between steering and incompatibility of quantum measurements. Finally, applications of steering in quantum information processing and further related topics are reviewed.

Cornelia Spee, Costantino Budroni and Otfried Gühne
*
Simulating extremal temporal correlations
*

New J. Phys. *22*,
103037
(2020),
arXiv:2004.14854

The correlations arising from sequential measurements on a single quantum system form a polytope. This is defined by the arrow-of-time (AoT) constraints, meaning that future choices of measurement settings cannot influence past outcomes. We discuss the resources needed to simulate the extreme points of the AoT polytope, where resources are quantified in terms of the minimal dimension, or "internal memory" of the physical system. First, we analyze the equivalence classes of the extreme points under symmetries. Second, we characterize the minimal dimension necessary to obtain a given extreme point of the AoT polytope, including a lower scaling bound in the asymptotic limit of long sequences. Finally, we present a general method to derive dimension-sensitive temporal inequalities for longer sequences, based on inequalities for shorter ones, and investigate their robustness to imperfections.

Andreas Ketterer, Nikolai Wyderka and Otfried Gühne
*
Entanglement characterization using quantum designs
*

Quantum *4*,
325
(2020),
arXiv:2004.08402

We present in detail a statistical approach for the reference-frame-independent detection and characterization of multipartite entanglement based on moments of randomly measured correlation functions. We start by discussing how the corresponding moments can be evaluated with designs, linking methods from group and entanglement theory. Then, we illustrate the strengths of the presented framework with a focus on the multipartite scenario. We discuss a condition for characterizing genuine multipartite entanglement for three qubits, and we prove criteria that allow for a discrimination of $W$-type entanglement for an arbitrary number of qubits.

Zhen-Peng Xu, Jing-Ling Chen and Otfried Gühne
*
Proof of the Peres conjecture for contextuality
*

Phys. Rev. Lett. *124*,
230401
(2020),
arXiv:2001.07656

A central result in the foundations of quantum mechanics is the Kochen-Specker theorem. In short, it states that quantum mechanics cannot be reconciled with classical models that are noncontextual for ideal measurements. The first explicit derivation by Kochen and Specker was rather complex, but considerable simplifications have been achieved thereafter. We propose a systematic approach to find minimal Hardy-type and Greenberger-Horne-Zeilinger-type (GHZ-type) proofs of the Kochen-Specker theorem, these are characterized by the fact that the predictions of classical models are opposite to the predictions of quantum mechanics. Based on our results, we show that the Kochen-Specker set with 18 vectors from Cabello et al. [A. Cabello et al., Phys. Lett. A 212, 183 (1996)] is the minimal set for any dimension, verifying a longstanding conjecture by Peres. Our results allow to identify minimal contextuality scenarios and to study their usefulness for information processing.

Andreas Ketterer and Otfried Gühne
*
Entropic uncertainty relations from quantum designs
*

Phys. Rev. Research *se*,
rch 2, 023130
(2020),
arXiv:1911.07533

In the course of the last decades entropic uncertainty relations have attracted much attention not only due to their fundamental role as manifestation of non-classicality of quantum mechanics, but also as major tools for applications of quantum information theory. Amongst the latter are protocols for the detection of quantum correlations or for the secure distribution of secret keys. In this work we show how to derive entropic uncertainty relations for sets of measurements whose effects form quantum designs. The key property of quantum designs is their indistinguishability from truly random quantum processes as long as one is concerned with moments up to some finite order. Exploiting this characteristic enables us to evaluate polynomial functions of measurement probabilities which leads to lower bounds on sums of generalized entropies. As an application we use the derived uncertainty relations to investigate the incompatibility of sets of binary observables.

H. Chau Nguyen and Otfried Gühne
*
Quantum steering of Bell-diagonal states with generalized measurements
*

Phys. Rev. A *10*,
, 042125
(2020),
arXiv:1909.03963

The phenomenon of quantum steering in bipartite quantum systems can be reduced to the question whether or not the first party can perform measurements such that the conditional states on the second party can be explained by a local hidden state model. Clearly, the answer to this depends on the measurements which the first party is able to perform. We introduce a local hidden state model explaining the conditional states for all generalized measurements on Bell-diagonal states of two qubits. More precisely, it is known for the restricted case of projective measurements and Bell-diagonal states characterised by the correlation matrix $T$ that a local hidden state model exists if and only if $R_T= 2 \pi N_T |\det (T)| \ge 1$, where $N_T$ is defined by an integral over the Bloch sphere. For generalized measurements described by positive operator valued measures we construct a model if $R_T \ge 6/5$. Our work paves the way for a systematic study of steerability of quantum states with generalized measurements beyond the highly-symmetric Werner states.

Cornelia Spee, Hendrik Siebeneich, Timm Florian Gloger, Peter Kaufmann, Michael Johanning, Matthias Kleinmann, Christof Wunderlich and Otfried Gühne
*
Genuine temporal correlations can certify the quantum dimension
*

New J. Phys. *22*,
023028
(2020),
arXiv:1811.12259

Temporal correlations in quantum mechanics are the origin of several non-classical phenomena, but they depend on the dimension of the underlying quantum system. This allows one to use such correlations for the certification of a minimal Hilbert space dimension. Here we provide a theoretical proposal and an experimental implementation of a device-independent dimension test, using temporal correlations observed on a single trapped $^{171}$Yb$^+$ ion. Our test goes beyond the prepare-and-measure scheme of previous approaches, demonstrating the advantage of genuine temporal correlations.

## 2019

Xiao-Dong Yu, Jiangwei Shang and Otfried Gühne
*
Optimal verification of general bipartite pure states
*

npj Quantum Information *5*,
112
(2019),
arXiv:1901.09856

The efficient and reliable verification of quantum states plays a crucial role in various quantum information processing tasks. We consider the task of verifying entangled states using one-way and two-way classical communication and completely characterize the optimal strategies via convex optimization. We solve these optimization problems using both analytical and numerical methods, and the optimal strategies can be constructed for any bipartite pure state. Compared with the nonadaptive approach, our adaptive strategies significantly improve the efficiency of quantum state verification. Moreover, these strategies are experimentally feasible, as only few local projective measurements are required.

Ye-Chao Liu, Xiao-Dong Yu, Jiangwei Shang, Huangjun Zhu and Xiangdong Zhang
*
Efficient verification of Dicke states
*

Phys. Rev. A *pl*,
ed 12, 044020
(2019),
arXiv:1904.01979

Among various multipartite entangled states, Dicke states stand out because their entanglement is maximally persistent and robust under particle losses. Although much attention has been attracted for their potential applications in quantum information processing and foundational studies, the characterization of Dicke states remains as a challenging task in experiments. Here, we propose efficient and practical protocols for verifying arbitrary $n$-qubit Dicke states in both adaptive and nonadaptive ways. Our protocols require only two distinct settings based on Pauli measurements besides permutations of the qubits. To achieve infidelity $\epsilon$ and confidence level $1-\delta$, the total number of tests required is only $O(n\epsilon^{-1}\ln\delta^{-1})$. This performance is exponentially more efficient than all previous protocols based on local measurements, including quantum state tomography and direct fidelity estimation, and is comparable to the best global strategy. Our protocols are readily applicable with current experimental techniques and are able to verify Dicke states of hundreds of qubits.

Nikolai Wyderka, Otfried Gühne
*
Characterizing quantum states via sector lengths
*

J. Phys. A *53*,
ed 345302
(2019),
arXiv:1905.06928

Correlations in multiparticle systems are constrained by restrictions from quantum mechanics. A prominent example for these restrictions are monogamy relations, limiting the amount of entanglement between pairs of particles in a three-particle system. A powerful tool to study correlation constraints is the notion of sector lengths. These quantify, for different k, the amount of k-partite correlations in a quantum state in a basis-independent manner. We derive tight bounds on the sector lengths in multi-qubit states and highlight applications of these bounds to entanglement detection, monogamy relations and the n-representability problem. For the case of two- and three qubits we characterize the possible sector lengths completely and prove a symmetrized version of strong subadditivity for the linear entropy.

Mariami Gachechiladze, Otfried Gühne and Akimasa Miyake
*
Changing the circuit-depth complexity of measurement-based quantum
computation with hypergraph states
*

Phys. Rev. A *99*,
052304
(2019),
arXiv:1805.12093

While the circuit model of quantum computation defines its logical depth or "computational time" in terms of temporal gate sequences, the measurement-based model could allow totally different temporal ordering and parallelization of logical gates. By developing techniques to analyze Pauli measurements on multi-qubit hypergraph states generated by the Controlled-Controlled-Z (CCZ) gates, we introduce a deterministic scheme of universal measurement-based computation. In contrast to the cluster-state scheme, where the Clifford gates are parallelizable, our scheme enjoys massive parallelization of CCZ and SWAP gates, so that the computational depth grows with the number of global applications of Hadamard gates, or, in other words, with the number of changing computational bases. A logarithmic-depth implementation of an N-times Controlled-Z gate illustrates a novel trade-off between space and time complexity.

Xiao-Dong Yu and Otfried Gühne
*
Detecting coherence via spectrum estimation
*

Phys. Rev. A *99*,
062310
(2019),
arXiv:1808.08884

Coherence is a basic phenomenon in quantum mechanics and considered to be an essential resource in quantum information processing. Although the quantification of coherence has attracted a lot of interest, the lack of efficient methods to measure the coherence in experiments limits the applications. We address this problem by introducing an experiment-friendly method for coherence and spectrum estimation. This method is based on the theory of majorization and can not only be used to prove the presence of coherence, but also result in a rather precise lower bound of the amount of coherence. As an illustration, we show how to characterize the freezing phenomenon of coherence with only two local measurements for any $N$-qubit quantum systems. Our approach also has other applications in quantum information processing, such as the characterization of distillability and entanglement transformations.

H. Chau Nguyen, Huy-Viet Nguyen and Otfried Gühne
*
The geometry of the Einstein--Podolsky--Rosen correlations
*

Phys. Rev. Lett. *122*,
240401
(2019),
arXiv:1808.09349

Correlations between distant particles are central to many puzzles and paradoxes of quantum mechanics and, at the same time, underpin various applications like quantum cryptography and metrology. Originally in 1935, Einstein, Podolsky and Rosen (EPR) used these correlations to argue against the completeness of quantum mechanics. To formalise their argument, Schr\"odinger subsequently introduced the notion of quantum steering. Still, the question which quantum states can be used for the EPR argument and which not remained open. Here we show that quantum steering can be viewed as an inclusion problem in convex geometry. For the case of two spin-$\frac{1}{2}$ particles, this approach completely characterises the set of states leading to the EPR argument and consequently to a full description of the quantum correlations that can be used for steering. Our results find applications in various protocols in quantum information processing, and moreover they are linked to quantum mechanical phenomena such as uncertainty relations and the question which observables in quantum mechanics are jointly measurable.

Timo Simnacher, Nikolai Wyderka, Cornelia Spee, Xiao-Dong Yu and Otfried Gühne
*
Certifying quantum memories with coherence
*

Phys. Rev. A *99*,
062319
(2019),
arXiv:1809.03403

Quantum memories are an important building block for quantum information processing. Ideally, these memories preserve the quantum properties of the input. We present general criteria for measures to evaluate the quality of quantum memories. Then, we introduce a quality measure based on coherence satisfying these criteria, which we characterize in detail for the qubit case. The measure can be estimated from sparse experimental data and may be generalized to characterize other building blocks, such as quantum gates and teleportation schemes.

Roope Uola, Tristan Kraft, Jiangwei Shang, Xiao-Dong Yu and Otfried Gühne
*
Quantifying quantum resources with conic programming
*

Phys. Rev. Lett. *122*,
130404
(2019),
arXiv:1812.09216

Resource theories can be used to formalize the quantification and manipulation of resources in quantum information processing such as entanglement, asymmetry and coherence of quantum states, and incompatibility of quantum measurements. Given a certain state or measurement, one can ask whether there is a task in which it performs better than any resourceless state or measurement. Using conic programming, we prove that any general robustness measure (with respect to a convex set of free states or measurements) can be seen as a quantifier of such outperformance in some discrimination task. We apply the technique to various examples, e.g. joint measurability, POVMs simulable by projective measurements, and state assemblages preparable with a given Schmidt number.

Timo Simnacher, Nikolai Wyderka, René Schwonnek and Otfried Gühne
*
Entanglement detection with scrambled data
*

Phys. Rev. A *99*,
062339
(2019),
arXiv:1901.07946

In the usual entanglement detection scenario the possible measurements and the corresponding data are assumed to be fully characterized. We consider the situation where the measurements are known, but the data is scrambled, meaning the assignment of the probabilities to the measurement outcomes is unknown. We investigate in detail the two-qubit scenario with local measurements in two mutually unbiased bases. First, we discuss the use of entropies to detect entanglement from scrambled data, showing that Tsallis- and R\'enyi entropies can detect entanglement in our scenario, while the Shannon entropy cannot. Then, we introduce and discuss scrambling-invariant families of entanglement witnesses. Finally, we show that the set of non-detectable states in our scenario is non-convex and therefore in general hard to characterize.

Christina Ritz, Cornelia Spee and Otfried Gühne
*
Characterizing multipartite entanglement classes via higher-dimensional
embeddings
*

J. Phys. A: Math. Theor. *52*,
335302
(2019),
arXiv:1901.08847

Witness operators are a central tool to detect entanglement or to distinguish among the different entanglement classes of multiparticle systems, which can be defined using stochastic local operations and classical communication (SLOCC). We show a one-to-one correspondence between general SLOCC witnesses and a class of entanglement witnesses in an extended Hilbert space. This relation can be used to derive SLOCC witnesses from criteria for full separability of quantum states; moreover, given SLOCC witness can be viewed as entanglement witnesses. As applications of this relation we discuss the calculation of overlaps between different SLOCC classes, and the SLOCC classification in $2\times 3\times 3$-dimensional systems.

Jiang Zhang, Xiao-Dong Yu, Gui-Lu Long and Qi-Kun Xue
*
Topological Dynamical Decoupling
*

SCIENCE CHINA Physics, Mechanics & Astronomy *62*,
12036
(2019),
arXiv:1909.10697

We show that topological equivalence classes of circles in a two-dimensional square lattice can be used to design dynamical decoupling procedures to protect qubits attached on the edges of the lattice. Based on the circles of the topologically trivial class in the original and the dual lattices, we devise a procedure which removes all kinds of local Hamiltonians from the dynamics of the qubits while keeping information stored in the homological degrees of freedom unchanged. If only the linearly independent interaction and nearest-neighbor two-qubit interactions are concerned, a much simpler procedure which involves the four equivalence classes of circles can be designed. This procedure is compatible with Eulerian and concatenated dynamical decouplings, which make it possible to implement the procedure with bounded-strength controls and for a long time period. As an application, it is shown that our method can be directly generalized to finite square lattices to suppress uncorrectable errors in surface codes.

Ernest Y.-Z. Tan, René Schwonnek, Koon Tong Goh, Ignatius William Primaatmaja, Charles C.-W. Lim
*
Computing secure key rates for quantum cryptography with untrusted devices
*

npj Quantum Inf 7, 158 (2021) *7*,
158
(2019),
arXiv:1908.11372

Device-independent quantum key distribution (DIQKD) provides the strongest form of secure key exchange, using only the input-output statistics of the devices to achieve information-theoretic security. Although the basic security principles of DIQKD are now well-understood, it remains a technical challenge to derive reliable and robust security bounds for advanced DIQKD protocols that go beyond the previous results based on violations of the CHSH inequality. In this work, we present a framework based on semi-definite programming that gives reliable lower bounds on the asymptotic secret key rate of any QKD protocol using untrusted devices. In particular, our method can in principle be utilized to find achievable secret key rates for any DIQKD protocol, based on the full input-output probability distribution or any choice of Bell inequality. Our method also extends to other DI cryptographic tasks.

C. L. Liu, Xiao-Dong Yu and D. M. Tong
*
Flag Additivity in Quantum Resource Theories
*

Phys. Rev. A *99*,
04232
(2019),
arXiv:1904.07627

Quantum resource theories offer a powerful framework for studying various phenomena in quantum physics. Despite considerable effort has been devoted to developing a unified framework of resource theories, there are few common properties that hold for all quantum resources. In this paper, we fill this gap by introducing the flag additivity based on the tensor product structure and the flag basis for the general quantum resources. To illustrate the usefulness of flag additivity, we show that flag additivity can be used to derive other nontrivial properties in quantum resource theories, e.g., strong monotonicity, convexity, and full additivity.

Fabian Bernards, Matthias Kleinmann, Otfried Gühne and Mauro Paternostro
*
Daemonic ergotropy: generalised measurements and multipartite settings
*

Entropy *21*,
771
(2019),
arXiv:1907.01970

Recently, the concept of daemonic ergotropy has been introduced to quantify the maximum energy that can be obtained from a quantum system through an ancilla-assisted work extraction protocol based on information gain via projective measurements [G. Francica {\it et al.}, npj Quant. Inf. {\bf 3}, 12 (2018)]. We prove that quantum correlations are not advantageous over classical correlations if projective measurements are considered. We go beyond the limitations of the original definition to include generalised measurements and provide an example in which this allows for a higher daemonic ergotropy. Moreover, we propose a see-saw algorithm to find a measurement that attains the maximum work extraction. Finally, we provide a multipartite generalisation of daemonic ergotropy that pinpoints the influence of multipartite quantum correlations, and study it for multipartite entangled and classical~states.

Andreas Ketterer, Nikolai Wyderka and Otfried Gühne
*
Characterizing multipartite entanglement with moments of random
correlations
*

Phys. Rev. Lett. *122*,
120505
(2019),
arXiv:1808.06558

The experimental detection of multipartite entanglement usually requires a number of appropriately chosen local quantum measurements which are aligned with respect to a previously shared common reference frame. The latter, however, can be a challenging prerequisite e.g. for satellite-based photonic quantum communication, making the development of alternative detection strategies desirable. One possibility for avoiding the distribution of classical reference frames is to perform a number of local measurements with settings distributed uniformly at random. In this work we follow such a treatment and show that an improved detection and characterization of multipartite entanglement is possible by combining statistical moments of different order. To do so, we make use of designs which are pseudo-random processes allowing to link the present entanglement criteria to ordinary reference frame independent ones. The strengths of our methods are illustrated in various cases starting with two qubits and followed by more involved multipartite scenarios.

## 2018

Ana C. S. Costa, Roope Uola and Otfried Gühne
*
Entropic Steering Criteria: Applications to Bipartite and Tripartite
Systems
*

Entropy *20*,
763
(2018),
arXiv:1808.01198

The effect of quantum steering describes a possible action at a distance via local measurements. Whereas many attempts on characterizing steerability have been pursued, answering the question as to whether a given state is steerable or not remains a difficult task. Here, we investigate the applicability of a recently proposed method for building steering criteria from generalized entropic uncertainty relations. This method works for any entropy which satisfy the properties of (i) (pseudo-) additivity for independent distributions; (ii) state independent entropic uncertainty relation (EUR); and (iii) joint convexity of a corresponding relative entropy. Our study extends the former analysis to Tsallis and R\'enyi entropies on bipartite and tripartite systems. As examples, we investigate the steerability of the three-qubit GHZ and W states.

Gael Sentís, Johannes N. Greiner, Jiangwei Shang, Jens Siewert and Matthias Kleinmann
*
Bound entangled states fit for robust experimental verification
*

Quantum *2*,
113
(2018),
arXiv:1804.07562

Preparing and certifying bound entangled states in the laboratory is an intrinsically hard task, due to both the fact that they typically form narrow regions in the state space, and that a certificate requires a tomographic reconstruction of the density matrix. Indeed, the previous experiments that have reported the preparation of a bound entangled state relied on such tomographic reconstruction techniques. However, the reliability of these results crucially depends on the extra assumption of an unbiased reconstruction. We propose an alternative method for certifying the bound entangled character of a quantum state that leads to a rigorous claim within a desired statistical significance, while bypassing a full reconstruction of the state. The method is comprised by a search for bound entangled states that are robust for experimental verification, and a hypothesis test tailored for the detection of bound entanglement that is naturally equipped with a measure of statistical significance. We apply our method to families of states of $3\times 3$ and $4\times 4$ systems, and find that the experimental certification of bound entangled states is well within reach.

O. Gühne*Ist der Zufall in der Quantenmechanik real?*

K. Kleinknecht (Ed.), Quanten 6 (Schriften der Heisenberg-Gesellschaft), Hirzel-Verlag ,
p. 84
(2018)

Gael Sentís, Esteban Martínez-Vargas and Ramon Muñoz-Tapia
*
Online optimal exact identification of a quantum change point
*

Phys. Rev. A *98*,
052305
(2018),
arXiv:1802.00280

We consider online detection strategies for identifying a change point in a stream of quantum particles allegedly prepared in identical states. We show that the identification of the change point can be done without error via sequential local measurements while attaining the optimal performance bound set by quantum mechanics. In this way, we establish the task of exactly identifying a quantum change point as an instance where local protocols are as powerful as global ones. The optimal online detection strategy requires only one bit of memory between subsequent measurements, and it is amenable to experimental realization with current technology.

Mariami Gachechiladze, Nikolai Wyderka and Otfried Gühne
*
The structure of ultrafine entanglement witnesses
*

J. Phys. A: Math. Theor. *51*,
365307
(2018),
arXiv:1805.06404

An entanglement witness is an observable with the property that a negative expectation value signals the presence of entanglement. The question arises how a witness can be improved if the expectation value of a second observable is known, and methods for doing this have recently been discussed as so-called ultrafine entanglement witnesses. We present several results on the characterization of entanglement given the expectation values of two observables. First, we explain that this problem can naturally be tackled with the method of the Legendre transformation, leading even to a quantification of entanglement. Second, we present necessary and sufficient conditions that two product observables are able to detect entanglement. Finally, we explain some fallacies in the original construction of ultrafine entanglement witnesses [F. Shahandeh et al., Phys. Rev. Lett. 118, 110502 (2017)].

Shang Yu, Chang-Jiang Huang, Jian-Shun Tang, Zhih-Ahn Jia, Yi-Tao Wang, Zhi-Jin Ke, Wei Liu, Xiao Liu, Zong-Quan Zhou, Ze-Di Cheng, Jin-Shi Xu, Yu-Chun Wu, Yuan-Yuan Zhao, Guo-Yong Xiang, Chuan-Feng Li, Guang-Can Guo, Gael Sentís and Ramon Muñoz-Tapia
*
Experimentally detecting a quantum change point via Bayesian inference
*

Phys. Rev. A *98*,
040301(R)
(2018),
arXiv:1801.07508

Detecting a change point is a crucial task in statistics that has been recently extended to the quantum realm. A source state generator that emits a series of single photons in a default state suffers an alteration at some point and starts to emit photons in a mutated state. The problem consists in identifying the point where the change took place. In this work, we consider a learning agent that applies Bayesian inference on experimental data to solve this problem. This learning machine adjusts the measurement over each photon according to the past experimental results finds the change position in an online fashion. Our results show that the local-detection success probability can be largely improved by using such a machine learning technique. This protocol provides a tool for improvement in many applications where a sequence of identical quantum states is required.

Cornelia Spee, Katharina Schwaiger, Géza Giedke and Barbara Kraus
*
Mode-entanglement of Gaussian fermionic states
*

Phys. Rev. A *97*,
042325
(2018),
arXiv:1712.07560

We investigate the entanglement of n-mode n-partite Gaussian fermionic states (GFS). First, we identify a reasonable definition of separability for GFS and derive a standard form for mixed states, to which any state can be mapped via Gaussian local unitaries (GLU). As the standard form is unique two GFS are equivalent under GLU if and only if their standard forms coincide. Then, we investigate the important class of local operations assisted by classical communication (LOCC). These are central in entanglement theory as they allow to partially order the entanglement contained in states. We show, however, that there are no non-trivial Gaussian LOCC (GLOCC). That is, any GLOCC transformation can be accomplished via GLUs. To still obtain insights into the various entanglement properties of n-mode n-partite GFS we investigate the richer class of Gaussian stochastic LOCC. We characterize Gaussian SLOCC classes of pure states and derive them explicitly for few-mode states. Furthermore, we consider certain fermionic LOCC and show how to identify the maximally entangled set (MES) of pure n-mode n-partite GFS, i.e., the minimal set of states having the property that any other state can be obtained from one state inside this set via fermionic LOCC. We generalize these findings also to the pure m-mode n-partite (for m>n) case.

Jannik Hoffmann, Cornelia Spee, Otfried Gühne and Costantino Budroni
*
Structure of temporal correlations of a qubit
*

New J. Phys. *20*,
102001
(2018),
arXiv:1712.01234

In quantum mechanics, spatial correlations arising from measurements at separated particles are well studied. This is not the case, however, for the temporal correlations arising from a single quantum system subjected to a sequence of generalized measurements. We first characterize the polytope of temporal quantum correlations coming from the most general measurements. We then show that if the dimension of the quantum system is bounded, only a subset of the most general correlations can be realized and identify the correlations in the simplest scenario that can not be reached by two-dimensional systems. This leads to a temporal inequality for a dimension test, and we discuss a possible implementation using nitrogen-vacancy centers in diamond.

Ana C. S. Costa, Roope Uola and Otfried Gühne
*
Steering criteria from general entropic uncertainty relations
*

Phys. Rev. A *98*,
050104
(2018),
arXiv:1710.04541

The effect of steering describes a possible action at a distance via measurements but characterizing the quantum states that can be used for this task remains difficult. We provide a method to derive sufficient criteria for steering from entropic uncertainty relations using generalized entropies. We demonstrate that the resulting criteria outperform existing criteria in several scenarios; moreover, they allow one to detect weakly steerable states.

Joshua Lockhart, Otfried Gühne and Simone Severini
*
Entanglement properties of quantum grid states
*

Phys. Rev. A *97*,
062340
(2018),
arXiv:1705.09261

Grid states form a discrete set of mixed quantum states that can be described by graphs. We characterize the entanglement properties of these states and provide methods to evaluate entanglement criteria for grid states in a graphical way. With these ideas we find bound entangled grid states for two-particle systems of any dimension and multiparticle grid states that provide examples for the different aspects of genuine multiparticle entanglement. Our findings suggest that entanglement theory for grid states, although being a discrete set, has already a complexity similar to the one for general states.

Marius Paraschiv, Nikolai Miklin, Tobias Moroder and Otfried Gühne
*
Proving genuine multiparticle entanglement from separable
nearest-neighbor marginals
*

Phys. Rev. A *98*,
062102
(2018),
arXiv:1705.02696

We address the question of whether or not global entanglement of a quantum state can be inferred from local properties. Specifically, we are interested in genuinely multiparticle entangled states whose two-body marginals are all separable, but where the entanglement can be proven using knowledge of a subset of the marginals only. Using an iteration of semidefinite programs we prove that for any possible marginal configuration up to six particles multiqubit states with the desired properties can be found. We then present a method to construct states with the same properties for more particles in higher dimensions.

Nikolai Wyderka, Felix Huber and Otfried Gühne
*
Constraints on correlations in multiqubit systems
*

Phys. Rev. A *97*,
060101
(2018),
arXiv:1710.00758

The set of correlations between particles in multipartite quantum systems is larger than those in classical systems. Nevertheless, it is subject to restrictions by the underlying quantum theory. In order to better understand the structure of this set, a possible strategy is to divide all correlations into two components, depending on the question of whether they involve an odd or an even number of particles. For pure multi-qubit states we prove that these two components are inextricably interwoven and often one type of correlations completely determines the other. As an application, we prove that all pure qubit states with an odd number of qubits are uniquely determined among all mixed states by the odd component of the correlations. In addition, our approach leads to invariants under the time evolution with Hamiltonians containing only odd correlations and can simplify entanglement detection.

M. Hebenstreit, M. Gachechiladze, O. Gühne and B. Kraus
*
The Entanglement Hierarchy 2 x m x n Systems
*

Phys. Rev. A *97*,
032330
(2018),
arXiv:1710.00981

We consider three-partite pure states in the Hilbert space $\mathbb{C}^2 \otimes \mathbb{C}^m \otimes \mathbb{C}^n$ and investigate to which states a given state can be locally transformed with a non-vanishing probability. Whenever the initial and final states are elements of the same Hilbert space, the problem can be solved via the characterization of the entanglement classes which are determined via stochastic operations and classical communication (SLOCC). In general, there are infinitely many SLOCC classes. However, when considering transformations from higher- to lower-dimensional Hilbert spaces, an additional hierarchy among the classes can be found. This hierarchy of SLOCC classes coarse grains SLOCC classes which can be reached from a common resource state of higher dimension. We first show that a generic set of states in $\mathbb{C}^2 \otimes \mathbb{C}^m \otimes \mathbb{C}^n$ for $n=m$ is the union of infinitely many SLOCC classes, which can be parameterized by $m-3$ parameters. However, for $n \neq m$ there exists a single SLOCC class which is generic. Using this result, we then show that there is a full-measure set of states in $\mathbb{C}^2 \otimes \mathbb{C}^m \otimes \mathbb{C}^n$ such that any state within this set can be transformed locally to a full measure set of states in any lower-dimensional Hilbert space. We also investigate resource states, which can be transformed to any state (not excluding any zero-measure set) in the smaller-dimensional Hilbert space. We explicitly derive a state in $\mathbb{C}^2 \otimes \mathbb{C}^m \otimes \mathbb{C}^{2m-2}$ which is the optimal common resource of all states in $\mathbb{C}^2 \otimes \mathbb{C}^m \otimes \mathbb{C}^m$. We also show that for any $n < 2m$ it is impossible to reach all states in $\mathbb{C}^2 \otimes \mathbb{C}^m \otimes \mathbb{C}^{\tilde{n}}$ whenever $\tilde{n}>m$.

Felix Huber, Christopher Eltschka, Jens Siewert and Otfried Gühne
*
Bounds on absolutely maximally entangled states from shadow
inequalities, and the quantum MacWilliams identity
*

J. Phys. A: Math. Theor. *51*,
175301
(2018),
arXiv:1708.06298

A pure multipartite quantum state is called absolutely maximally entangled (AME), if all reductions obtained by tracing out at least half of its parties are maximally mixed. Maximal entanglement is then present across every bipartition. The existence of such states is in many cases unclear. With the help of the weight enumerator machinery known from quantum error correction and the generalized shadow inequalities, we obtain new bounds on the existence of AME states in dimensions larger than two. To complete the treatment on the weight enumerator machinery, the quantum MacWilliams identity is derived in the Bloch representation. Finally, we consider AME states whose subsystems have different local dimensions, and present an example for a $2 \times3 \times 3 \times 3$ system that shows maximal entanglement across every bipartition.

Roope Uola, Fabiano Lever, Otfried Gühne and Juha-Pekka Pellonpää
*
Unified picture for spatial, temporal and channel steering
*

Phys. Rev. A *97*,
032301
(2018),
arXiv:1707.09237

Quantum steering describes how local actions on a quantum system can affect another, space-like separated, quantum state. Lately, quantum steering has been formulated also for time-like scenarios and for quantum channels. We approach all the three scenarios as one using tools from Stinespring dilations of quantum channels. By applying our technique we link all three steering problems one-to-one with the incompatibility of quantum measurements, a result formerly known only for spatial steering. We exploit this connection by showing how measurement uncertainty relations can be used as tight steering inequalities for all three scenarios. Moreover, we show that certain notions of temporal and spatial steering are fully equivalent and prove a hierarchy between temporal steering and macrorealistic hidden variable models.

Andreas Ketterer, Adrien Laversanne-Finot and Leandro Aolita
*
Continuous-variable supraquantum nonlocality
*

Phys. Rev. A *97*,
012133
(2018),
arXiv:1707.05337

Supraquantum nonlocality refers to correlations that are more nonlocal than allowed by quantum theory but still physically conceivable in post-quantum theories, in the sense of respecting the basic no-faster-than-light communication principle. While supraquantum correlations are relatively well understood for finite-dimensional systems, little is known in the infinite-dimensional case. Here, we study supraquantum nonlocality for bipartite systems with two measurement settings and infinitely many outcomes per subsystem. We develop a formalism for generic no-signaling black-box measurement devices with continuous outputs in terms of probability measures, instead of probability distributions, which involves a few technical subtleties. We show the existence of a class of supraquantum Gaussian correlations, which violate the Tsirelson bound of an adequate continuous-variable Bell inequality. We then introduce the continuous-variable version of the celebrated Popescu-Rohrlich (PR) boxes, as a limiting case of the above-mentioned Gaussian ones. Finally, we perform a characterisation of the geometry of the set of continuous-variable no-signaling correlations. Namely, we show that that the convex hull of the continuous-variable PR boxes is dense in the no-signaling set. We also show that these boxes are extreme in the set of no-signaling behaviours and provide evidence suggesting that they are indeed the only extreme points of the no-signaling set. Our results lay the grounds for studying generalized-probability theories in continuous-variable systems.

Jiangwei Shang and Otfried Gühne
*
Convex optimization over classes of multiparticle entanglement
*

Phys. Rev. Lett. *120*,
050506
(2018),
arXiv:1707.02958

A well-known strategy to characterize multiparticle entanglement utilizes the notion of stochastic local operations and classical communication (SLOCC), but characterizing the resulting entanglement classes is difficult. Given a multiparticle quantum state, we first show that Gilbert's algorithm can be adapted to prove separability or membership in a certain entanglement class. We then present two algorithms for convex optimization over SLOCC classes. The first algorithm uses a simple gradient approach, while the other one employs the accelerated projected-gradient method. For demonstration, the algorithms are applied to the likelihood-ratio test using experimental data on bound entanglement of a noisy four-photon Smolin state [Phys. Rev. Lett. 105, 130501 (2010)].

Tristan Kraft, Christina Ritz, Nicolas Brunner, Marcus Huber and Otfried Gühne
*
Characterizing Genuine Multilevel Entanglement
*

Phys. Rev. Lett. *120*,
060502
(2018),
arXiv:1707.01050

Entanglement of high-dimensional quantum systems has become increasingly important for quantum communication and experimental tests of nonlocality. However, many effects of high-dimensional entanglement can be simulated by using multiple copies of low-dimensional systems. We present a general theory to characterize those high-dimensional quantum states for which the correlations cannot simply be simulated by low-dimensional systems. Our approach leads to general criteria for detecting multilevel entanglement in multiparticle quantum states, which can be used to verify these phenomena experimentally.

## 2017

Sabine Wölk and Christof Wunderlich
*
Quantum dynamics of trapped ions in a dynamic field gradient using
dressed states
*

New J. Phys. 19 083021 ,
(2017),
arXiv:1606.04821

Novel ion traps that provide either a static or a dynamic magnetic gradient field allow for the use of radio frequency (rf) radiation for coupling internal and motional states of ions, which is essential for conditional quantum logic. We show that the coupling mechanism in the presence of a dynamic gradient is the same, in a dressed state basis, as in the case of a static gradient. Then, it is shown how demanding experimental requirements arising when using a dynamic gradient could be overcome. Thus, using dressed states in a dynamic gradient field could decisively reduce experimental complexity on the route towards a scalable device for quantum information science based on rf-driven trapped ions.

Sanah Altenburg, Michał Oszmaniec, Sabine Wölk and Otfried Gühne
*
Estimation of gradients in quantum metrology
*

Phys. Rev. A *96*,
042319
(2017),
arXiv:1703.09123

We develop a general theory to estimate magnetic field gradients in quantum metrology. We consider a system of $N$ particles distributed on a line whose internal degrees of freedom interact with a magnetic field. Usually gradient estimation is based on precise measurements of the magnetic field at two different locations, performed with two independent groups of particles. This approach, however, is sensitive to fluctuations of the off-set field determining the level-splitting of the particles and results in collective dephasing. In this work we use the framework of quantum metrology to assess the maximal accuracy for gradient estimation. For arbitrary positioning of particles, we identify optimal entangled and separable states allowing the estimation of gradients with the maximal accuracy, quantified by the quantum Fisher information. We also analyze the performance of states from the decoherence-free subspace (DFS), which are insensitive to the fluctuations of the magnetic offset field. We find that these states allow to measure a gradient directly, without the necessity of estimating the magnetic offset field. Moreover, we show that DFS states attain a precision for gradient estimation comparable to the optimal entangled states. Finally, for the above classes of states we find simple and feasible measurements saturating the quantum Cram\'er-Rao bound.

Nikolai Wyderka, Felix Huber and Otfried Gühne
*
Almost all four-particle pure states are determined by their two-body
marginals
*

Phys. Rev. A *96*,
010102
(2017),
arXiv:1703.10950

We show that generic pure states (states drawn according to the Haar measure) of four particles of equal internal dimension are uniquely determined among all other pure states by their two-body marginals. In fact, certain subsets of three of the two-body marginals suffice for the characterization. We also discuss generalizations of the statement to pure states of more particles, showing that these are almost always determined among pure states by three of their $(n-2)$-body marginals. Finally, we present special families of symmetric pure four-particle states that share the same two-body marginals and are therefore undetermined. These are four-qubit Dicke states in superposition with generalized GHZ states.

Mariana R. Barros, Andreas Ketterer, Osvaldo Jiménez Farías and Stephen P. Walborn
*
Free-Space Entangled Quantum Carpets
*

Phys. Rev. A *95*,
042311
(2017),
arXiv:1702.07391

The Talbot effect in quantum physics is known to produce intricate patterns in the probability distribution of a particle, known as "quantum carpets", corresponding to the revival and replication of the initial wave function. Recently, it was shown that one can encode a $D$-level qudit, in such a way that the Talbot effect can be used to process the $D$-dimensional quantum information [Far\'{\i}as et al, PRA (2015)]. Here we introduce a scheme to produce free-propagating "entangled quantum carpets" with pairs of photons produced by spontaneous parametric down-conversion. First we introduce an optical device that can be used to synthesize arbitrary superposition states of Talbot qudits. Sending spatially entangled photon pairs through a pair of these devices produces an entangled pair of qudits. As an application, we show how the Talbot effect can be used to test a $D$-dimensional Bell inequality. Numerical simulations show that violation of the Bell inequality depends strongly on the amount of spatial correlation in the initial two-photon state. We briefly discuss how our optical scheme might be adapted to matter wave experiments.

Frank E. S. Steinhoff, Christina Ritz, Nikolai Miklin and Otfried Gühne
*
Qudit Hypergraph States
*

Phys. Rev. A *95*,
052340
(2017),
arXiv:1612.06418

We generalize the class of hypergraph states to multipartite systems of qudits, by means of constructions based on the d-dimensional Pauli group and its normalizer. For simple hypergraphs, the different equivalence classes under local operations are shown to be governed by a greatest common divisor hierarchy. Moreover, the special cases of three qutrits and three ququarts is analysed in detail.

Nikoloz Tsimakuridze and Otfried Gühne
*
Graph states and local unitary transformations beyond local Clifford
operations
*

J. Phys. A: Math. Theor. *50*,
195302
(2017),
arXiv:1611.06938

Graph states are quantum states that can be described by a stabilizer formalism and play an important role in quantum information processing. We consider the action of local unitary operations on graph states and hypergraph states. We focus on non-Clifford operations and find for certain transformations a graphical description in terms of weighted hypergraphs. This leads to the indentification of hypergraph states that are locally equivalent to graph states. Moreover, we present a systematic way to construct pairs of graph states which are equivalent under local unitary operations, but not equivalent under local Clifford operations. This generates counterexamples to a conjecture known as LU-LC conjecture. So far, the only counterexamples to this conjecture were found by random search. Our method reproduces the smallest known counterexample as a special case and provides a physical interpretation.

Felix Huber, Otfried Gühne and Jens Siewert
*
Absolutely maximally entangled states of seven qubits do not exist
*

Phys. Rev. Lett. *118*,
200502
(2017),
arXiv:1608.06228

Pure multiparticle quantum states are called absolutely maximally entangled if all reduced states obtained by tracing out at least half of the particles are maximally mixed. We provide a method to characterize these states for a general multiparticle system. With that, we prove that a seven-qubit state whose three-body marginals are all maximally mixed, or equivalently, a pure $((7,1,4))_2$ quantum error correcting code, does not exist. Furthermore, we obtain an upper limit on the possible number of maximally mixed three-body marginals and identify the state saturating the bound. This solves the seven-particle problem as the last open case concerning maximally entangled states of qubits.

M. Gachechiladze, N. Tsimakuridze, O. Gühne*Graphical description of unitary transformations on hypergraph states*

J. Phys. A: Math. Theor. *50*,
19LT01
(2017),
arXiv:1612.01447

Hypergraph states form a family of multiparticle quantum states that generalizes cluster states and graph states. We study the action and graphical representation of nonlocal unitary transformations between hypergraph states. This leads to a generalization of local complementation and graphical rules for various gates, such as the CNOT gate and the Toffoli gate. As an application we show that already for five qubits local Pauli operations are not sufficient to check local equivalence of hypergraph states. Furthermore, we use our rules to construct entanglement witnesses for three-uniform hypergraph states.

I. Apellaniz, M. Kleinmann, O. Gühne, G. Toth*Optimal witnessing of the quantum Fisher information with few measurements*

Phys. Rev. A *95*,
032330
(2017),
arXiv:
1511.05203

We show how to verify the metrological usefulness of quantum states based on the expectation values of an arbitrarily chosen set of observables. In particular, we estimate the quantum Fisher information as a figure of merit of metrological usefulness. Our approach gives a tight lower bound on the quantum Fisher information for the given incomplete information. We apply our method to the results of various multiparticle quantum states prepared in experiments with photons and trapped ions, as well as to spin-squeezed states and Dicke states realized in cold gases. Our approach can be used for detecting and quantifying metrologically useful entanglement in very large systems, based on a few operator expectation values. We also gain new insights into the difference between metrological useful multipartite entanglement and entanglement in general.

M. Gachechiladze, O. Gühne*Completing the proof of "Generic quantum nonlocality"*

Phys. Lett. A *381*,
1281
(2017),
arXiv:
1607.02948

In a paper by Popescu and Rohrlich [Phys. Lett. A 166, 293 (1992)] a proof has been presented showing that any pure entangled multiparticle quantum state violates some Bell inequality. We point out a gap in this proof, but we also give a construction to close this gap. It turns out that with some extra effort all the results from the aforementioned publication can be proven. Our construction shows how two-particle entanglement can be generated via performing local projections on a multiparticle state.

O. Gühne*Der Zufall und die Quantenphysik*

U. Herkenrath, A. Schwaetzer (Eds.), Zufall, Roderer-Verlag ,
p. 79
(2017)

O. Gühne*Annahmen in der Physik: Ein Beispiel aus der Quantenmechanik*

U. Lüke, G. Souvignier(Eds.), Wie objektiv ist Wissenschaft?, WBG ,
p. 81
(2017)

O. Gühne, M. Kleinmann, T. Moroder*Analysing multiparticle quantum states*

R. Bertlmann, A. Zeilinger (Eds.), Quantum [Un]speakables II, Springer ,
p. 345
(2017),
arXiv:1506.06976

The analysis of multiparticle quantum states is a central problem in quantum information processing. This task poses several challenges for experimenters and theoreticians. We give an overview over current problems and possible solutions concerning systematic errors of quantum devices, the reconstruction of quantum states, and the analysis of correlations and complexity in multiparticle density matrices.

## 2016

S. Wölk
*
Revealing quantum properties with simple measurements
*

Foundations of quantum theory (Proceedings of the International School of Physics "Enrico Fermi") ,
(2016),
arXiv:1611.07678

Since the beginning of quantum mechanics, many puzzling phenomena which distinguish the quantum from the classical world, have appeared such as complementarity, entanglement or contextuality. All of these phenomena are based on the existence of non-commuting observables in quantum mechanics. Furthermore, theses effects generate advantages which allow quantum technologies to surpass classical technologies. In this lecture note, we investigate two prominent examples of these phenomenons: complementarity and entanglement. We discuss some of their basic properties and introduce general methods for their experimental investigation. In this way, we find many connections between the investigation of complementarity and entanglement. One of these connections is given by the Cauchy-Schwarz inequality which helps to formulate quantitative measurement procedures to observe complementarity as well as entanglement.

S. Wölk, O. Gühne*Characterizing the width of entanglement*

New J. Phys. *18*,
123024
(2016),
arXiv:1507.07226

The size of controllable quantum systems has grown in recent times. Therefore, the spatial degree of freedom becomes more and more important in experimental quantum systems. However, the investigation of entanglement in many-body systems mainly concentrated on the number of entangled particles and ignored the spatial degree of freedom so far. As a consequence, a general concept together with experimentally realizable criteria has been missing to describe the spatial distribution of entanglement. We close this gap by introducing the concept of entanglement width as measure of the spatial distribution of entanglement in many-body systems. We develop criteria to detect the width of entanglement based solely on global observables. As a result, our entanglement criteria can be applied easily to many-body systems since single-particle addressing is not necessary.

S. Altenburg, S. Wölk, G. Toth, O. Gühne*Optimized parameter estimation in the presence of collective phase noise*

Phys. Rev. A *94*,
052306
(2016),
arXiv:1607.05160

We investigate phase and frequency estimation with different measurement strategies under the effect of collective phase noise. First, we consider the standard linear estimation scheme and present an experimentally realisable optimization of the initial probe states by collective rotations. We identify the optimal rotation angle for different measurement times. Second, we show that sub-shot noise sensitivity - up to the Heisenberg limit - can be reached in presence of collective phase noise by using differential interferometry, where one part of the system is used to monitor the noise. For this, not only GHZ states but also symmetric Dicke states are suitable. We investigate the optimal splitting for a general symmetric Dicke state at both inputs and discuss possible experimental realisations of differential interferometry.

A. Neven, P. Mathonet, O. Gühne, T. Bastin*Quantum fidelity of symmetric multipartite states*

Phys. Rev. A *94*,
052332
(2016),
arXiv:
1606.02675

For two symmetric quantum states one may be interested in maximizing the overlap under local operations applied to one of them. The question arises whether the maximal overlap can be obtained by applying the same local operation to each party. We show that for two symmetric multiqubit states and local unitary transformations this is the case; the maximal overlap can be reached by applying the same unitary matrix everywhere. For local invertible operations (SLOCC equivalence), however, we present counterexamples, demonstrating that considering the same operation everywhere is not enough.

A. Cabello, M. Gu, O. Gühne, J.-Å. Larsson, K. Wiesner*Thermodynamical cost of some interpretations of quantum theory*

Phys. Rev. A *94*,
052127
(2016),
arXiv:
1509.03641

The interpretation of quantum theory is one of the longest-standing debates in physics. Type I interpretations see quantum probabilities as determined by intrinsic properties of the observed system. Type II see them as relational experiences between an observer and the system. It is usually believed that a decision between these two options cannot be made simply on purely physical grounds but requires an act of metaphysical judgment. Here we show that, under some assumptions, the problem is decidable using thermodynamics. We prove that type I interpretations are incompatible with the following assumptions: (i) The choice of which measurement is performed can be made randomly and independently of the system under observation, (ii) the system has limited memory, and (iii) Landauer's erasure principle holds.

C. Budroni, N. Miklin, R. Chaves*Indistinguishability of causal relations from limited marginals*

Phys. Rev. A *94*,
042127
(2016),
arXiv:1607.08540

We investigate the possibility of distinguishing among different causal relations starting from a limited set of marginals. Our main tool is the notion of adhesivity, that is, the extension of probability or entropies defined only on subsets of variables, which provides additional independence constraints among them. Our results provide a criterion for recognizing which causal structures are indistinguishable when only limited marginal information is accessible. Furthermore, the existence of such extensions greatly simplifies the characterization of a marginal scenario, a result that facilitates the derivation of Bell inequalities both in the probabilistic and entropic frameworks, and the identification of marginal scenarios where classical, quantum, and postquantum probabilities coincide.

M. Paraschiv, S. Wölk, T. Mannel, O. Gühne*Generalized Effective Operator Formalism for Decaying Systems*

Phys. Rev. A *94*,
042103
(2016),
arXiv:
1607.00797

Systems of neutral kaons can be used to observe entanglement and the violation of Bell inequalities. The decay of these particles poses some problems, however, and recently an effective formalism for treating such systems has been derived. We generalize this formalism and make it applicable to other quantum systems that can be made to behave in a similar manner. As examples, we discuss two possible implementations of the generalized formalism using trapped ions such as 171Yb or 172Yb, which may be used to simulate kaonic behavior in a quantum optical system.

G. Sentís, C. Eltschka, O. Gühne, M. Huber, J. Siewert*Quantifying entanglement of maximal dimension in bipartite mixed states*

Phys. Rev. Lett. *117*,
190502
(2016),
arXiv:
1605.09783

The Schmidt coefficients capture all entanglement properties of a pure bipartite state and therefore determine its usefulness for quantum information processing. While the quantification of the corresponding properties in mixed states is important both from a theoretical and a practical point of view, it is considerably more difficult, and methods beyond estimates for the concurrence are elusive. In particular this holds for a quantitative assessment of the most valuable resource, the maximum possible Schmidt number of an arbitrary mixed state. We derive a framework for lower bounding the appropriate measure of entanglement, the so-called G-concurrence, through few local measurements. Moreover, we show that these bounds have relevant applications also for multipartite states.

A. Asadian, P. Erker, M. Huber, C. Klöckl*Heisenberg-Weyl basis observables and related applications*

Phys. Rev. A *94*,
010301(R)
(2016),
arXiv:
1512.05640

We introduce a Hermitian generalization of Pauli matrices to higher dimensions which is based on Heisenberg-Weyl operators. The complete set of Heisenberg-Weyl observables allows us to identify a real-valued Bloch vector for an arbitrary density operator in discrete phase space, with a smooth transition to infinite dimensions. Furthermore, we derive bounds on the sum of expectation values of any set of anti-commuting observables. Such bounds can be used in entanglement detection and we show that Heisenberg-Weyl observables provide a first non-trivial example beyond the dichotomic case.

F. Huber, O. Gühne*Characterizing ground and thermal states of few-body Hamiltonians*

Phys. Rev. Lett. *117*,
010403
(2016),
arXiv:
1601.01630

The question whether a given quantum state is a ground or thermal state of a few-body Hamiltonian can be used to characterize the complexity of the state and is important for possible experimental implementations. We provide methods to characterize the states generated by two- and, more generally, k-body Hamiltonians as well as the convex hull of these sets. This leads to new insights into the question which states are uniquely determined by their marginals and to a generalization of the concept of entanglement. Finally, certification methods for quantum simulation can be derived.

S.-L. Chen, C. Budroni, Y.-C. Liang, Y.-N. Chen*Natural Framework for Device-Independent Quantification of Quantum Steerability, Measurement Incompatibility, and Self-Testing*

Phys. Rev. Lett. *116*,
240401
(2016),
arXiv:1603.08532

We introduce the concept of assemblage moment matrices, i.e., a collection of matrices of expectation values, each associated with a conditional quantum state obtained in a steering experiment. We demonstrate how it can be used for quantum states and measurements characterization in a device-independent manner, i.e., without invoking any assumption about the measurement or the preparation device. Specifically, we show how the method can be used to lower bound the steerability of an underlying quantum state directly from the observed correlation between measurement outcomes. Combining such device-independent quantifications with earlier results established by Piani and Watrous [Phys. Rev. Lett. 114, 060404 (2015)], our approach immediately provides a device-independent lower bound on the generalized robustness of entanglement, as well as the usefulness of the underlying quantum state for a type of subchannel discrimination problem. In addition, by proving a quantitative relationship between steering robustness and the recently introduced incompatibility robustness, our approach also allows for a device-independent quantification of the incompatibility between various measurements performed in a Bell-type experiment. Explicit examples where such bounds provide a kind of self-testing of the performed measurements are provided.

R. Chaves, C. Budroni*Entropic nonsignalling correlations*

Phys. Rev. Lett. *116*,
240501
(2016),
arXiv:1601.07555

We introduce the concept of entropic nonsignalling correlations, i.e., entropies arising from probabilistic theories that are compatible with the fact that we cannot transmit information instantaneously. We characterize and show the relevance of these entropic correlations in a variety of different scenarios, ranging from typical Bell experiments to more refined descriptions such as bilocality and information causality. In particular, we apply the framework to derive the first entropic inequality testing genuine tripartite nonlocality in quantum systems of arbitrary dimension and also prove the first known monogamy relation for entropic Bell inequalities. Further, within the context of complex Bell networks, we show that entropic nonlocal correlations can be activated.

Ch. Piltz, Th. Sriarunothai, S. Ivanov, S. Wölk, Ch. Wunderlich*Versatile microwave-driven trapped ion spin system for quantum information processing*

Science Advances *2*,
e1600093
(2016),
arXiv:
1509.01478

Using trapped atomic ions, we demonstrate a tailored and versatile effective spin system suitable for quantum simulations and universal quantum computation. By simply applying microwave pulses, selected spins can be decoupled from the remaining system and, thus, can serve as a quantum memory, while simultaneously, other coupled spins perform conditional quantum dynamics. Also, microwave pulses can change the sign of spin-spin couplings, as well as their effective strength, even during the course of a quantum algorithm. Taking advantage of the simultaneous long-range coupling between three spins, a coherent quantum Fourier transform—an essential building block for many quantum algorithms—is efficiently realized. This approach, which is based on microwave-driven trapped ions and is complementary to laser-based methods, opens a new route to overcoming technical and physical challenges in the quest for a quantum simulator and a quantum computer.

A. Asadian, M. Abdi*Heralded entangled coherent states between spatially separated massive resonators*

Phys. Rev. A *93*,
052315
(2016),
arXiv:1507.02540

We put forward an experimentally feasible scheme for heralded entanglement generation between two distant macroscopic mechanical resonators. The protocol exploits a hybrid quantum device, a qubit interacting with a mechanical resonator as well as a cavity mode, for each party. The cavity modes interfere on a beam-splitter followed by suitable heralding detections which post-select a hybrid entangled state with success probability 1/2. Subsequently, by local measurements on the qubits a mechanical entangled coherent state can be achieved. The mechanical entanglement can be further verified via monitoring the entanglement of the qubit pair. The setup is envisioned as a test bench for sensing gravitational effects on the quantum dynamics of gravitationally coupled massive objects. As a concrete example, we illustrate the implementation of our protocol using the current circuit QED architectures.

L.E. Buchholz, T. Moroder, O. Gühne*Evaluating the geometric measure of multiparticle entanglement*

Ann. Phys. (Berlin) *528*,
278
(2016),
arXiv:1412.7471

We present an analytical approach to evaluate the geometric measure of multiparticle entanglement for mixed quantum states. Our method allows the computation of this measure for a family of multiparticle states with a certain symmetry and delivers lower bounds on the measure for general states. It works for an arbitrary number of particles, for arbitrary classes of multiparticle entanglement, and can also be used to determine other entanglement measures.

T. Moroder, O. Gittsovich, M. Huber, R. Uola, O. Gühne*Steering maps and their application to dimension-bounded steering*

Phys. Rev. Lett. *116*,
090403
(2016),
arXiv:1412.2623

The existence of quantum correlations that allow one party to steer the quantum state of another party is a counterintuitive quantum effect that has been described already at the beginning of the past century. Steering occurs if entanglement can be proven although the description of the measurements on one party is not known, while the other side is characterized. We introduce the concept of steering maps that allow to unlock the sophisticated techniques developed in regular entanglement detection to be used for certifying steerability. As an application we show that this allows to go even beyond the canonical steering scenario, enabling a generalized dimension-bounded steering where one only assumes the Hilbert space dimension on the characterized side, but no description of the measurements. Surprisingly this does not weaken the detection strength of very symmetric scenarios that have recently been carried out in experiments.

M. Gachechiladze, C. Budroni, O. Gühne*Extreme violation of local realism in quantum hypergraph states*

Phys. Rev. Lett. *116*,
070401
(2016),
arXiv:1507.03570

Hypergraph states form a family of multiparticle quantum states that generalizes the well-known concept of Greenberger-Horne-Zeilinger states, cluster states, and more broadly graph states. We study the nonlocal properties of quantum hypergraph states. We demonstrate that the correlations in hypergraph states can be used to derive various types of nonlocality proofs, including Hardy-type arguments, Bell inequalities for genuine multiparticle nonlocality, and an exponentially increasing violation of local realism. Our results suggest that certain classes of hypergraph states are novel resources for quantum metrology and measurement-based quantum computation.

N. Killoran, F. E. S. Steinhoff, M. B. Plenio*Converting non-classicality into entanglement*

Phys. Rev. Lett. *116*,
080402
(2016),
arXiv:1505.07393

Quantum mechanics exhibits a wide range of nonclassical features, of which entanglement in multipartite systems takes a central place. In several specific settings, it is well known that nonclassicality (e.g., squeezing, spin squeezing, coherence) can be converted into entanglement. In this work, we present a general framework, based on superposition, for structurally connecting and converting nonclassicality to entanglement. In addition to capturing the previously known results, this framework also allows us to uncover new entanglement convertibility theorems in two broad scenarios, one which is discrete and one which is continuous. In the discrete setting, the classical states can be any finite linearly independent set. For the continuous setting, the pertinent classical states are 'symmetric coherent states,' connected with symmetric representations of the group SU(K). These results generalize and link convertibility properties from the resource theory of coherence, spin coherent states, and optical coherent states, while also revealing important connections between local and nonlocal pictures of nonclassicality.

N. Miklin, T. Moroder, O. Gühne*Multiparticle entanglement as an emergent phenomenon*

Phys. Rev. A *93*,
020104(R)
(2016),
arXiv:1506.05766

The question whether global entanglement of a multiparticle quantum system can be inferred from local properties is of great relevance for the theory of quantum correlations as well as for experimental implementations. We present a method to systematically find quantum states, for which the two- or three-body marginals do not contain any entanglement, nevertheless, the knowledge of these reduced states is sufficient to prove genuine multiparticle entanglement of the global state. With this, we show that the emergence of global entanglement from separable local quantum states occurs frequently and for an arbitrary number of particles. We discuss various extensions of the phenomenon and present examples where global entanglement can be proven from marginals, even if entanglement cannot be localized in the marginals with measurements on the other parties.

O. Gühne*Keine Ausreden mehr!*

Physik Journal *15(2)*,
18
(2016)

Drei Experimente schließen durch Verletzung der Bellschen Ungleichungen lokal-realistische Modelle aus.

## 2015

R. Uola, C. Budroni, O. Gühne, J.-P. Pellonpää*One-to-one mapping between steering and joint measurability problems*

Phys. Rev. Lett. *115*,
230402
(2015),
arXiv:1507.08633

Quantum steering refers to the possibility for Alice to remotely steer Bob's state by performing local measurements on her half of a bipartite system. Two necessary ingredients for steering are entanglement and incompatibility of Alice's measurements. In particular, it has been recently proven that for the case of pure states of maximal Schmidt rank the problem of steerability for Bob's assemblage is equivalent to the problem of joint measurability for Alice observables. We show that such an equivalence holds in general, namely, the steerability of any assemblage can always be formulated as a joint measurability problem, and vice versa. We use this connection to introduce steering inequalities from joint measurability criteria and develop quantifiers for the incompatibility of measurements.

C. Lancien, O. Gühne, R. Sengupta, M. Huber*Relaxations of separability in multipartite systems: Semidefinite programs, witnesses and volumes*

J. Phys. A: Math. Theor. *48*,
505302
(2015),
arXiv:1504.01029

While entanglement is believed to be an important ingredient in understanding quantum many-body physics, the complexity of its characterization scales very unfavorably with the size of the system. Finding super-sets of the set of separable states that admit a simpler description has proven to be a fruitful approach in the bipartite setting. In this paper we discuss a systematic way of characterizing multiparticle entanglement via various relaxations. We furthermore describe an operational witness construction arising from such relaxations that is capable of detecting every entangled state. Finally, we also derive analytic upper-bounds on the volume of biseparable states and show that the volume of the states with a positive partial transpose for any split exponentially outgrows this volume. This proves that simple semi-definite relaxations in the multiparticle case cannot be an equally good approximation for any scenario.

A. S. Arora, A. Asadian*Proposal for a macroscopic test of local realism with phase-space measurements*

Phys. Rev. A *92*,
062107
(2015),
arXiv:1508.04588

We propose a new test of local realism based on correlation measurements of continuum valued functions of positions and momenta, known as modular variables. The Wigner representation of these observables are bounded in phase space, and therefore, the associated inequality holds for any state described by a non-negative Wigner function. This agrees with Bell's remark that positive Wigner functions, serving as a valid probability distribution over local (hidden) phase space coordinates, do not reveal non-locality. We construct a class of entangled states resulting in a violation of the inequality, and thus truly demonstrate non-locality in phase space. The states can be realized through grating techniques in space-like separated interferometric setups. The non-locality is verified from the spatial correlation data, collected from the screens.

C. Budroni, G. Vitagliano, G. Colangelo, R.J. Sewell, O. Gühne, G. Toth, M. Mitchell*Quantum non-demolition measurement enables macroscopic Leggett-Garg tests*

Phys. Rev. Lett. *115*,
200403
(2015),
arXiv:1503.08433

We show how a test of macroscopic realism based on Leggett-Garg inequalities (LGIs) can be performed in a macroscopic system. Using a continuous-variable approach, we consider quantum non-demolition (QND) measurements applied to atomic ensembles undergoing magnetically-driven coherent oscillation. We identify measurement schemes requiring only Gaussian states as inputs and giving a significant LGI violation with realistic experimental parameters and imperfections. The predicted violation is shown to be due to true quantum effects rather than to a classical invasivity of the measurement. Using QND measurements to tighten the "clumsiness loophole" forces the stubborn macrorealist to re-create quantum back action in his or her account of measurement.

A. Asadian, C. Budroni, F. E. S. Steinhoff, P. Rabl, O. Gühne*Contextuality in phase space*

Phys. Rev. Lett. *114*,
250403
(2015),
arXiv:1502.05799

We present a general framework for contextuality tests in phase space using displacement operators. First, we derive a general condition that a single-mode displacement operator should fulfill in order to construct Peres-Mermin square and similar scenarios. This approach offers a straightforward scheme for experimental implementations of the tests via modular variable measurements. In addition to the continuous variable case, our condition can be also applied to finite-dimensional systems in discrete phase space, using Heisenberg-Weyl operators. This approach, therefore, offers a unified picture of contextuality with a geometric flavor.

A. Cabello, M. Kleinmann, C. Budroni*Necessary and sufficient condition for quantum state-independent contextuality*

Phys. Rev. Lett. *114*,
250402
(2015),
arXiv:1501.03432

We solve the problem of whether a set of quantum tests reveals state-independent contextuality and use this result to identify the simplest set of minimal dimension. We also show that identifying state-independent contextuality graphs [R. Ramanathan and P. Horodecki, Phys. Rev. Lett. 112, 040404 (2014)] is not sufficient for revealing state-independent contextuality.

G. Toth, T. Moroder, O. Gühne*Evaluating convex roof entanglement measures*

Phys. Rev. Lett. *114*,
160501
(2015),
arXiv:1409.3806

We show an efficient method to compute entanglement measures based on convex roof constructions. In particular, our method is applicable to measures that, for pure states, can be written as low order polynomials of operator expectation values. We show how to compute the linear entropy of entanglement, the linear entanglement of assistance, and a bound on the dimension of the quantum state for bipartite systems. We discuss how to obtain the convex roof of the three-tangle for three-qubit states. We also show how to calculate the linear entropy of entanglement and the quantum Fisher information based on partial information or device independent information. We demonstrate the usefulness of our method by concrete examples.

E. Haapasalo, J.-P. Pellonpää, R. Uola*Compatibility properties of extreme quantum observables*

Lett. Math. Phys. *105*,
661
(2015),
arXiv:1404.4172

Recently, a problem concerning the equivalence of joint measurability and coexistence of quantum observables was solved (Reeb at al. J Phys A Math Theor 46:462002, 2013). In this paper, we generalize two known joint measurability results from sharp observables to the class of extreme observables and study relationships between coexistence, joint measurability, and post-processing of quantum observables when an extreme observable is involved. We also discuss another notion of compatibility and provide a counterexample separating this from the former notions.

C. Schwemmer, L. Knips, D. Richart, H. Weinfurter, T. Moroder, M. Kleinmann, O. Gühne*Systematic errors in current quantum state tomography tools*

Phys. Rev. Lett. *114*,
080403
(2015),
arXiv:1310.8465

Common tools for obtaining physical density matrices in experimental quantum state tomography are shown here to cause systematic errors. For example, using maximum likelihood or least squares optimization to obtain physical estimates for the quantum state, we observe a systematic underestimation of the fidelity and an overestimation of entanglement. Such strongly biased estimates can be avoided using linear evaluation of the data or by linearizing measurement operators yielding reliable and computational simple error bounds.

S. Wölk, C. Piltz, T. Sriarunothai, C. Wunderlich*State selective detection of hyperfine qubits*

J. Phys. B: At. Mol. Opt. Phys. *48*,
075101
(2015),
arXiv:1406.5821

In order to faithfully detect the state of an individual two-state quantum system (qubit) realized using, for example, a trapped ion or atom, state selective scattering of resonance fluorescence is well established. The simplest way to read out this measurement and assign a state is the threshold method. The detection error can be decreased by using more advanced detection methods like the time-resolved method or the $\pi$-pulse detection method. These methods were introduced to qubits with a single possible state change during the measurement process. However, there exist many qubits like the hyperfine qubit of $^{171}Yb^+$ where several state change are possible. To decrease the detection error for such qubits, we develope generalizations of the time-resolved method and the $\pi$-pulse detection method for such qubits. We show the advantages of these generalized detection methods in numerical simulations and experiments using the hyperfine qubit of $^{171}Yb^+$. The generalized detection methods developed here can be implemented in an efficient way such that experimental real time state discrimination with improved fidelity is possible.

O. Gittsovich, T. Moroder, A. Asadian, O. Gühne, P. Rabl*Non-classicality tests and entanglement witnesses for macroscopic mechanical superposition states*

Phys. Rev. A *91*,
022114
(2015),
arXiv:1412.2167

We describe a set of measurement protocols for performing non-classicality tests and the verification of entangled superposition states of macroscopic continuous variable systems, such as nanomechanical resonators. Following earlier works, we first consider a setup where a two-level system is used to indirectly probe the motion of the mechanical system via Ramsey measurements and discuss the application of this methods for detecting non-classical mechanical states. We then show that the generalization of this techniques to multiple resonator modes allows the conditioned preparation and the detection of entangled mechanical superposition states. The proposed measurement protocols can be implemented in various qubit-resonator systems that are currently under experimental investigation and find applications in future tests of quantum mechanics at a macroscopic scale.

## 2014

O. Gittsovich and T. Moroder*Key rate for calibration robust entanglement based BB84 quantum key distribution protocol*

AIP Conf. Proc. *1633*,
156
(2014),
arXiv:1303.3484

We apply the approach of verifying entanglement, which is based on the sole knowledge of the dimension of the underlying physical system to the entanglement based version of the BB84 quantum key distribution protocol. We show that the familiar one-way key rate formula holds already if one assumes the assumption that one of the parties is measuring a qubit and no further assumptions about the measurement are needed.

M. Kleinmann*Sequences of projective measurements in generalized probabilistic models*

J. Phys. A: Math. Theor. *47*,
455304
(2014),
arXiv:1402.3583

We define a simple rule to describe sequences of projective measurements for such generalized probabilistic models that can be described by an Archimedean order-unit vector space. For quantum mechanics, this definition yields the established L\"uders's rule, while in the general case it can be seen as the least disturbing or most coherent way to perform sequential measurements. As example we show that Spekkens toy model is an instance of our definition. We also demonstrate the possibility of strong post-quantum correlations and triple-slit correlations for certain non-quantum toy models.

M. Ali*Quantum dissonance provide power to deterministic quantum computation with single qubit*

Int. J. Quantum Inform. *12*,
1450037
(2014),
arXiv:1312.1572

Mixed state quantum computation can perform certain tasks which are believed to be efficiently intractable on a classical computer. For a specific model of mixed state quantum computation, namely, {\it deterministic quantum computation with a single qubit} (DQC1), recent investigations suggest that quantum correlations other than entanglement might be responsible for the power of DQC1 model. However, strictly speaking, the role of entanglement in this model of computation was not entirely clear. We provide conclusive evidence that there are instances where quantum entanglement is not present in any part of this model, nevertheless we have advantage over classical computation. This establishes the fact that quantum dissonance (quantum correlations) present in fully separable states provide power to DQC1 model.

R. Uola, T. Moroder, O. Gühne*Joint measurability of generalized measurements implies classicality*

Phys. Rev. Lett. *113*,
160403
(2014),
arXiv:1407.2224

The fact that not all measurements can be carried out simultaneously is a peculiar feature of quantum mechanics and is responsible for many key phenomena in the theory, such as complementarity or uncertainty relations. For the special case of projective measurements, quantum behavior can be characterized by the commutator but for generalized measurements it is not easy to decide whether two measurements can still be understood in classical terms or whether the already show quantum features. We prove that a set of generalized measurements which does not satisfy the notion of joint measurability is nonclassical, as it can be used for the task of quantum steering. This shows that the notion of joint measurability is, among several definitions, the proper one to characterize quantum behavior. Moreover, the equivalence allows one to derive novel steering inequalities from known results on joint measurability and new criteria for joint measurability from known results on the steerability of states.

Mazhar Ali, A. R. P. Rau*Sudden change in dynamics of genuine multipartite entanglement of cavity-reservoir qubits*

Phys. Rev. A *90*,
042330
(2014),
arXiv:1406.5767

We study the dynamics of genuine multipartite entanglement for a system of four qubits. Using a computable entanglement monotone for multipartite systems, we investigate the as yet unexplored aspects of a cavity-reservoir system of qubits. For one specific initial state, we observe a sudden transition in the dynamics of genuine entanglement for the four qubits. This sudden change occurs only during a time window where neither cavity-cavity qubits nor reservoir-reservoir qubits are entangled. We show that the sudden change in dynamics of this specific state is extremely sensitive to white noise.

N. Brunner, O. Gühne, M. Huber*Editorial: Fifty years of Bell's theorem*

J. Phys. A: Math. Theor. *47*,
420301
(2014)

S. Wölk, M. Huber, O. Gühne*Unified approach to entanglement criteria using the Cauchy-Schwarz and Hölder inequalities*

Phys. Rev. A *90*,
022315
(2014),
arXiv:1405.0986

We present unified approach to different recent entanglement criteria. Although they were developed in different ways, we show that they are all applications of a more general principle given by the Cauchy-Schwarz inequality. We explain this general principle and show how to derive with it not only already known but also new entanglement criteria. We systematically investigate its potential and limits to detect bipartite and multipartite entanglement.

T. Moroder, O. Gittsovich, M. Huber, O. Gühne*Steering bound entangled states: A counterexample to the stronger Peres conjecture*

Phys. Rev. Lett. *113*,
050404
(2014),
arXiv:1405.0262

Quantum correlations are at the heart of many applications in quantum information science and, at the same time, they form the basis for discussions about genuine quantum effects and their difference to classical physics. On one hand, entanglement theory provides the tools to quantify correlations in information processing and many results have been obtained to discriminate useful entanglement, which can be distilled to a pure form, from bound entanglement, being of limited use in many applications. On the other hand, for discriminating quantum phenomena from their classical counterparts, Schr\"odinger and Bell introduced the notions of steering and local hidden variable models. We provide a method to generate systematically bound entangled quantum states which can still be used for steering and therefore to rule out local hidden state models. This sheds light on the relations between the various views on quantum correlations and disproves a widespread conjecture known as the stronger Peres conjecture. For practical applications, it implies that even the weakest form of entanglement can be certified in a semi-device independent way.

C. Budroni and C. Emary*Temporal quantum correlations and Leggett-Garg inequalities in multi-level systems*

Phys. Rev. Lett. *113*,
050401
(2014),
arXiv:1309.3678

We show that the quantum bound for temporal correlations in a Leggett-Garg test, analogous to the Tsirelson bound for spatial correlations in a Bell test, strongly depends on the number of levels N that can be accessed by the measurement apparatus via projective measurements. We provide exact bounds for small N, that exceed the known bound for the Leggett-Garg inequality, and show that in the limit N\rightarrow \infty the Leggett-Garg inequality can be violated up to its algebraic maximum.

O. Gühne, M. Cuquet, F.E.S. Steinhoff, T. Moroder, M. Rossi, D. Bruß, B. Kraus, C. Macchiavello*Entanglement and nonclassical properties of hypergraph states*

J. Phys. A: Math. Theor. *47*,
335303
(2014),
arXiv:1404.6492

Hypergraph states are multi-qubit states that form a subset of the locally maximally entangleable states and a generalization of the well--established notion of graph states. Mathematically, they can conveniently be described by a hypergraph that indicates a possible generation procedure of these states; alternatively, they can also be phrased in terms of a non-local stabilizer formalism. In this paper, we explore the entanglement properties and nonclassical features of hypergraph states. First, we identify the equivalence classes under local unitary transformations for up to four qubits, as well as important classes of five- and six-qubit states, and determine various entanglement properties of these classes. Second, we present general conditions under which the local unitary equivalence of hypergraph states can simply be decided by considering a finite set of transformations with a clear graph-theoretical interpretation. Finally, we consider the question whether hypergraph states and their correlations can be used to reveal contradictions with classical hidden variable theories. We demonstrate that various noncontextuality inequalities and Bell inequalities can be derived for hypergraph states.

C. Schwemmer, G. Tóth, A. Niggebaum, T. Moroder, D. Gross, O. Gühne, H. Weinfurter*Experimental Comparison of Efficient Tomography Schemes for a Six-Qubit State*

Phys. Rev. Lett. *113*,
040503
(2014),
arXiv:1401.7526

Quantum state tomography suffers from the measurement effort increasing exponentially with the number of qubits. Here, we demonstrate permutationally invariant tomography for which, contrary to conventional tomography, all resources scale polynomially with the number of qubits both in terms of the measurement effort as well as the computational power needed to process and store the recorded data. We evaluate permutationally invariant tomography by comparing it to full tomography for six-photon states obtained from spontaneous parametric down-conversion. We show that their results are compatible within the statistical errors. For low rank states, we further optimize both schemes using compressed sensing. We demonstrate the benefits of combining permutationally invariant tomography with compressed sensing by studying the influence of the pump power on the noise present in a six-qubit symmetric Dicke state, a case where full tomography is possible only for very high pump powers.

O. Gühne, C. Budroni, A. Cabello, M. Kleinmann, J.-Å. Larsson*Bounding the quantum dimension with contextuality*

Phys. Rev. A *89*,
062107
(2014),
arXiv:1302.2266

We show that the phenomenon of quantum contextuality can be used to certify lower bounds on the dimension accessed by the measurement devices. To prove this, we derive bounds for different dimensions and scenarios of the simplest noncontextuality inequalities. The resulting dimension witnesses work independently of the prepared quantum state. Our constructions are robust against noise and imperfections, and we show that a recent experiment can be viewed as an implementation of a state-independent quantum dimension witness.

M. Hofmann, T. Moroder, and O. Gühne*Analytical characterization of the genuine multiparticle negativity*

J. Phys. A: Math. Theor. *47*,
155301
(2014),
arXiv:1401.2424

The genuine multiparticle negativity is a measure of genuine multiparticle entanglement which can be computed numerically. We present several results how this entanglement measure can be characterized analytically. First, we show that with an appropriate normalization this measure can be seen as coming from a mixed convex roof construction. Based on this, we determine its value for $n$-qubit GHZ-diagonal states and four-qubit cluster-diagonal states.

O. Gittsovich, N.J. Beaudry, V. Narasimhachar, R.R. Alvarez, T. Moroder, N. Lütkenhaus*Squashing model for detectors and applications to quantum key distribution protocols*

Phys. Rev. A *89*,
012325
(2014),
arXiv:1310.5059

We develop a framework that allows a description of measurements in Hilbert spaces that are smaller than their natural representation. This description, which we call a "squashing model", consists of a squashing map that maps the input states of the measurement from the original Hilbert space to the smaller one, followed by a targeted prescribed measurement on the smaller Hilbert space. This framework has applications in quantum key distribution, but also in other cryptographic tasks, as it greatly simplifies the theoretical analysis under adversarial conditions.

M. Ali, O. Gühne*Robustness of multiparticle entanglement: specific entanglement classes and random states*

J. Phys. B: At. Mol. Opt. Phys. *47*,
055503
(2014),
arXiv:1310.7336

We investigate the robustness of genuine multiparticle entanglement under decoherence. We consider different kinds of entangled three- and four-qubit states as well as random pure states. For amplitude damping noise, we find that the W-type states are most robust, while other states are not more robust than generic states. For phase damping noise the GHZ state is the most robust state, and for depolarizing noise several states are significantly more robust than random states.

M. Hofmann, A. Osterloh, and O. Gühne*Scaling of genuine multiparticle entanglement at a quantum phase transition*

Phys. Rev. B *89*,
134101
(2014),
arXiv:1309.2217

We investigate the scaling and spatial distribution of genuine multiparticle entanglement in three- and four-spin reduced states of the one-dimensional XY-model at the quantum phase transition. We observe a logarithmic divergence and show that genuine three- and four-particle entanglement obeys finite-size scaling.

## 2013

M. Bergmann and O. Gühne*Entanglement criteria for Dicke states*

J. Phys. A: Math. Theor. *46*,
385304
(2013),
arXiv:1305.2818

Dicke states are a family of multi-qubit quantum states with interesting entanglement properties and have been observed in many experiments. We construct entanglement witnesses for detecting genuine multiparticle entanglement in the vicinity of these states. We use the approach of PPT mixtures to derive the conditions analytically. For nearly all cases, our criteria are stronger than all conditions previously known.

M. Araujo, M.T. Quintino, C. Budroni, M. Terra Cunha, and A. Cabello*All noncontextuality inequalities for the n-cycle scenario*

Phys. Rev. A *88*,
022118
(2013),
arXiv:1206.3212

The problem of separating classical from quantum correlations is in general intractable and has been solved explicitly only in few cases. In particular, known methods cannot provide general solutions for an arbitrary number of settings. We provide the complete characterization of the classical correlations and the corresponding maximal quantum violations for the case of n >= 4 observables X_0, ...,X_{n-1}, where each consecutive pair {X_i,X_{i+1}}, sum modulo n, is jointly measurable. This generalizes both the Clauser-Horne-Shimony-Holt and the Klyachko-Can-Binicioglu-Shumovsky scenarios, which are the simplest ones for, respectively, locality and noncontextuality. In addition, we provide explicit quantum states and settings with maximal quantum violation and minimal quantum dimension.

O. Gühne, T. Moroder*Squeezing out more information about entanglement*

Physics *6*,
79
(2013)

An experimental demonstration of a novel quantum analysis tool will allow diagnosis of entanglement in a much broader set of states.

C. Budroni, T. Moroder, M. Kleinmann, O. Gühne*Bounding temporal quantum correlations*

Phys. Rev. Lett. *111*,
020403
(2013),
arXiv:1302.6223

Sequential measurements on a single particle play an important role in fundamental tests of quantum mechanics. We provide a general method to analyze temporal quantum correlations, which allows us to compute the maximal correlations for sequential measurements in quantum mechanics. As an application, we present the full characterization of temporal correlations in the simplest Leggett-Garg scenario and in the sequential measurement scenario associated with the most fundamental proof of the Kochen-Specker theorem.

T. Moroder, J.-D. Bancal, Y.-C. Liang, M. Hofmann, O. Gühne*Device-independent entanglement quantification and related applications*

Phys. Rev. Lett. *111*,
030501
(2013),
arXiv:1302.1336

We present a general method to quantify both bipartite and multipartite entanglement in a device-independent manner, meaning that we put a lower bound on the amount of entanglement present in a system based on observed data only but independently of any quantum description of the employed devices. Some of the bounds we obtain, such as for the Clauser-Horne-Shimony-Holt Bell inequality or the Svetlichny inequality, are shown to be tight. Besides, device-independent entanglement quantification can serve as a basis for numerous tasks. We show in particular that our method provides a rigorous way to construct dimension witnesses, gives new insights into the question whether bound entangled states can violate a Bell inequality, and can be used to construct device independent entanglement witnesses involving an arbitrary number of parties.

L. Novo, T. Moroder, O. Gühne*Genuine multiparticle entanglement of permutationally invariant states*

Phys. Rev. A *88*,
012305
(2013),
arXiv:1302.4100

We consider the problem of characterizing genuine multiparticle entanglement for permutationally invariant states using the approach of PPT mixtures. We show that the evaluation of this necessary biseparability criterion scales polynomially with the number of particles. In practice, it can be evaluated easily up to ten qubits and improves existing criteria significantly. Finally, we show that our approach solves the problem of characterizing genuine multiparticle entanglement for permutationally invariant three-qubit states.

J. Szangolies, M. Kleinmann, and O. Gühne*Tests against noncontextual models with measurement disturbances*

Phys. Rev. A *87*,
050101(R)
(2013),
arXiv:1303.3837

The testability of the Kochen-Specker theorem is a subject of ongoing controversy. A central issue is that experimental implementations relying on sequential measurements cannot achieve perfect compatibility between the measurements and that therefore the notion of noncontextuality does not apply. We demonstrate by an explicit model that such compatibility violations may yield a violation of noncontextuality inequalities, even if we assume that the incompatibilities merely originate from context-independent noise. We show, however, that this problem can be circumvented by combining the ideas behind Leggett-Garg inequalities with those of the Kochen-Specker theorem.

T. Moroder, M. Kleinmann, P. Schindler, T. Monz, O. Gühne, and R. Blatt*Certifying Systematic Errors in Quantum Experiments*

Phys. Rev. Lett. *110*,
180401
(2013),
arXiv:1204.3644

When experimental errors are ignored in an experiment, the subsequent analysis of its results becomes questionable. We develop tests to detect systematic errors in quantum experiments where only a finite amount of data is recorded and apply these tests to tomographic data taken in an ion trap experiment. We put particular emphasis on quantum state tomography and present three detection methods: the first two employ linear inequalities while the third is based on the generalized likelihood ratio.

S. Niekamp, T. Galla, M. Kleinmann, O. Gühne*Computing complexity measures for quantum states based on exponential families*

J. Phys. A: Math. Theor. *46*,
125301
(2013),
arXiv:1212.6163

Given a multiparticle quantum state, one may ask whether it can be represented as a thermal state of some Hamiltonian with k-particle interactions only. The distance from the exponential family defined by these thermal states can be considered as a measure of complexity of a given state. We investigate the resulting optimization problem and show how symmetries can be exploited to simplify the task of finding the nearest thermal state in a given exponential family. We also present an algorithm for the computation of the complexity measure and consider specific examples to demonstrate its applicability.

E. Amselem, M. Bourennane, C. Budroni, A. Cabello, O. Gühne, M. Kleinmann, J.-Å. Larsson, M. Wieśniak*Comment on ”State-Independent Experimental Test of Quantum Contextuality in an Indivisible System”*

Phys. Rev. Lett. *110*,
078901
(2013),
arXiv:1302.0617

We argue that the experiment described in the recent Letter by Zu et al. [Phys. Rev. Lett. 109, 150401 (2012); arXiv:1207.0059v1] does not allow to make conclusions about contextuality, since the measurement of the observables as well as the preparation of the state manifestly depend on the chosen context.

M. Hofmann, G. Rudolph and M. Schmidt*On the reflection type decomposition of the adjoint reduced phase space of a compact semisimple Lie group *

Journal of Mathematical Physics *54*,
083505
(2013),
arXiv:1302.6118

We consider a system with symmetries whose configuration space is a compact Lie group, acted upon by inner automorphisms. The classical reduced phase space of this system decomposes into connected components of orbit type subsets. To investigate hypothetical quantum effects of this decomposition one has to construct the associated costratification of the Hilbert space of the quantum system in the sense of Huebschmann. In the present paper, instead of the decomposition by orbit types, we consider the related decomposition by reflection types (conjugacy classes of reflection subgroups). These two decompositions turn out to coincide, e.g., for the classical groups SU(n) and Sp(n). We derive defining relations for reflection type subsets in terms of irreducible characters and discuss how to obtain from that the corresponding costratification of the Hilbert space of the system. To illustrate the method, we give explicit results for some low rank classical groups.

O. Gühne, M. Kleinmann*Auf den Kontext kommt es an*

Physik Journal *12(2)*,
25
(2013)

Die Quantenmechanik hat viele, scheinbar paradoxe Konsequenzen. Diese Tatsache hat zu Spekulationen darüber verleitet, ob es eine übergeordnete Theorie geben könnte, die im Einklang mit der klassischen Physik ist. Neben der Bellschen Ungleichung gibt es ein weitreichendes Theorem von Ernst Specker und Simon Kochen, das es ermöglicht, „klassische Modelle“ quantenmechanischer Systeme auszuschließen. Was als Nachdenken über die logische Struktur der Quantenmechanik begann, lässt sich nun auch im Experiment beobachten.

M. Kleinmann, T.J. Osborne, V.B. Scholz, A.H. Werner*Typical local measurements in generalised probabilistic theories: emergence of quantum bipartite correlations*

Phys. Rev. Lett *110*,
040403
(2013),
arXiv:1205.3358

What singles out quantum mechanics as the fundamental theory of nature? Here we study local measurements in generalized probabilistic theories (GPTs) and investigate how observational limitations affect the production of correlations. We find that if only a subset of typical local measurements can be made then all the bipartite correlations produced in a GPT can be simulated to a high degree of accuracy by quantum mechanics. Our result makes use of a generalization of Dvoretzky’s theorem for GPTs. The tripartite correlations can go beyond those exhibited by quantum mechanics, however.

## 2012

T. Moroder, M. Curty, C. C. W. Lim, L. P. Thinh, H. Zbinden, and N. Gisin*Security of distributed-phase-reference quantum key distribution*

Phys. Rev. Lett. *109*,
260501
(2012),
arXiv:1207.5544

Distributed-phase-reference quantum key distribution stands out for its easy implementation with present day technology. Since many years, a full security proof of these schemes in a realistic setting has been elusive. For the first time, we solve this long standing problem and present a generic method to prove the security of such protocols against general attacks. To illustrate our result we provide lower bounds on the key generation rate of a variant of the coherent-one-way quantum key distribution protocol. In contrast to standard predictions, it appears to scale quadratically with the system transmittance.

Z.-H. Chen, Z.-H. Ma, O. Gühne, and S. Severini*Estimating entanglement monotones with a generalization of the Wootters formula*

Phys. Rev. Lett. *109*,
200503
(2012),
arXiv:1207.2889

Entanglement monotones, such as the concurrence, are useful tools to characterize quantum correlations in various physical systems. The computation of the concurrence involves, however, difficult optimizations and only for the simplest case of two qubits a closed formula was found by Wootters [Phys. Rev. Lett. 80, 2245 (1998)]. We show how this approach can be generalized, resulting in lower bounds on the concurrence for higher dimensional systems as well as for multipartite systems. We demonstrate that for certain families of states our results constitute the strongest bipartite entanglement criterion so far; moreover, they allow to recognize novel families of multiparticle bound entangled states.

J.-A. Larsson, M. Kleinmann, C. Budroni, O. Gühne, and A. Cabello*Maximal violation of state-independent contextuality inequalities*

AIP Conf. Proc. *1508*,
265
(2012)

The discussion on noncontextual hidden variable models as an underlying description for the quantum-mechanical predictions started in ernest with 1967 paper by Kochen and Specker. There, it was shown that no noncontextual hidden-variable model can give these predictions. The proof used in that paper is complicated, but recently, a paper by Yu and Oh [PRL, 2012] proposes a simpler statistical proof that can also be the basis of an experimental test. Here we report on a sharper version of that statistical proof, and also explain why the algebraic upper bound to the expressions used are not reachable, even with a reasonable contextual hidden variable model. Specifically, we show that the quantum mechanical predictions reach the maximal possible value for a contextual model that keeps the expectation value of the measurement outcomes constant.

T. Moroder, P. Hyllus, G. Toth, C. Schwemmer, A. Niggebaum, S. Gaile, O. Gühne and H. Weinfurter*Permutationally invariant state reconstruction*

New J. Phys. *14*,
105001
(2012),
arXiv:1205.4941

Feasible tomography schemes for large particle numbers must possess, besides an appropriate data acquisition protocol, also an efficient way to reconstruct the density operator from the observed finite data set. Since state reconstruction typically requires the solution of a non-linear large-scale optimization problem, this is a major challenge in the design of scalable tomography schemes. Here we present an efficient state reconstruction scheme for permutationally invariant quantum state tomography. It works for all common state-of-the-art reconstruction principles, including, in particular, maximum likelihood and least squares methods, which are the preferred choices in today's experiments. This high efficiency is achieved by greatly reducing the dimensionality of the problem employing a particular representation of permutationally invariant states known from spin coupling combined with convex optimization, which has clear advantages regarding speed, control and accuracy in comparison to commonly employed numerical routines. First prototype implementations easily allow reconstruction of a state of 20 qubits in a few minutes on a standard computer.

M. Kleinmann, C. Budroni, J.-A. Larsson, O. Gühne, A. Cabello*Optimal inequalities for state-independent contextuality*

Phys. Rev. Lett. *109*,
250402
(2012),
arXiv:1204.3741

Contextuality is a natural generalization of nonlocality which does not need composite systems or spacelike separation and offers a wider spectrum of interesting phenomena. Most notably, in quantum mechanics there exist scenarios where the contextual behavior is independent of the quantum state. We show that the quest for an optimal inequality separating quantum from classical noncontextual correlations in an state-independent manner admits an exact solution, as it can be formulated as a linear program. We introduce the noncontextuality polytope as a generalization of the locality polytope, and apply our method to identify two different tight optimal inequalities for the most fundamental quantum scenario with state-independent contextuality.

H. Kampermann, O. Gühne, C. Wilmott, D. Bruß*An algorithm for characterizing SLOCC classes of multiparticle entanglement*

Phys. Rev. A *86*,
032307
(2012),
arXiv:1203.5872

It is well known that the classification of pure multiparticle entangled states according to stochastic local operations leads to a natural classification of mixed states in terms of convex sets. We present a simple algorithmic procedure to prove that a quantum state lies within a given convex set. Our algorithm generalizes a recent algorithm for proving separability of quantum states [J. Barreiro {\it et al.}, Nature Phys. {\bf 6}, 943 (2010)]. We give several examples which show the wide applicability of our approach. We also propose a procedure to determine a vicinity of a given quantum state which still belongs to the considered convex set.

T. Galla and O. Gühne*Complexity measures, emergence, and multiparticle correlations*

Phys. Rev. E *85*,
046209
(2012),
arXiv:1107.1180

We study correlation measures for complex systems. First, we investigate some recently proposed measures based on information geometry. We show that these measures can increase under local transformations as well as under discarding particles, thereby questioning their interpretation as a quantifier for complexity or correlations. We then propose a refined definition of these measures, investigate its properties and discuss its numerical evaluation. As an example, we study coupled logistic maps and study the behavior of the different measures for that case. Finally, we investigate other local effects during the coarse graining of the complex system.

T. Moroder and O. Gittsovich*Calibration robust entanglement detection beyond Bell inequalities*

Phys. Rev. A *85*,
032301
(2012),
arXiv:1111.5874

In its vast majority entanglement verification is examined either in the complete characterized or totally device independent scenario. The assumptions imposed by these extreme cases are often either too weak or strong for real experiments. Here we investigate this detection task for the intermediate regime where partial knowledge of the measured observables is known, considering cases like orthogonal, sharp or only dimension bounded measurements. We show that for all these assumptions it is not necessary to violate a corresponding Bell inequality in order to detect entanglement. We derive strong detection criteria that can be directly evaluated for experimental data and which are robust against large classes of calibration errors. The conditions are even capable of detecting bound entanglement under the sole assumption of dimension bounded measurements.

S. Niekamp, M. Kleinmann, and O. Gühne*Entropic uncertainty relations and the stabilizer formalism*

J. Math. Phys. *53*,
012202
(2012),
arXiv:1103.2316

## 2011

M. Kleinmann, H. Kampermann, and D. Bruß*Asymptotically perfect discrimination in the LOCC paradigm*

Phys. Rev. A *84*,
042326
(2011),
arXiv:1105.5132

We revisit the problem of discriminating orthogonal quantum states within the local-quantum-operation-and-classical-communication (LOCC) paradigm. Our particular focus is on the asymptotic situation where the parties have infinite resources and the protocol may become arbitrarily long. Our main result is a necessary condition for perfect asymptotic LOCC discrimination. As an application, we prove that for complete product bases, unlimited resources are of no advantage. On the other hand, we identify an example for which it still remains undecided whether unlimited resources are superior.

O. Gühne, B. Jungnitsch, T. Moroder, Y.S. Weinstein*Multiparticle entanglement in graph-diagonal states: Necessary and sufficient conditions for four qubits*

Phys. Rev. A *84*,
052319
(2011),
arXiv:1107.4863

The characterization of genuine multiparticle entanglement is important for entanglement theory as well as experimental studies related to quantum information theory. Here, we completely characterize genuine multiparticle entanglement for four-qubit states diagonal in the cluster-state basis. In addition, we give a complete characterization of multiparticle entanglement for all five-qubit graph states mixed with white noise, for states diagonal in the basis corresponding to the five-qubit Y-shaped graph, and for a family of graph states with an arbitrary number of qubits.

B. Jungnitsch, T. Moroder and O. Gühne*Entanglement Witnesses for Graph States: General Theory and Examples*

Phys. Rev. A *84*,
032310
(2011),
arXiv:1106.1114

We present a general theory for the construction of witnesses that detect genuine multipartite entanglement in graph states. First, we present explicit witnesses for all graph states of up to six qubits which are better than all criteria so far. Therefore, lower fidelities are required in experiments that aim at the preparation of graph states. Building on these results, we develop analytical methods to construct two different types of entanglement witnesses for general graph states. For many classes of states, these operators exhibit white noise tolerances that converge to one when increasing the number of particles. We illustrate our approach for states such as the linear and the 2D cluster state. Finally, we study an entanglement monotone motivated by our approach for graph states.

B. Jungnitsch, T. Moroder and O. Gühne*Taming multiparticle entanglement*

Phys. Rev. Lett. *106*,
190502
(2011),
arXiv:1010.6049

We present an approach to characterize genuine multiparticle entanglement using appropriate approximations in the space of quantum states. This leads to a criterion for entanglement which can easily be calculated using semidefinite programming and improves all existing approaches significantly. Experimentally, it can also be evaluated when only some observables are measured. Furthermore, it results in a computable entanglement monotone for genuine multiparticle entanglement. Based on this, we develop an analytical approach for the entanglement detection in cluster states, leading to an exponentially improved noise robustness compared with existing schemes.

M. Kleinmann, O. Gühne, J.R. Portillo, J.-A. Larsson, and A. Cabello*Memory cost of quantum contextuality*

New J. Phys. *13*,
113011
(2011),
arXiv:1007.3650

The simulation of quantum effects requires certain classical resources, and quantifying them is an important step to characterize the difference between quantum and classical physics. For a simulation of the phenomenon of state-independent quantum contextuality, we show that the minimum amount of memory used by the simulation is the critical resource. We derive optimal simulation strategies for important cases and prove that reproducing the results of sequential measurements on a two-qubit system requires more memory than the information-carrying capacity of the system.

J.-A. Larsson, M. Kleinmann, O. Gühne, and A. Cabello*Violating noncontextual realism through sequential measurements*

AIP Conf. Proc. *1327*,
401
(2011)

The question of whether noncontextual hidden variable models can give the quantum‐mechanical predictions has been under discussion for a long time. The question originates in the sixties, perhaps best known from the 1967 paper by Kochen and Specker where it was shown that no noncontextual hidden‐variable model can give these predictions. Recently, the question has gained interest from experimentalists trying to test this in the laboratory. The experimental setups in question have used a sequential setup rather than the alternative, joint (simultaneous) measurement. There has been discussion in the community whether this is appropriate. This brief paper argues that sequential measurement is not only the correct choice, but the best possible.

O. Gühne*Entanglement criteria and full separability of multi-qubit quantum states*

Phys. Lett. A *375*,
406
(2011),
arXiv:1009.3782

M. Curty and T. Moroder*Heralded qubit amplifiers for practical device-independent quantum key distribution*

Phys. Rev. A *84*,
010304(R)
(2011),
arXiv:1105.2573

Device-independent quantum key distribution does not need a precise quantum mechanical model of employed devices to guarantee security. Despite its beauty, it is still a very challenging experimental task. We compare a recent proposal by Gisin et al. [Phys. Rev. Lett. 105, 070501 (2010)] to close the detection loophole problem with that of a simpler quantum relay based on entanglement swapping with linear optics. Our full-mode analysis for both schemes confirms that, in contrast to recent beliefs, the second scheme can indeed provide a positive key rate which is even considerably higher than that of the first alternative. The resulting key rates and required detection efficiencies of approximately 95% for both schemes, however, strongly depend on the underlying security proof.

## 2010

B. Jungnitsch, S. Niekamp, M. Kleinmann, O. Gühne, H. Lu, W.-B. Gao, Y.-A. Chen, Z.-B. Chen, and Jian-Wei Pan*Increasing the statistical significance of entanglement detection in experiments*

Phys. Rev. Lett. *104*,
210401
(2010),
arXiv:0912.0645

J. T. Barreiro, P. Schindler, O. Gühne, T. Monz, M. Chwalla, C. F. Roos, M. Hennrich, and R. Blatt*Experimental multiparticle entanglement dynamics induced by decoherence*

Nature Physics *6*,
943
(2010),
arXiv:1005.1965

W.-B. Gao, X.-C. Yao, P. Xu, H. Lu, O. Gühne, A. Cabello, C.-Y. Lu, T. Yang, Z.-B. Chen, and J.-W. Pan*Bell inequality tests of four-photon six-qubit graph states *

Phys. Rev. A *82*,
042334
(2010),
arXiv:0906.3390

O. Gittsovich, P. Hyllus, and O. Gühne*Multiparticle covariance matrices and the impossibility of detecting graph state entanglement with two-particle correlations*

Phys. Rev. A *82*,
032306
(2010),
arXiv:1006.1594

S. Niekamp, M. Kleinmann, and O. Gühne*Discrimination strategies for inequivalent classes of multipartite entangled states*

Phys. Rev. A *82*,
022322
(2010),
arXiv:1006.1313

P. Hyllus, O. Gühne, and A. Smerzi*Not all pure entangled states are useful for sub shot-noise interferometry*

Phys. Rev. A *82*,
012337
(2010),
arXiv:0912.4349

T. Moroder, O. Gühne, N.J. Beaudry, M.Piani, and N. Lütkenhaus*Entanglement verification with realistic measurement devices via squashing operations*

Phys. Rev. A *81*,
052342
(2010),
arXiv:0909.4212

O. Gittsovich and O. Gühne*Quantifying entanglement with covariance matrices*

Phys. Rev. A *81*,
032333
(2010),
arXiv:0912.3018

O. Gühne and M. Seevinck*Separability criteria for genuine multiparticle entanglement*

New J. Phys. *12*,
053002
(2010),
arXiv:0905.1349

O. Gühne, M. Kleinmann, A. Cabello, J.-A. Larsson, G. Kirchmair, F. Zähringer, R. Gerritsma, and C.F. Roos*Compatibility and noncontextuality for sequential measurements*

Phys. Rev. A *81*,
022121
(2010),
arXiv:0912.4846

W.-B. Gao, C.-Y Lu, X.-C. Yao, P. Xu, O. Gühne, A. Goebel, Y.-A. Chen, C.-Z. Peng, Z.-B. Chen, and J.-W. Pan*Experimental demonstration of a hyper-entangled ten-qubit "Schrödinger cat" state*

Nature Physics *6*,
331
(2010),
arXiv:0809.4277

G. Tóth and O. Gühne*Separability criteria and entanglement witnesses for symmetric quantum states*

Applied Phys. B *98*,
617
(2010),
arXiv:0908.3679

W.-B. Gao, P. Xu, X.-C. Yao, O. Gühne, A. Cabello, C.-Y. Lu, C.-Z. Peng, Z.-B. Chen, and J.-W. Pan*Experimental Realization of a controlled-NOT gate with four-photon six-qubit cluster states*

Phys. Rev. Lett. *104*,
020501
(2010),
arXiv:0905.2103

M. Kleinmann, H. Kampermann, D. Bruß*Unambiguous discrimination of mixed quantum states: Optimal solution and case study*

Phys. Rev. A *81*,
020304(R)
(2010),
arXiv:0807.3923

M. Kleinmann, H. Kampermann, D. Bruß*Structural approach to unambiguous discrimination of two mixed states*

J. Math. Phys. *51*,
032201
(2010),
arXiv:0803.1083

Mazhar Ali*Quantum Discord for a two parameter class of states in 2 x d quantum systems*

J. Phys. A: Math. Theor. *43*,
495303
(2010),
arXiv:1008.4013

Mazhar Ali, A. R. P. Rau, and G. Alber*Quantum Discord for two-qubit X-states*

Phys. Rev. A *81*,
042105
(2010),
arXiv:1002.3429

Mazhar Ali*Distillability sudden death for qutrit-qutrit systems under global and multi-local dephasing*

Phys. Rev. A *81*,
042303
(2010),
arXiv:0911.0767

Mazhar Ali*Distillability sudden death in qutrit-qutrit systems under amplitude damping*

J. Phys. B: At. Mol. Opt. Phys. *43*,
045504
(2010),
arXiv:0912.2868

## 2009

R. Hübener, M. Kleinmann, T.-C. Wei, C. González-Guillén and O. Gühne*Geometric measure of entanglement for symmetric states*

Phys. Rev. A *80*,
032324
(2009),
arXiv:0905.4822

G. Kirchmair, F. Zähringer, R. Gerritsma, M. Kleinmann, O. Gühne, A. Cabello, R. Blatt, and C. F. Roos*State-independent experimental test of quantum contextuality*

Nature *460*,
494
(2009),
arXiv:0904.1655

F. Bodoky, O. Gühne, and M. Blaauboer*Modeling the decay of entanglement for electron spin qubits in quantum dots*

J. Phys.: Condens. Matter *21*,
395602
(2009),
arXiv:0809.3561

G. Tóth and O. Gühne*Entanglement and permutational symmetry*

Phys. Rev. Lett. * 102*,
170503
(2009),
arXiv:0812.4453

O. Gühne and G. Tóth*Entanglement detection*

Physics Reports *474*,
1
(2009),
arXiv:0811.2803

G. Tóth, C. Knapp, O. Gühne, and H.J. Briegel*Generalized spin squeezing criteria: Entanglement detection with collective measurements*

AIP Conf. Proc. *1110*,
41
(2009)

O. Gittsovich, O. Gühne, P. Hyllus, and J. Eisert*Covariance matrix criterion for separability*

AIP Conf. Proc. *1110*,
63
(2009)

G. Tóth, C. Knapp, O. Gühne, and H.J. Briegel*Spin squeezing and entanglement*

Phys. Rev. A *79*,
042334
(2009),
arXiv:0806.1048

C.-Y. Lu, W.-B. Gao, O. Gühne, X.-Q. Zhou, Z.-B. Chen, and J.-W. Pan*Demonstrating anyonic fractional statistics with a six-qubit quantum simulator*

Phys. Rev. Lett. * 102*,
030502
(2009),
arXiv:0710.0278

S. Niekamp, T. Wirth, and H. Frahm*The XXZ model with anti-periodic twisted boundary conditions*

J. Phys. A: Math. Theor. *42*,
195008
(2009),
arXiv:0902.1079

Mazhar Ali, G. Alber, and A. R. P. Rau*Manipulating entanglement sudden death of two-qubit X-states in zero- and finite-temperature reservoirs*

J. Phys. B: At. Mol. Opt. Phys. *42*,
025501
(2009),
arXiv:0810.2936

## 2008

O. Gühne, F. Bodoky, and M. Blaauboer*Multiparticle entanglement under the influence of decoherence*

Phys. Rev. A *78*,
060301(R)
(2008),
arXiv:0805.2873

O. Gittsovich, O. Gühne, P. Hyllus, and J. Eisert*Unifying several separability conditions using the covariance matrix criterion*

Phys. Rev. A *78*,
052319
(2008),
arXiv:0803.0757

T. Moroder, O. Gühne, and N. Lütkenhaus*Iterations of nonlinear entanglement witnesses*

Phys. Rev. A *78*,
032306
(2008),
arXiv:0806.0855

W. Wieczorek, C. Schmidt, N. Kiesel, R. Pohlner, O. Gühne, and H. Weinfurter*Experimental observation of an entire family of four-photon entangled states*

Phys. Rev. Lett. *101*,
010503
(2008),
arXiv:0806.1882

J. Richert and O. Gühne*Low energy properties of even-legged d-dimensional quantum spin systems: a variational approach*

Phys. Status Solidi B *245*,
1552
(2008)

A. Cabello, O. Gühne, and D. Rodriguez* Mermin inequalities for perfect correlations*

Phys. Rev. A *77*,
062106
(2008),
arXiv:0708.3208

O. Gühne, M. Reimpell, and R.F. Werner*Lower bounds on entanglement measures from incomplete information*

Phys. Rev. A. *77*,
052317
(2008),
arXiv:0802.1734

A. Cabello, O. Gühne, P. Moreno and D. Rodriguez*Nonlocality for graph states*

Laser Phys. *18*,
335
(2008)

O. Gühne and A. Cabello*Generalized Ardehali-Bell inequalities for graph states*

Phys. Rev. A *77*,
032108
(2008),
arXiv:0806.2769

A. R. P. Rau, Mazhar Ali, and G. Alber*Hastening, delaying, or averting sudden death of quantum entanglement*

Eur. Phys. Lett. *82*,
40002
(2008),
arXiv:0711.0317

## 2007

G. Tóth, C. Knapp, O. Gühne and H.J. Briegel*Optimal spin squeezing inequalities detect bound entanglement in spin models*

Phys. Rev. Lett. *99*,
250405
(2007),
arXiv:quant-ph/0702219

O. Gühne, C.-Y. Lu, W.-B. Gao, and J.-W. Pan*Toolbox for entanglement detection and fidelity estimation*

Phys. Rev. A *76*,
030305(R)
(2007),
arXiv:0706.2432

O. Gühne, P. Hyllus, O. Gittsovich, and J. Eisert*Covariance matrices and the separability problem*

Phys. Rev. Lett. *99*,
130504
(2007),
arXiv:quant-ph/0611282

T. Konrad, O. Gühne, J. Audretsch and H.J. Briegel*Parameter estimation for mixed states from a single copy*

Phys. Rev. A *75*,
062101
(2007),
arXiv:quant-ph/0702211

O. Gühne and N. Lütkenhaus* Nonlinear entanglement witnesses, covariance matrices and the geometry of separable states*

J. Phys.: Conf. Ser. *67*,
012004
(2007),
arXiv:quant-ph/0612108

O. Gühne and H. Häffner*Tomografie eines Quantenzustands: Verschränkung und Reinheit*

Elektrotechnik und Informationstechnik *124*,
131
(2007)

O. Gühne, M. Reimpell, and R.F. Werner*Estimating entanglement measures in experiments*

Phys. Rev. Lett. *98*,
110502
(2007),
arXiv:quant-ph/0607163

C.-Y. Lu, X.-Q. Zhou, O. Gühne, W.-B. Gao, J. Zhang, Z.-S. Yuan, A. Goebel, T. Yang and J.-W. Pan*Experimental entanglement of six photons in graph states*

Nature Physics *3*,
91
(2007),
arXiv:quant-ph/0609130

M. Kleinmann, H. Kampermann, Ph. Raynal, D. Bruß*Commutator Relations Reveal Solvable Structures in Unambiguous State Discrimination*

J. Phys. A: Math. Theor. *40*,
F871
(2007),
arXiv:0705.3391

P. Skwara, H. Kampermann, M. Kleinmann, D. Bruß*Entanglement witnesses and a loophole problem*

Phys. Rev. A *76*,
012312
(2007),
arXiv:quant-ph/0608058

M. Kleinmann, H. Kampermann, T. Meyer, D. Bruß*Purifying and Reversible Physical Processes*

Appl. Phys. B *86*,
371
(2007),
arXiv:quant-ph/0608053

K. S. Ranade and Mazhar Ali*The Jamiolkowski Isomorphism and a Simplified Proof for the Correspondence Between Vectors Having Schmidt Number k and k-Positive Maps*

Open. Sys. Information Dyn. *14*,
371
(2007),
arXiv:0702255

Mazhar Ali, A. R. P. Rau, and K. Ranade*Disentanglement in qubit-qutrit systems*

arXiv (2007),
url,
arXiv:0710.2238

## 2006

J. K. Korbicz, O. Gühne, M. Lewenstein, H. Häffner, C.F. Roos and R. Blatt*Generalized spin squeezing inequalities in N qubit systems: theory and experiment*

Phys. Rev. A *74*,
052319
(2006),
arXiv:quant-ph/0601038

O. Gühne, M. Mechler, G. Tóth, and P. Adam*Entanglement criteria based on local uncertainty relations are strictly stronger than the computable cross norm criterion*

Phys. Rev. A *74*,
010301(R)
(2006),
arXiv:quant-ph/0604050

O. Gühne and G. Tóth*Energy and multipartite entanglement in multidimensional and frustrated spin models*

Phys. Rev. A *73*,
052319
(2006),
arXiv:quant-ph/0510186

O. Gühne and N. Lütkenhaus*Nonlinear entanglement witnesses*

Phys. Rev. Lett. *96*,
170502
(2006),
arXiv:quant-ph/0512164

G. Tóth, O. Gühne, and H.J. Briegel*Two-setting Bell inequalities for graph states*

Phys. Rev. A *73*,
022303
(2006),
arXiv:quant-ph/0510007

J. Rigas, O. Gühne, and N. Lütkenhaus*Entanglement verification for quantum key distribution systems with an underlying bipartite qubit-mode structure*

Phys. Rev. A *73*,
012341
(2006),
arXiv:quant-ph/0510022

G. Tóth and O. Gühne*Detection of multipartite entanglement with two-body correlations*

Applied Phys. B *82*,
237
(2006),
arXiv:quant-ph/0602068

T. Meyer, H. Kampermann, M. Kleinmann, D. Bruß *Finite key analysis for symmetric attacks in quantum key distribution*

Phys. Rev. A *74*,
042340
(2006),
arXiv:quant-ph/0607141

M. Kleinmann, H. Kampermann, T. Meyer, D. Bruß*Physical Purification of Quantum States*

Phys. Rev. A *73*,
062309
(2006),
arXiv:quant-ph/0509100

## 2005

H. Häffner, W. Hänsel, C. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Körber, U. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Gühne, W. Dür, and R. Blatt*Scalable multiparticle entanglement of trapped ions*

Nature *438*,
643
(2005),
arXiv:quant-ph/0603217

N. Kiesel, C. Schmid, U. Weber, G. Tóth, O. Gühne, R. Ursin, and H. Weinfurter*Experimental analysis of a four-qubit photon cluster state*

Phys. Rev. Lett. *95*,
201502
(2005),
arXiv:quant-ph/0508128

G. Tóth, O. Gühne, M. Seevinck, and J. Uffink*Addendum to "Sufficient conditions for three-particle entanglement and their tests in recent experiments"*

Phys. Rev. A *72*,
014101
(2005),
arXiv:quant-ph/0505100

P. Hyllus, O. Gühne, D. Bruß, and M. Lewenstein*Relations between entanglement witnesses and Bell inequalities*

Phys. Rev. A *72*,
012321
(2005),
arXiv:quant-ph/0504079

O. Gühne, G. Tóth, and H.J. Briegel*Multipartite entanglement in spin chains*

New J. Phys. *7*,
229
(2005),
arXiv:quant-ph/0502160

G. Tóth and O. Gühne*Entanglement detection in the stabilizer formalism*

Phys. Rev. A *72*,
022340
(2005),
arXiv:quant-ph/0501020

O. Gühne, G. Tóth, P. Hyllus and H.J. Briegel*Bell inequalities for graph states*

Phys. Rev. Lett. *95*,
120405
(2005),
arXiv:quant-ph/0410059

M. Curty, O. Gühne, M. Lewenstein and N. Lütkenhaus*Detecting quantum correlations for quantum key distribution*

Proc. SPIE *5631*,
9
(2005)

M. Curty, O. Gühne, M. Lewenstein and N. Lütkenhaus*Detecting two-party quantum correlations in quantum key distribution protocols*

Phys. Rev. A *71*,
022306
(2005),
arXiv:quant-ph/0409047

G. Tóth and O. Gühne*Detecting genuine multipartite entanglement with two local measurements*

Phys. Rev. Lett. *94*,
060501
(2005),
arXiv:quant-ph/0405165

M. Kleinmann, H. Kampermann, D. Bruß*Generalization of quantum state comparison*

Phys. Rev. A *72*,
032308
(2005),
arXiv:quant-ph/0503012

## 2004

J. Eisert, P. Hyllus, O. Gühne and M. Curty*Complete hierarchies of efficient approximations to problems in entanglement theory*

Phys. Rev. A *70*,
062317
(2004),
arXiv:quant-ph/0407135

O. Gühne and M. Lewenstein*Entropic uncertainty relations and entanglement*

Phys. Rev. A *70*,
022316
(2004),
arXiv:quant-ph/0403219

O. Gühne and M. Lewenstein*Separability criteria from uncertainty relations*

AIP Conf. Proc. *734*,
230
(2004),
arXiv:quant-ph/0409140

G. Tóth and O. Gühne*Two measurement settings can suffice to verify multipartite entanglement*

AIP Conf. Proc. *734*,
234
(2004),
arXiv:quant-ph/0409132

M. Curty, O. Gühne, M. Lewenstein and N. Lütkenhaus*Quantum correlations for quantum key distribution protocols*

AIP Conf. Proc. *734*,
307
(2004)

M. Bourennane, M. Eibl, S. Gaertner, C. Kurtsiefer, H. Weinfurter, A. Cabello, O. Gühne, P. Hyllus, D.Bruß, M. Lewenstein, and A. Sanpera*Four photon polarization entanglement: tests and applications*

Int. J. Quant. Inf. *2*,
133
(2004)

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera*Experimental detection of multipartite entanglement using witness operators*

Phys. Rev. Lett. *92*,
087902
(2004),
arXiv:quant-ph/0309043

O. Gühne*Characterizing entanglement via uncertainty relations*

Phys. Rev. Lett. *92*,
117903
(2004),
arXiv:quant-ph/0306194

## 2003

O. Gühne and P. Hyllus*Investigating three qubit entanglement with local measurements*

Int. J. Theor. Phys. *42*,
1001
(2003),
arXiv:quant-ph/0301162

O. Gühne, P. Hyllus, D. Bruß, A. Ekert, M. Lewenstein, C. Macchiavello, and A. Sanpera*Experimental detection of entanglement via witness operators and local measurements*

J. Mod. Opt. *50*,
1079
(2003),
arXiv:quant-ph/0210134

## 2002

O. Gühne, P. Hyllus, D. Bruß, A. Ekert, M. Lewenstein, C. Macchiavello, and A. Sanpera*Detection of entanglement with few local measurements*

Phys. Rev. A *66*,
062305
(2002),
arXiv:quant-ph/0205089