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All Publications

Preprints

Timo Simnacher, Nikolai Wyderka, Cornelia Spee, Xiao-Dong Yu and Otfried Gühne
Certifying quantum memories with coherence
arXiv:1809.03403

Quantum memories are an important building block for quantum information processing. We present a general method to characterize and test these devices based on their ability to preserve coherence. We introduce a quality measure for quantum memories and characterize it 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 or teleportation schemes.

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

Xiao-Dong Yu and Otfried Gühne
Detecting Coherence via Spectrum Estimation
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.

Andreas Ketterer, Nikolai Wyderka and Otfried Gühne
Characterizing multipartite entanglement with moments of random correlations
arXiv:1808.06558

The trustworthy detection of multipartite entanglement usually requires a number of judiciously chosen local quantum measurements which are aligned with respect to a previously shared common reference frame. If such a reference frame is not available, one has to develop alternative detection strategies which do not rely on a specific choice of the local measurement bases. One possibility in this direction 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 characterization of multipartite entanglement is possible by combining statistical moments of different order. To do so, we make use of unitary designs which link entanglement criteria that are based on moments to 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.

Mariami Gachechiladze, Otfried Gühne and Akimasa Miyake
Changing the circuit-depth complexity of measurement-based quantum computation with hypergraph states
arXiv:1805.12093

The circuit model of quantum computation defines its logical depth or "computational time" in terms of temporal gate sequences, but the measurement-based model could allow totally different time ordering and parallelization of logical gates. We introduce a deterministic scheme of universal measurement-based computation, using only Pauli measurements on multi-qubit hypergraph states generated by the Controlled-Controlled-Z (CCZ) gates. 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. An exponentially-short depth implementation of an N-times Controlled-Z gate illustrates a novel trade-off between space and time complexity.

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

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

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
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
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
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
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 to detect weakly steerable states.

Joshua Lockhart, Otfried Gühne and Simone Severini
Entanglement properties of quantum grid states
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
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 discuss in detail all possible marginal configurations up to six particles and decide which configurations are sufficient. We then present a method to construct states with the same properties for larger systems.

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.

S. Wölk
Revealing quantum properties with simple measurements
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.

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

F. E. S. Steinhoff and M. C. de Oliveira
Violations of complementarity enable beyond-quantum nonlocality, distinguishability and cloning
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.

Publications

2018

O. Gühne
Ist der Zufall in der Quantenmechanik real?
K. Kleinknecht (Ed.), Quanten 6 (Schriften der Heisenberg-Gesellschaft), Hirzel-Verlag , p. 84 (2018)

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)].

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

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, 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