# Prof. Dr. Otfried Gühne

ProfessorRoom: B-109

Phone: +49 271 740 3707

## Lectures

see the teaching page

## Preprints

See also arxiv

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

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.

I. Apellaniz, M. Kleinmann, O. Gühne, G. Toth*Optimal detection of metrologically useful entanglement*

arXiv:
1511.05203

We show how to verify the metrological usefulness of quantum states based on few measurements. In particular, we estimate the quantum Fisher information as a figure of merit of metrological usefulness. Our approach is optimal since it gives a tight lower bound on the quantum Fisher information for the given incomplete information. We apply our method to the results of various multi-particle quantum states prepared in experiments with photons and trapped ions, as well as to spin-squeezed states and Dicke states realized in cold gases.

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

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 world. Type-II interpretations see quantum probabilities as not directly dealing with intrinsic properties of the world but with relational experiences between an observer and the world. It is usually believed that deciding between these two types cannot be made simply on purely physical grounds but it requires an act of metaphysical judgement. Here we show that, although the problem is undecidable within the framework of quantum theory, it is decidable, under some assumptions, within the framework of thermodynamics. We prove that type-I interpretations are incompatible with the following assumptions: (i) the decision of which measurement is performed on a quantum system can be made independently of the system, (ii) a quantum system has limited memory, and (iii) Landauer's principle is valid. We consider an ideal experiment in which an individual quantum system is submitted to a sequence of quantum projective measurements that leave the system in pure quantum states. We show that in any type-I interpretation satisfying (i)-(iii) the system must reset its internal state, which implies that a minimum amount of heat per measurement has to be dissipated into the system's environment. We calculate a lower bound to the heat dissipated per measurement assuming that the measurements are chosen from a set of size 2^n. Then, we show that this lower bound becomes infinite in the limit of n tending to infinity. This leads to the conclusion that either type-I interpretations are untenable or at least one of the assumptions (i)-(iii) has to be abandoned.

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

arXiv:1507.07226

We introduce the concept of entanglement width as measure of the spatial distribution of entanglement in multiparticle systems. We develop criteria to detect the width of entanglement using global observables such as energy and magnetic susceptibility. Therefore, the introduced entanglement criteria can be applied to systems where addressing of single particles is not possible. We apply the criteria to different examples such as the J1-J2- Heisenberg model and point out the difference between entanglement depth and entanglement width.

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

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 multiparticle density matrices.

## Publications

### 2016

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. 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.

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.

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.

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.

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

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

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

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.

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.

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.

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.

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.

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.

### 2012

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.

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.

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.

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

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

### 2011

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.

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.

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

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

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

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

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

### 2010

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

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

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

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

### 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

### 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

See also: M. Aspelmeyer and J. Eisert*Entangled families*

Nature (News and Views) *455*,
180
(2008)

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

### 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

### 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

### 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

### 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

## Book contributions

### 2005

M. Curty, O. Gühne, M. Lewenstein und N. Lütkenhaus*Quantum correlations as basic resource for quantum key distribution*

In: G. Leuchs, T. Beth (Eds.): "Quantum information processing" (second edition), Wiley-VCH (Berlin) (2005)

url

C. Becher, J. Benhelm, D. Chek-al-kar, M. Chwalla, W. Dür, O. Gühne, H. Häffner, W. Hänsel, T. Körber, A. Kreuter, G.P.T. Lancaster, T. Monz, E.S. Phillips, U.D. Rapol, M. Riebe, C.F. Roos, C. Russo, F. Schmidt-Kaler, and R. Blatt*Entanglement of trapped ions*

In: E.A. Hinds, A. Ferguson, E. Riis (Eds.) Laser Spectroscopy, p. 381-392, World Scientific (Singapore) (2005)

url

### 2003

K. Eckert, O. Gühne, F. Hulpke, P. Hyllus, J. Korbicz, J. Mompart, D. Bruß, M. Lewenstein, and A. Sanpera*Entanglement properties of composite quantum systems*

In: G. Leuchs, T. Beth (Eds.): "Quantum information processing", Wiley-VCH (Berlin) (2003)

arXiv:quant-ph/0210107