- O. Gühne, M. Seevinck, Separability criteria for genuine multiparticle entanglement, New Journal of Physics 12, 053002, (2010), URL doi: 10.1088/1367-2630/12/5/053002 (ID: 680400) Toggle Abstract
We present a method to derive separability criteria for the different classes of multiparticle entanglement, especially genuine multiparticle entanglement. The resulting criteria are necessary and sufficient for certain families of states. Further, the criteria are superior to all known entanglement criteria for many other families; also they allow the detection of bound entanglement. We next demonstrate that they are easily implementable in experiments and discuss applications to the decoherence of multiparticle entangled states.
- W. Gao, P. Xu, X. Yao, O. Gühne, A. Cabello, C. Lu, C. Peng, T. Yang, Z. Chen, J. Pan, Experimental Realization of a Controlled-NOT Gate with Four-Photon Six-Qubit Cluster States, Phys. Rev. Lett. 104, 020501, (2010-01-15), URL doi:10.1103/PhysRevLett.104.020501 (ID: 681065) Toggle Abstract
We experimentally demonstrate an optical controlled-NOT (CNOT) gate with arbitrary single inputs based on a 4-photon 6-qubit cluster state entangled both in polarization and spatial modes. We first generate the 6-qubit state, and then by performing single-qubit measurements the CNOT gate is applied to arbitrary single input qubits. To characterize the performance of the gate, we estimate its quantum process fidelity and prove its entangling capability. The results show that the gate cannot be reproduced by local operations and classical communication. Our experiment shows that cluster states are promising candidates for efficient optical quantum computation.
- O. Gittsovich, O. Gühne, Quantifying entanglement with covariance matrices, Phys. Rev. A 81, 032333, (2010), URL doi:10.1103/PhysRevA.81.032333 (ID: 716972) Toggle Abstract
Covariance matrices are a useful tool to investigate correlations and entanglement in quantum systems. They are widely used in continuous variable systems, but recently also for finite dimensional systems powerful entanglement criteria in terms of covariance matrices have been derived. We show how these results can be used for the quantification of entanglement in bipartite systems. To that aim we introduce an entanglement parameter that quantifies the violation of the covariance matrix criterion and can be used to give a lower bounds on the concurrence. These lower bounds are easily computable and give entanglement estimates for many weakly entangled states.
- W. Gao, C. Lu, X. Yao, P. Xue, O. Gühne, A. Goebel, Y. Chen, C. Peng, Z. Chen, J. Pan, Experimental demonstration of a hyper-entangled ten-qubit 'Schrödinger cat' state, Nature Physics 6, 331, (2010-05-01), URL doi:10.1038/nphys1603 (ID: 632645) Toggle Abstract
Coherent manipulation of a large number of qubits and the generation of entangled states between them has been an important goal and benchmark in quantum information science, leading to various applications such as measurement-based quantum computing and high-precision quantum metrology. However, the experimental preparation of multiparticle entanglement remains challenging. Using atoms, entangled states of up to eight qubits have been created, and up to six photons have been entangled. Here, by exploiting both the photons’ polarization and momentum degrees of freedom, we experimentally generate hyper-entangled six-, eight- and ten-qubit Schrödinger cat states with verified genuine multi-qubit entanglement. We also demonstrate super-resolving phase measurements enhanced by entanglement, with a precision to beat the standard quantum limit. Modifications of the experimental set-up would enable the generation of other graph states up to ten qubits. Our method offers a way of expanding the effective Hilbert space and should provide a versatile test-bed for various quantum applications.
- S. Niekamp, M. Kleinmann, O. Gühne, Discrimination strategies for inequivalent classes of multipartite entangled states, Phys. Lett. A 82, 022322, (2010-06-08), URL doi:10.1103/PhysRevA.82.022322 (ID: 717237) Toggle Abstract
How can one discriminate different inequivalent classes of multiparticle entanglement experimentally? We present an approach for the discrimination of an experimentally prepared state from the equivalence class of another state. We consider two possible measures for the discrimination strength of an observable. The first measure is based on the difference of expectation values, the second on the relative entropy of the probability distributions of the measurement outcomes. The interpretation of these measures and their usefulness for experiments with limited resources are discussed. In the case of graph states, the stabilizer formalism is employed to compute these quantities and to find sets of observables that result in the most decisive discrimination.
- O. Gühne, M. Kleinmann, A. Cabello, J. Larson, G. Kirchmair, F. Zähringer, R. Gerritsma, C. F. Roos, Compatibility and noncontextuality for sequential measurements, Phys. Rev. A 81, 022121, (2010-02-26), doi:10.1103/PhysRevA.81.022121 (ID: 717143)
- B. Jungnitsch, S. Niekamp, M. Kleinmann, O. Gühne, H. Lu (Hefei), W. Gao, Y. Chen, Z. Chen, J. Pan, Increasing the statistical significance of entanglement detection in experiments, Phys. Rev. Lett. 104, 210401, (2010), doi:10.1103/PhysRevLett.104.210401 (ID: 716975) Toggle Abstract
Entanglement is often verified by a violation of an inequality like a Bell inequality or an entanglement witness. Considerable effort has been devoted to the optimization of such inequalities in order to obtain a high violation. We demonstrate theoretically and experimentally that such an optimization does not necessarily lead to a better entanglement test, if the statistical error is taken into account. Theoretically, we show for different error models that reducing the violation of an inequality can improve the significance. Experimentally, we observe this phenomenon in a four-photon experiment, testing the Mermin and Ardehali inequality for different levels of noise. Furthermore, we provide a way to develop entanglement tests with high statistical significance.
- G. Toth, O. Gühne, Separability criteria and entanglement witnesses for symmetric quantum states, Appl. Phys. B 98, 617, (2010), URL doi:10.1007/s00340-009-3839-7 (ID: 707006) Toggle Abstract
We study the separability of symmetric bipartite quantum states and show that a single correlation measurement is sufficient to detect the entanglement of any bipartite symmetric state with a non-positive partial transpose. We also discuss entanglement conditions and entanglement witnesses for states with a positive partial transpose.
- T. Moroder, O. Gühne, N. J. Beaudry, M. Piani, N. Lütkenhaus, Entanglement verification with realistic measurement devices via squashing operations, Phys. Rev. A 81, 052342, (2010), URL doi:10.1103/PhysRevA.81.052342 (ID: 712574) Toggle Abstract
Many protocols and experiments in quantum information science are described in terms of simple measurements on qubits. However in a real implementation the exact description is more difficult and more complicated observables are used. The question arises whether a claim of entanglement in the simplified description still holds, if the difference between the realistic and simplified models is taken into account. We show that a positive entanglement statement remains valid if a certain positive linear map connecting the two descriptions—a so-called squashing operation—exists; then lower bounds on the amount of entanglement are also possible. We apply our results to polarization measurements of photons using only threshold detectors, and derive procedures under which multiphoton events can be neglected.
- P. Hyllus, O. Gühne, A. Smerzi, Not all pure entangled states are useful for sub shot-noise interferometry, Phys. Rev. A 82, 012337, (2010-07-31), URL doi:10.1103/PhysRevA.82.012337 (ID: 716973) Toggle Abstract
We investigate the connection between the shot-noise limit in linear interferometers and particle entanglement. In particular, we ask whether or not sub shot-noise sensitivity can be reached with all pure entangled input states of $N$ particles if they can be optimized with local operations. Results on the optimal local transformations allow us to show that for $N=2$ all pure entangled states can be made useful for sub shot-noise interferometry while for $N>2$ this is not the case. We completely classify the useful entangled states available in a bosonic two-mode interferometer. We apply our results to several states, in particular to multi-particle singlet states and to cluster states. The latter turn out to be practically useless for sub shot-noise interferometry. Our results are based on the Cramer-Rao bound and the Fisher information.
- J. T. Barreiro, P. Schindler, O. Gühne, T. Monz, M. Chwalla, C. F. Roos, M. Hennrich, R. Blatt, Experimental multiparticle entanglement dynamics induced by decoherence, (2010), URL oai:arxiv.org:1005.1965v1 (ID: 717216) Toggle Abstract
Multiparticle entanglement leads to richer correlations than two-particle entanglement and gives rise to striking contradictions with local realism, inequivalent classes of entanglement, and applications such as one-way or topological quantum computing. When exposed to decohering or dissipative environments, multiparticle entanglement yields subtle dynamical features and access to new classes of states and applications. Here, using a string of trapped ions, we experimentally characterize the dynamics of entanglement of a multiparticle state under the influence of decoherence. By embedding an entangled state of four qubits in a decohering environment (via spontaneous decay), we observe a rich dynamics crossing distinctive domains: Bell-inequality violation, entanglement superactivation, bound entanglement, and full separability. We also develop new theoretical tools for characterizing entanglement in quantum states. Our techniques to control the environment can be used to enable novel quantum-computation, state-engineering, and simulation paradigms based on dissipation and decoherence
- O. Gittsovich, P. Hyllus, O. Gühne, Multiparticle covariance matrices and the impossibility of detecting graph state entanglement with two-particle correlations, (2010-06-09), URL oai:arXiv.org:1006.1594 (ID: 717238) Toggle Abstract
We present a criterion for multiparticle entanglement based on covariance matrices. On the one hand, the criterion allows to detect bound entangled states which are not detected by other criteria; on the other hand, some strongly entangled pure states such as the GHZ states are not detected. We show, however, that this is a general phenomenon: No separability criterion based on two-particle correlations can recognize the entanglement in the family of graph states, to which the GHZ states belong.
- M. Kleinmann, O. Gühne, J. R. Portillo, J. Larsson, A. Cabello, Memory cost of quantum contextuality, (2010-07-28), URL oai:arxiv.org:1007.3650 (ID: 717280) Toggle Abstract
The simulation of quantum effects requires certain classical resources, and quantifying them is an important step in order to understand the difference between quantum and classical physics. We investigate the minimum classical memory needed to simulate the phenomenon of state-independent quantum contextuality in sequential measurements. We derive optimal simulation strategies for several important cases and prove that two bits of classical memory do not suffice to reproduce the results of sequential measurements on a two-qubit system.
- G. Toth, O. Gühne, Entanglement and permutational symmetry, Phys. Rev. Lett. 102, 170503, (2009), URL oai:arXiv.org:0812.4453 (ID: 646578) Toggle Abstract
We study the separability of permutationally symmetric quantum states. We show that for bipartite symmetric systems most of the relevant entanglement criteria coincide. However, we provide a method to generate examples of bound entangled states in symmetric systems, for the bipartite and the multipartite case. These states shed some new light on the nature of bound entanglement.
- R. Hübener, M. Kleinmann, T. Wei, C. Gonzalés-Guillén, O. Gühne, Geometric measure of entanglement for symmetric states, Phys. Rev. A 80, 032324, (2009), URL doi:10.1103/PhysRevA.80.032324 (ID: 682424) Toggle Abstract
Is the closest product state to a symmetric entangled multiparticle state also symmetric? This question has appeared in the recent literature concerning the geometric measure of entanglement. First, we show that a positive answer can be derived from results concerning symmetric multilinear forms and homogeneous polynomials, implying that the closest product state can be chosen to be symmetric. We then prove the stronger result that the closest product state to any symmetric multiparticle quantum state is necessarily symmetric. Moreover, we discuss generalizations of our result and the case of translationally invariant states, which can occur in spin models.
- G. Toth, C. Knapp, O. Gühne, H. J. Briegel, Spin squeezing and entanglement, Phys. Rev. A 79, 042334, (2009), URL doi:10.1103/PhysRevA.79.042334 (ID: 596901) Toggle Abstract
What is the relation between spin squeezing and entanglement? To clarify this, we derive the full set of generalized spin squeezing inequalities for the detection of entanglement. These are inequalities for the mean values and variances of the collective angular momentum components J_k. They can be used for the experimental detection of entanglement in a system of spin-1/2 particles in which the spins cannot be individually addressed. We present various sets of inequalities that can detect all entangled states that can be detected based on the knowledge of: (i) the mean values and variances of J_k in three orthogonal directions, or (ii) the variances of J_k in three orthogonal directions, or (iii) the mean values of J_k^2 in three orthogonal directions or (iv) the mean values and variances of J_k in arbitrary directions. We compare our inequalities to known spin squeezing entanglement criteria and discuss to which extent spin squeezing is related to entanglement in the reduced two-qubit states. Finally, we apply our criteria for entanglement detection in spin models, showing that they can be used to detect bound entanglement in these systems.
- F. Bodoky, O. Gühne, M. Blaauboer, Modeling the decay of entanglement for electron spin qubits in quantum dots, J. Phys.: Condens. Matter 21, 395602, (2009), URL doi:10.1088/0953-8984/21/39/395602 (ID: 632646) Toggle Abstract
We investigate the time evolution of entanglement under various models of decoherence: a general heuristic model based on local relaxation and dephasing times, and two microscopic models describing decoherence of electron spin qubits in quantum dots due to the hyperfine interaction with the nuclei. For each of the decoherence models, we investigate and compare how long the entanglement can be detected. We also introduce filtered witness operators, which extend the available detection time and investigate this detection time for various multipartite entangled states. By comparing the time required for detection with the time required for generation and manipulation of entanglement, we estimate for a range of different entangled states how many qubits can be entangled in a one-dimensional array of electron spin qubits.
- O. Gühne, G. Toth, Entanglement detection, Physics Reports 474, 1, (2009), URL doi:10.1016/j.physrep.2009.02.004 (ID: 632647) Toggle Abstract
How can one prove that a given quantum state is entangled? In this paper we review different methods that have been proposed for entanglement detection. We first explain the basic elements of entanglement theory for two or more particles and then entanglement verification procedures such as Bell inequalities, entanglement witnesses, the determination of nonlinear properties of a quantum state via measurements on several copies, and spin squeezing inequalities. An emphasis is given on the theory and application of entanglement witnesses. We also discuss several experiments, where some of the presented methods have been implemented.
- C. Lu, W. Gao, O. Gühne, X. Zhou, Z. Chen, J. Pan, Demonstrating Anyonic Fractional Statistics with a Six-Qubit Quantum Simulator, Phys. Rev. Lett. 102, 030502, (2009), doi:10.1103/PhysRevLett.102.030502 (ID: 527865) Toggle Abstract
Anyons are exotic quasiparticles living in two dimensions that do not fit into the usual categories of fermions and bosons, but obey a new form of fractional statistics. Following a recent proposal [Phys. Rev. Lett. 98, 150404 (2007)], we present an experimental demonstration of the fractional statistics of anyons in the Kitaev spin lattice model using a photonic quantum simulator. We dynamically create the ground state and excited states (which are six-qubit graph states) of the Kitaev model Hamiltonian, and implement the anyonic braiding and fusion operations by single-qubit rotations. A phase shift of pi related to the anyon braiding is observed, confirming the prediction of the fractional statistics of Abelian 1/2 anyons.
- G. Kirchmair, F. Zähringer, R. Gerritsma, M. Kleinmann, O. Gühne, A. Cabello, R. Blatt, C. Roos, State-independent experimental test of quantum contextuality, Nature 460, 494, (2009), doi:10.1038/nature08172 (ID: 695207) Toggle Abstract
The question of whether quantum phenomena can be explained by classical models with hidden variables is the subject of a long-lasting debate. In 1964, Bell showed that certain types of classical models cannot explain the quantum mechanical predictions for specific states of distant particles, and some types of hidden variable models have been experimentally ruled out. An intuitive feature of classical models is non-contextuality: the property that any measurement has a value independent of other compatible measurements being carried out at the same time. However, a theorem derived by Kochen, Specker and Bell shows that non-contextuality is in conflict with quantum mechanics. The conflict resides in the structure of the theory and is independent of the properties of special states. It has been debated whether the Kochen–Specker theorem could be experimentally tested at all. First tests of quantum contextuality have been proposed only recently, and undertaken with photons and neutrons. But these tests required the generation of special quantum states and left various loopholes open. Here we perform an experiment with trapped ions that demonstrates a state-independent conflict with non-contextuality. The experiment is not subject to the detection loophole and we show that, despite imperfections and possible measurement disturbances, our results cannot be explained in non-contextual terms.
- O. Gühne, Multiparticle entanglement: Decoherence and separability criteria, Capital Normal University (Beijing, 2009-07-25),
(2009), (ID: 698994) Toggle Abstract
In recent years, many experiments succeeded in preparing
multiparticle entangled states. From a theoretical point
of view, however, multiparticle entanglement turns out to
be much more complicated than two-particle entanglement.
Consequently, many problems -- such as the computation of
entanglement measures or the derivation of separability
criteria -- are completely open.
In this talk, I will present two results concerning these
problems. The first topic is the decoherence of multiparticle
quantum states. Here, I will show how one can compute the
geometric measure of entanglement for certain states and
how this can be used to compare the robustness of states
under decoherence. The second topic concerns the derivation
of entanglement criteria for genuine multipartite entanglement.
Here, I will present a simple way to derive entanglement
criteria for the different classes of multipartite entanglement,
which are often stronger than all known criteria.
- O. Gühne, Experimental test of quantum contextuality, University of Manchester (Manchester, 2009-09-30),
(2009-09-30), (ID: 716749) Toggle Abstract
Many debates in the last decades concern the difference between
quantum mechanics and classical physics. In this discussion, the
Kochen-Specker theorem is a central result showing that
non-contextuality of compatible observables is in conflict with
quantum mechanics. Here, compatible observables are observables
which can be measured simultaneously or in any order, and
non-contextuality means that the value of an observable does not
depend on which other compatible observable is measured jointly
with it.
In this talk I will first give an introduction into the Kochen-Specker
theorem. Then, I will report on a recent ion-trap experiment, where
a violation of non-contextuality has been found. Remarkably, the
observation of quantum contextuality occurs for any quantum state,
hence it does not require the generation of special entangled states.
Finally, I will discuss possible loopholes in this experiment.
- O. Gühne, An experimental test of quantum contextuality, TU Delft (2009-11-03),
(2009-11-03), (ID: 716785) Toggle Abstract
Many debates in the last decades concern the difference between
quantum mechanics and classical physics. In this discussion, the
Kochen-Specker theorem is a central result showing that
non-contextuality of compatible observables is in conflict with
quantum mechanics. Here, compatible observables are observables
which can be measured simultaneously or in any order, and
non-contextuality means that the value of an observable does not
depend on which other compatible observable is measured jointly
with it.
In this talk I will first give an introduction into the Kochen-Specker
theorem. Then, I will report on a recent ion-trap experiment, where
a violation of non-contextuality has been found. Remarkably, the
observation of quantum contextuality occurs for any quantum state,
hence it does not require the generation of special entangled states.
Finally, I will discuss possible loopholes in this experiment.
- O. Gühne, Experimental test of quantum contextuality, University of Manchester (Manchester),
(2009-09-30), (ID: 716967) Toggle Abstract
Many debates in the last decades concern the difference between quantum mechanics and classical physics. In this discussion, the Kochen-Specker theorem is a central result showing that non-contextuality of compatible observables is in conflict with quantum mechanics. Here, compatible observables are observables which can be measured simultaneously or in any order, and non-contextuality means that the value of an observable does not depend on which other compatible observable is measured jointly with it. In this talk I will first give an introduction into the Kochen-Specker theorem. Then, I will report on a recent ion-trap experiment, where a violation of non-contextuality has been found. Remarkably, the observation of quantum contextuality occurs for any quantum state, hence it does not require the generation of special entangled states. Finally, I will discuss possible loopholes in this experiment.
- O. Gühne, State-independent experimental test of quantum contextuality, University of Geneva (2009-04-27),
(2009), (ID: 683408) Toggle Abstract
The question of whether quantum phenomena can be explained by classical models with hidden variables is the subject of a long lasting debate. In 1964, Bell showed that certain types of classical models cannot explain the quantum mechanical predictions for specific states of distant particles. Along this line, some types of hidden variable models have been experimentally ruled out. An intuitive feature for classical models is non-contextuality: the property that any measurement has a value which is independent of other compatible measurements being carried out at the same time. However, the results of Kochen, Specker, and Bell show that non-contextuality is in conflict with quantum mechanics. The conflict resides in the structure of the theory and is independent of the properties of special states. It has been debated whether the Kochen-Specker theorem could be experimentally tested at all. Only recently, first tests of quantum contextuality have been proposed and undertaken with photons and neutrons. Yet these tests required the generation of special quantum states and left various loopholes open. Here, using trapped ions, we experimentally demonstrate a state-independent conflict with non-contextuality. The experiment is not subject to the detection loophole and we show that, despite imperfections and possible measurement disturbances, our results cannot be explained in non-contextual terms.
- O. Gühne, Spin squeezing and entanglement, University of Trento (Trento, 2009-05-26),
(2009), (ID: 682428) Toggle Abstract
Entanglement is one of the key resources in quantum information
science and many physical systems are studied concerning their
entanglement properties. For the case of many particle systems
such as ensembles of cold atoms it was found that it is sometimes
related to spin squeezing and second moments of collective angular
momenta.
In this talk, I will clarify the relation between entanglement
and first and second moments of collective angular momenta.
To this aim, I will present a set of eight spin squeezing
inequalities which completely characterize the fully separable
states, any other spin squeezing inequality for the detection
of entanglement can be derived from these. As an example,
I will apply these inequalities to several spin models. There,
it turns out that the inequalities are able to detect multipartite
bound entanglement -- a special form of entanglement which is of
great theoretical interest -- in the thermal states of these models.
- O. Gühne, Experimental tests of quantum contextuality, International Conference on Quantum Foundations and Technology (Shanghai, 2009-07-17),
(2009), (ID: 698992) Toggle Abstract
Many debates in the last decades concern the difference
between quantum mechanics and classical physics. In this
discussion, the Kochen-Specker theorem is a central result
showing that non-contextuality of compatible observables
is in conflict with quantum mechanics. Here, compatible
observables are observables which can be measured
simultaneously or in any order, and non-contextuality
means that the value of an observable does not depend
on which other compatible observable is measured jointly
with it.
In this talk I will discuss how the Kochen-Specker theorem
can be tested experimentally. I will report on a ion-trap
experiment, where a violation of non-contextuality has been
found [1]. Remarkably, the observation of quantum
contextuality occurs for any quantum state, hence it
does not require the generation of special entangled states.
Then I will discuss how noise affects the refutation of
non-contextuality and I will introduce inequalities
that allow to rule out certain dynamics of hidden
variables.
- O. Gühne, Separability criteria for genuine multipartite entanglement, Joint ÖPG / SPS / ÖGAA Meeting (Innsbruck, 2009-09-03),
(2009), (ID: 708341) Toggle Abstract
We present a method to derive separability criteria for the different classes of multiparticle entanglement, especially genuine multiparticle entanglement. The resulting criteria are necessary and sufficient for certain families of states. Further, the criteria are superior to all known entanglement criteria for many other families; also they allow the detection of bound entanglement. We next demonstrate that they are easily implementable in experiments and discuss applications to the decoherence of multiparticle entangled states.
- O. Gühne, Geheime Botschaften aus Licht, Gymnasium Zum Altenforst (Troisdorf, 2009-11-04),
(2009-11-04), (ID: 716804)
- O. Gühne, Decoherence of multiparticle entanglement, DPG Frühjahrstagung (Hamburg, 2009-03-06),
(2009), (ID: 683410) Toggle Abstract
Decoherence of quantum states is a fundamental obstacle for imple-
mentations of quantum information processing. Therefore, it is inter-
esting to know how the entanglement of a multiparticle quantum state
is affected by decoherence and how this depends on the state and
the number of qubits. This is, however, difficult to investigate, since
most entanglement measures are practically impossible to compute for
mixed states.
In this contribution we present a method to determine the decay
of quantum correlations as quantified by the geometric measure of
entanglement under the influence of decoherence. With this, one can
compare the robustness of entanglement in GHZ, cluster, W and Dicke
states of four qubits and show that the Dicke state is most robust. Fur-
thermore, the method allows to compare different decoherence models
and to investigate the scaling of the entanglement decay for an increas-
ing number of particles.
- J. Richert, O. Gühne, Low energy properties of even-legged d -dimensional quantum spin systems: a variational approach, Physica Status Solidi B 245, 1552, (2008), doi:10.1002/pssb.200743512 (ID: 603483) Toggle Abstract
We develop a variational formalism in order to study the gap structure in the spectrum of frustrated quantum spin systems. We introduce a trial wave function of a two-leg ladder with one spin 1/2 on each site. The domains in which the wave function behaves realistically are determined. In these domains the spectra show a finite energy gap between the ground state and excited states. Under some approximations which are discussed the result can be extended to 2d and higher dimensional systems with an even number of rows. The gap vanishes for specific values of the coupling strengths which correspond to the location of phase transitions. In a second step we introduce quantitative estimates of the relevance of the variational ansatz which rest on the entanglement concept.
- A. Cabello, O. Gühne, P. Moreno, D. Rodriguez, Nonlocality for graph states, Laser Physics 18, 335, (2008), doi:10.1007/s11490-008-3024-4 (ID: 641481) Toggle Abstract
The possibility of preparing two-photon entangled states encoding three or more qubits in each photon leads to the following problem: If n quabits were distributed between two parties, which quantum pure states and qubit distributions would allow all-versus-nothing (or Greenberger-Horne-Zeilinger-like) proofs of Bell’s theorem using only single-qubit measurements? We show a necessary and sufficient condition for the existence of these proofs and provide all existing proofs up to n = 7 qubits. On the other hand, the possibility of preparing n-photon n-qubit graph states leads to the following problem: If n qubits were distributed between n parties, which would be the optimal Bell inequalities? We show all optimal n-party Bell inequalities for the perfect correlations of any graph state of n < 6 qubits. Optimal means that the ratio between the quantum violation and the bound for local hidden-variable theories is the maximum over all possible combinations of perfect correlations. This implies that the required detection efficiencies for loophole-free Bell tests are minimal.
- W. Wieczorek, C. Schmid, N. Kiesel, R. Pohlner, O. Gühne, H. Weinfurter, Experimental observation of an entire family of four-photon entangled states, Phys. Rev. Lett. 101, 010503, (2008), URL doi:10.1103/PhysRevLett.101.010503 (ID: 596902) Toggle Abstract
A single linear optical set-up is used to observe an entire family of four-photon entangled states. This approach breaks with the inflexibility of present linear-optical set-ups usually designed for the observation of a particular multi-partite entangled state only. The family includes several prominent entangled states that are known to be highly relevant for quantum information applications.
- T. Moroder, O. Gühne, N. Lütkenhaus, Iterations of nonlinear entanglement witnesses, Phys. Rev. A 78, 032306, (2008), URL oai:arXiv:0806.0855v1 (ID: 596900) Toggle Abstract
We describe a generic way to improve a given linear entanglement witness by a quadratic, nonlinear term. This method can be iterated, leading to a whole sequence of nonlinear witnesses, which become stronger in each step of the iteration. We show how to optimize this iteration with respect to a given state, and prove that in the limit of the iteration the nonlinear witness detects all states that can be detected by the positive map corresponding to the original linear witness.
- O. Gühne, F. Bodoky, M. Blaauboer, Multiparticle entanglement under the influence of decoherence, Phys. Rev. A 78, 060301(R), (2008), URL doi:10.1103/PhysRevA.78.060301 (ID: 596899) Toggle Abstract
We present a rigorous approach to determine the decay of quantum correlations as quantified by the geometric measure of entanglement under the influence of decoherence. With this, we compare the robustness of entanglement in GHZ, cluster, W and Dicke states of four qubits and show that the Dicke state is most robust. Finally, we determine the geometric measure analytically for decaying GHZ and cluster states of an arbitrary number of qubits.
- O. Gittsovich, O. Gühne, P. Hyllus, J. Eisert, Covariance matrix criterion for separability, Phys. Rev. A 78, 052319, (2008), URL oai:arXiv:0803.0757 (ID: 572429) Toggle Abstract
We present a framework for deciding whether a quantum state is separable or entangled using covariance matrices of locally measurable observables. This leads to the covariance matrix criterion as a general separability criterion. We demonstrate that this criterion allows to detect many states where the familiar criterion of the positivity of the partial transpose fails. It turns out that a large number of criteria which have been proposed to complement the positive partial transpose criterion - the computable cross norm or realignment criterion, the criterion based on local uncertainty relations, criteria derived from extensions of the realignment map, and others - are in fact a corollary of the covariance matrix criterion.
- O. Gühne, M. Reimpell, R. Werner, Lower bounds on entanglement measures from incomplete information, Phys. Rev. A 77, 052317, (2008), URL doi:10.1103/PhysRevA.77.052317 (ID: 572428) Toggle Abstract
How can we quantify the entanglement in a quantum state, if only the expectation value of a single observable is given? This question is of great interest for the analysis of entanglement in experiments, since in many multiparticle experiments the state is not completely known. We present several results concerning this problem by considering the estimation of entanglement measures via Legendre transforms. First, we present a simple algorithm for the estimation of the concurrence and extensions thereof. Second, we derive an analytical approach to estimate the geometric measure of entanglement, if the diagonal elements of the quantum state in a certain basis are known. Finally, we compare our bounds with exact values and other estimation methods for entanglement measures.
- O. Gühne, A. Cabello, Generalized Ardehali-Bell inequalities for graph states, Phys. Rev. A 77, 032108, (2008), URL doi:10.1103/PhysRevA.77.032108 (ID: 572427) Toggle Abstract
We derive Bell inequalities for graph states by generalizing the approach proposed by Ardehali [Phys. Rev. A 46, 5375 (1992)] for Greenberger-Horne-Zeilinger (GHZ) states. Using this method, we demonstrate that Bell inequalities with nonstabilizer observables are often superior to the optimal GHZ-Mermin-type (or stabilizer-type) Bell inequalities.
- A. Cabello, O. Gühne, D. Rodriguez, Mermin inequalities for perfect correlations, Phys. Rev. A 77, 062106, (2008), URL oai:arXiv.org:0708.3208 (ID: 513840) Toggle Abstract
Any n-qubit state with n independent perfect correlations is equivalent to a graph state. We present the optimal Bell inequalities for perfect correlations and maximal violation for all classes of graph states with n < 7 qubits. Twelve of them were previously unknown and four give the same violation as the Greenberger-Horne-Zeilinger state, although the corresponding states are more resistant to decoherence.
- O. Gühne, Entanglement meets uncertainty relations, Key Laboratory of Quantum Information, Chinese Academy of Sciences, (Hefei (China), 2008-04-25),
(2008), (ID: 596904)
- O. Gühne, The covariance matrix criterion for separability, Universität Düsseldorf (Düsseldorf, Germany, 2008-01-28),
(2008), (ID: 572430) Toggle Abstract
Entanglement is one of the key phenomena in quantum
information theory. In the last years, it has attracted
an increasing attention, however, many of its properties
are still not understood. For instance, the simple
question whether a given state is entangled or separable,
is, in general, not answered.
In this talk I will present an approach for the investigation
of separability and entanglement using covariance matrices
of locally measurable observables. This leads to the covariance
matrix criterion as a general separability criterion. We show
that this criterion allows to detect many states where the
criterion of the positivity of the partial transpose (PPT)
fails. Moreover, it turns out that most criteria, which have
been proposed to complement the PPT criterion, are
incorporated in the covariance matrix criterion.
- O. Gühne, Characterizing entanglement in experiments, Department of Modern Physics,
University of Science and Technology of China, (Hefei, China, 2008-04-17),
(2008), (ID: 596903)
- O. Gühne, Multiparticle entanglement and decoherence, IQC, Waterloo (Canada, 12.11.08)
(2008), (ID: 632648) Toggle Abstract
Decoherence of quantum states is of eminent importance
for implementations of quantum information processing.
Therefore, it is interesting to know how the entanglement
of a multiparticle quantum state is affected by decoherence
and how this depends on the state and the number of qubits.
This is, however, difficult to investigate, since most
entanglement measures are practically impossible to compute
for mixed states.
In this talk I will present a method to determine the decay
of quantum correlations as quantified by the geometric measure
of entanglement under the influence of decoherence. With this,
one can compare the robustness of entanglement in GHZ, cluster,
W and Dicke states of four qubits and show that the Dicke state
is most robust. Furthermore, the method allows to compare
different decoherence models and to investigate the scaling
of the entanglement decay for an increasing number of particles.
- G. Toth, C. Knapp, O. Gühne, H. J. Briegel, Optimal spin squeezing inequalities detect bound entanglement in spin models, Phys. Rev. Lett. 99, 250405, (2007), URL doi:10.1103/PhysRevLett.99.250405 (ID: 448347) Toggle Abstract
We determine the complete set of generalized spin squeezing inequalities. These are entanglement criteria that can be used for the experimental detection of entanglement in a system of spin-(1/2) particles in which the spins cannot be individually addressed. They can also be used to show the presence of bound entanglement in the thermal states of several spin models.
Alternative URL (local restricted copy) - T. Konrad, O. Gühne, J. Audretsch, H. J. Briegel, Parameter estimation for mixed states from a single copy, Phys. Rev. A 75, 062101, (2007), URL doi:10.1103/PhysRevA.75.062101 (ID: 448346) Toggle Abstract
Given a single copy of a mixed state of the form \rho=\lambda\rho_1+(1-\lambda)\rho_2, what is the optimal measurement to estimate the parameter \lambda, if \rho_1 and \rho_2 are known? We present a general strategy to obtain the optimal measurements employing a Bayesian estimator. The measurements are chosen to minimize the deviation between the estimated- and the true value of \lambda. We explicitly determine the optimal measurements for a general two-dimensional system and for important higher dimensional cases.
Alternative URL (local restricted copy) - O. Gühne, N. Lütkenhaus, Nonlinear entanglement witnesses, covariance matrices and the geometry of separable states, J. Phys.: Conf. Ser. 67, 012004, (2007), URL doi:10.1088/1742-6596/67/1/012004 (ID: 428467) Toggle Abstract
Entanglement witnesses provide a standard tool for the analysis of entanglement in experiments. We investigate possible nonlinear entanglement witnesses from several perspectives. First, we demonstrate that they can be used to show that the set of separable states has no facets. Second, we give a new derivation of nonlinear witnesses based on covariance matrices. Finally, we investigate extensions to the multipartite case.
Alternative URL (local restricted copy) - O. Gühne, P. Hyllus, O. Gittsovich, J. Eisert, Covariance matrices and the separability problem, Phys. Rev. Lett. 99, 130504, (2007), doi:10.1103/PhysRevLett.99.130504 (ID: 423139) Toggle Abstract
We propose a unified approach to the separability problem which uses a representation of a
quantum state by a covariance matrix of suitable observables. From the practical point of view,
our approach leads to entanglement criteria that allow to detect the entanglement of many bound
entangled states in higher dimensions and which are at the same time necessary and sufficient for
two qubits. From a fundamental point of view, our approach leads to insights into the relations
between several known entanglement criteria as well as their limitations.
- C. Lu, X. Zhou, O. Gühne, W. Gao, J. Zhang, Z. Yuan, A. Goebel, T. Yang, J. Pan, Experimental entanglement of six photons in graph states, Nature Physics 3, 91, (2007), doi:10.1038/nphys507 (ID: 390238) Toggle Abstract
Graph states are special kinds of multipartite entangled states that correspond to mathematical graphs where the vertices take the role of quantum spin systems and the edges represent interactions. They not only provide an efficient model to study multiparticle entanglement, but also find wide applications in quantum error correction, multi-party quantum communication and most prominently, serve as the central resource in one-way quantum computation. Here we report the creation of two special instances of graph states, the six-photon Greenberger-Horne-Zeilinger states -- the largest photonic Schr\"{o}dinger cat, and the six-photon cluster states-- a state-of-the-art one-way quantum computer. Flexibly, slight modifications of our method allow creation of many other graph states. Thus we have demonstrated the ability of entangling six photons and engineering multiqubit graph states, and created a test-bed for investigations of one-way quantum computation and studies of multiparticle entanglement as well as foundational issues such as nonlocality and decoherence.
Alternative URL (local restricted copy) - O. Gühne, M. Reimpell, R. Werner, Estimating entanglement measures in experiments, Phys. Rev. Lett. 98, 110502, (2007), doi:10.1103/PhysRevLett.98.110502 (ID: 382012) Toggle Abstract
We present a method to estimate entanglement measures in experiments. We show how a lower bound on a generic entanglement measure can be derived from the measured expectation values of any finite collection of entanglement witnesses. Hence witness measurements are given a quantitative meaning without the need of further experimental data. We apply our results to a recent multi-photon experiment [M. Bourennane et al., Phys. Rev. Lett. 92, 087902 (2004)], giving bounds on the entanglement of formation and the geometric measure of entanglement in this experiment.
Alternative URL (local restricted copy) - O. Gühne, H. Häffner, Tomografie eines Quantenzustands – Verschränkung und Reinheit, e & i Elektrotechnik und Informationstechnik 124, 131, (2007), URL doi:10.1007/s00502-007-0431-x (ID: 488436) Toggle Abstract
Es wird die experimentelle Herstellung und Quantenzustandstomografie eines Acht-Teilchen-verschränkten Zustands in einem Ionenfallenquantencomputer diskutiert. Die so gewonnene vollständige quantenmechanische Beschreibung des Zustands dient nun weiteren Untersuchungen. Insbesondere werden Güte und Reinheit des komplexen Zustands berechnet. Darüber hinaus wird nachgewiesen, dass der Zustand verschränkt ist.
- O. Gühne, C. Lu, W. Gao, J. Pan, Toolbox for entanglement detection and fidelity estimation, 76, 030305(R), (2007), URL doi:10.1103/PhysRevA.76.030305 (ID: 495605) Toggle Abstract
The determination of the state fidelity and the detection of entanglement are fundamental problems in quantum information experiments. We investigate how these goals can be achieved with a minimal effort. We show that the fidelity of GHZ and W states can be determined with an effort increasing linearly with the number of qubits. We also present simple and robust methods for other states, such as cluster states and states in decoherence-free subspaces.
Alternative URL (local restricted copy)
- O. Gühne, Multipartite entanglement in graph states, National Institute for Theoretical Physics (Durban, South Africa, 2007-09-28),
(2007), (ID: 527867) Toggle Abstract
Due to the rapid development of the experimental techniques multi-particle entangled states of several ions or photons are available. Among the different multipartite states, the so-called graph states form an important class, since they are useful resources for tasks like measurement based quantum computing. In this talk, I will first explain graph states and discuss their physical properties. Then, I will discuss entanglement witnesses for graph states. These are certain observables, which can be used for the detection and quantification of entanglement in experiments. Finally, I will discuss a recent experiment, where six-photon graph states have been prepared, and will explain the analysis of the experimental data.
- O. Gühne, Estimating entanglement measures in experiments, Universität Heidelberg (Heidelberg, Germany, 2007-06-05),
(2007), (ID: 495606) Toggle Abstract
The quantification of entanglement via entanglement measures is an important
problem in quantum information science. Most of the entanglement measures,
are, however, very difficult to compute in practice, even if the quantum state is
completely known. In this talk I will present a method to estimate entanglement
measures in experiments. I will show how a lower bound on a generic entanglement
measure can be derived from the measured expectation value of any entanglement
witness. I will explain some experiments, where these methods have been used.
Finally, I will discuss how this estimation of entanglement measures can also be
used to study the decay of entanglement under the influence of decoherence.
- O. Gühne, Experimental entanglement characterization for graph states, Universität Basel (Basel, 2007-04-19),
(2007), (ID: 471474) Toggle Abstract
Due to the rapid development of the experimental techniques multi-particle entangled states of several ions or photons are available. To confirm the success of an experiment, the analysis of the state has to verify that genuine multipartite entanglement was indeed produced. This means that entanglement must be present between all parties, and not only between some of them. In this talk, I will first introduce entanglement witnesses as versatile tools for the experimental detection of entanglement. Then, I will show how they can be used to estimate entanglement measures, leading to a quantification of entanglement. Finally, I will discuss a recent experiment, where six-photon graph states have been prepared. These states serve as a central resource in one-way quantum computation and the above mentioned tools have been used for their analysis.
- O. Gühne, Entanglement properties of graph states, Universität Straßburg (Straßburg, 2007-03-09),
(2007), (ID: 462632) Toggle Abstract
Due to the rapid development of the experimental techniques
multi-particle entangled states of several ions or photons
are available. Among the different multipartite states, the
so-called graph states form an important class, since they
are useful resources for tasks like measurement based quantum
computing.
In this talk, I will first explain graph states and discuss
their physical properties. Then, I will discuss entanglement
witnesses for graph states. These are certain observables,
which can be used for the detection and quantification of
entanglement in experiments. Finally, I will discuss a
recent experiment, where six-photon graph states have
been prepared, and will explain the analysis of the
experimental data.
- O. Gühne, Optimal spin squeezing inequalities detect bound entanglement in spin models, Institute for Quantum Computing (Waterloo (Canada), 2007-11-15),
(2007), (ID: 546587) Toggle Abstract
Entanglement is one of the key resources in quantum information science, and many physical systems are studied concerning their entanglement properties. For the case of many particle systems such as ensembles of cold atoms it was found that it is sometimes related to spin squeezing and second moments of collective angular momenta.
In this talk, I will first clarify the relation between entanglement end first and second moments of collective angular momenta. To this aim, I will present a set of eight spin squeezing inequalities which completely characterize the fully separable states, any other spin squeezing inequality for the detection of entanglement can be derived from these.
In a second step, I will apply these inequalities to several spin models. There, it turns out that the inequalities are able to detect multipartite bound entanglement in the thermal states. Bound entanglement is a special form of entanglement which is of great interest, and it has not been found in natural systems so far.
- J. Korbicz, O. Gühne, M. Lewenstein, H. Häffner, C. Roos, R. Blatt, Generalized spin-queezing inequalities in N-qubit systems, Phys. Rev. A 74, 052319, (2006), URL doi:10.1103/PhysRevA.74.052319 (ID: 420124) Toggle Abstract
We present detailed derivations, various improvements and application to concrete
experimental data of spin squeezing inequalities formulated recently by some of us [Phys. Rev. Lett. 95,
120502 (2005)]. These inequalities generalize the concept of the spin squeezing parameter, and provide
necessary and sufficient conditions for genuine 2-, or 3- qubit entanglement for symmetric states,
and sufficient entanglement condition for general $N$-qubit states. We apply our method to theoretical
study of Dicke states, and, in particular, to W-states of N qubits. Then, we analyze the recently
experimentally generated 7- and 8-ion W-states [Nature 438, 643 (2005)]. We also present some novel
details concerning this experiment. Finally, we improve criteria for detection of genuine tripartite
entanglement based on entanglement witnesses.
- O. Gühne, M. Mechler, G. Toth, P. Adam, Entanglement criteria based on local uncertainty relations are strictly stronger than the computable cross norm criterion, Physical Review A (Atomic, Molecular, and Optical Physics) 74, 010301, (2006), doi:10.1103/PhysRevA.74.010301 (ID: 382018) Toggle Abstract
We show that any state that violates the computable cross norm (or realignment) criterion for separability also violates the separability criterion of the local uncertainty relations. The converse is not true. The local uncertainty relations provide a straightforward construction of nonlinear entanglement witnesses for the cross norm criterion.
Alternative URL (local restricted copy) - O. Gühne, G. Toth, Energy and multipartite entanglement in multidimensional and frustrated spin models, Physical Review A (Atomic, Molecular, and Optical Physics) 73, 052319, (2006), doi:10.1103/PhysRevA.73.052319 (ID: 368621) Toggle Abstract
We investigate the relation between the entanglement properties of a quantum state and its energy for macroscopic spin models. To this aim, we develop a general method to compute energy bounds for states without certain forms of multipartite entanglement. Violation of these bounds implies the presence of these types of multipartite entanglement. As examples, we investigate the Heisenberg model in different dimensions, the Ising model and the XX model in the presence of a magnetic field. Finally, by studying the Heisenberg model on a triangular lattice, we demonstrate that our techniques can be applied also to frustrated systems.
Alternative URL (local restricted copy) - J. Rigas, O. Gühne, N. Lütkenhaus, Entanglement verification for quantum-key-distribution systems with an underlying bipartite qubit-mode structures, Physical Review A (Atomic, Molecular, and Optical Physics) 73, 012341, (2006), doi:10.1103/PhysRevA.73.012341 (ID: 341124) Toggle Abstract
We consider entanglement detection for quantum-key-distribution systems that use two signal states and continuous-variable measurements. This problem can be formulated as a separability problem in a qubit-mode system. To verify entanglement, we introduce an object that combines the covariance matrix of the mode with the density matrix of the qubit. We derive necessary separability criteria for this scenario. These criteria can be readily evaluated using semidefinite programming and we apply them to the specific quantum key distribution protocol.
Alternative URL (local restricted copy) - G. Toth, O. Gühne, H. J. Briegel, Two-setting Bell inequalities for graph states, Physical Review A (Atomic, Molecular, and Optical Physics) 73, 022303, (2006), doi:10.1103/PhysRevA.73.022303 (ID: 341123) Toggle Abstract
We present Bell inequalities for graph states with a high violation of local realism. In particular, we show that there is a basic Bell inequality for every nontrivial graph state which is violated by the state at least by a factor of 2. This inequality needs the measurement of, at most, two operators for each qubit and involves only some of the qubits. We also show that for some families of graph states composite Bell inequalities can be constructed such that the violation of local realism increases exponentially with the number of qubits. We prove that some of our inequalities are facets of the convex polytope containing the many-body correlations consistent with local hidden variable models. Our Bell inequalities are built from stabilizing operators of graph states.
Alternative URL (local restricted copy) - O. Gühne, N. Lütkenhaus, Nonlinear entanglement witnesses, Phys. Rev. Lett. 96, 170502, (2006), URL doi:10.1103/PhysRevLett.96.170502 (ID: 326194) Toggle Abstract
Entanglement detection typically relies on linear inequalities for mean
values of certain observables, where violation indicates entanglement. We
provide a general method to improve any of these inequalities for bipartite
systems via nonlinear expressions. The nonlinearities are of different orders
and can be directly measured in experiments, often without any extra effort.
Alternative URL (local restricted copy) - G. Toth, O. Gühne, Detection of multipartite entanglement with two-body correlations, Applied Physics B: Lasers and Optics 82, 237, (2006), URL doi:10.1007/s00340-005-2057-1 (ID: 326222) Toggle Abstract
We show how to detect entanglement with criteria built from simple two-body correlation terms. Since many natural Hamiltonians are sums of such correlation terms, our ideas can be used to detect entanglement by energy measurement. Our criteria can straightforwardly be applied for detecting different forms of multipartite entanglement in familiar spin models in thermal equilibrium.
Alternative URL (local restricted copy)
- O. Gühne, Nonlinear entanglement detection, 6th Joint Conference on Mathematics and Computer Science (>Pecs, Hungary, 2006-03-13),
(2006-07-13), (ID: 382016) Toggle Abstract
The characterization of entanglement is one of the fundamental problems
in quantum information theory. In most of the current experiments, entanglement
is typically detected by so-called entanglement witnesses. These are linear
inequalities for mean values of some observables, if the inequality is violated,
the state under consideration must be entangled. For instance, Bell inequalities
are such inequalities: a state which violates some Bell inequality must be entangled,
hence Bell inequalities can be used for the detection of entanglement.
In my talk, I will investigate whether it is possible to improve linear entanglement
witnesses by some nonlinear expressions. For instance, the nonlinear expressions
may be some squares of mean values of observables. The resulting nonlinear
inequality should detect all states which are detected by the linear inequality,
and some states in addition.
In the first part of my talk I will present a general method to improve
any entanglement witness for bipartite systems. The resulting
nonlinear expressions can be directly measured in experiments, often without
any extra effort. The fact that all witnesses can be improved by nonlinear terms
has some interesting geometrical consequences. Namely, it shows that the set of separable
states has no facets.
In the second part I will present a different construction of nonlinear entanglement
witnesses. Namely, I will show that all states which violate the so-called
computable cross norm (or realignment) criterion for separability also violate the
separability criterion
of the local uncertainty relations. The local uncertainty relations can then be
viewed as the natural nonlinear
entanglement witnesses for the cross norm
criterion.
- O. Gühne, Improved entanglement detection, Feyman Festival (Maryland, MD, 2006-08-26),
(2006), (ID: 390239) Toggle Abstract
Due to the rapid development of the experimental techniques multi-particle entangled states of several ions or photons are now generally available. To confirm the success of an experiment, the analysis of the state has to verify that genuine multipartite entanglement was indeed produced. This means that entanglement must be present between all parties, and not only between some of them. In recent years, entanglement witnesses have turned out to be one of the most powerful tools for this task. These are linear inequalities for mean values of certain observables, and violation indicates entanglement. In this talk I will present several ideas how these witnesses can be constructed and measured in experiments. They can also be tailored for special experimental situations. Finally, I will discuss recent experiments with photons or trapped ions, where witnesses have been used for entanglement verification.
- O. Gühne, Improved entanglement witnesses, DPG Frühjahrstagung (Frankfurt, Germany, 2006-03-13),
(2006-03-13), (ID: 351947) Toggle Abstract
Due to the rapid development of experimental techniques multiparticle
entangled states of several ions or photons are now available. To confirm
the success of an experiment, the analysis of the state has to verify that
genuine multipartite entanglement was indeed produced. Entanglement
witnesses are one of the most powerful tools for this task. These are linear
inequalities for mean values of certain observables, where violation
indicates entanglement.
In this talk we present several ideas to improve witnesses for special
experimental situations. This can be done in several directions: First, one
can reduce the required measurements, minimizing the experimentalists
effort. Then, one can use new types of witnesses, which are more robust
against noise. Also, one may apply local operations on the state, which do
not change the entanglement properties. Finally, one may use nonlinear
entanglement witnesses. We will also explain recent experiments, where
some of these ideas have been used.
- O. Gühne, Detection of entanglement in experiments, DICE2006 (Piombino, Italy, 2006-09-13),
(2006), (ID: 390240) Toggle Abstract
Due to the rapid development of the experimental techniques multi-particle entangled states of several ions or photons are now generally available. To confirm the success of an experiment, the analysis of the state has to verify that genuine multipartite entanglement was indeed produced. This means that entanglement must be present between all parties, and not only between some of them. In recent years, entanglement witnesses have turned out to be one of the most powerful tools for this task. These are linear inequalities for mean values of certain observables, and violation indicates entanglement. In this talk I will present several ideas how these witnesses can be constructed and measured in experiments. They can also be tailored for special experimental situations. Finally, I will discuss recent experiments with photons or trapped ions, where witnesses have been used for entanglement verification.
- O. Gühne, Energy and multipartite entanglement in spin models, Universität Straßburg (Strassburg, France, 2006-02-10),
(2006-02-10), (ID: 351956) Toggle Abstract
In the last years the investigation of entanglement in condensed
matter systems has attracted an increasing interest. These studies
helped to understand quantum phase transitions and improved certain
simulation techniques.
In this talk we will dicuss the presence of multipartite entanglement
in spin models. After explaining some facts about multipartite
entanglement we develop a general method to compute energy bounds for
states without certain forms of multipartite entanglement. Violation
of these bounds (e.g. at low temperatures) implies the presence of these
types of multipartite entanglement. As examples, we investigate the
Heisenberg model in different dimensions, the Ising model and the XX
model in the presence of a magnetic field. Finally, by studying the
Heisenberg model on a triangular lattice, we demonstrate that our
techniques can be applied also to frustrated systems.
- O. Gühne, Entanglement detection in experiments, Institute for Quantum Computing (Waterloo, Canada, 2006-10-23),
(2006), (ID: 417968) Toggle Abstract
Abstract:
Due to the rapid development of the experimental techniques
multi-particle entangled states of several ions or photons
are now generally available. To confirm the success of an
experiment, the analysis of the state has to verify that
genuine multipartite entanglement was indeed produced. This
means that entanglement must be present between all parties,
and not only between some of them.
In recent years, entanglement witnesses have turned out to
be one of the most powerful tools for this task. These are
linear inequalities for mean values of certain observables,
and violation indicates entanglement. In this talk, I will
present several ideas how these witnesses can be constructed
and measured in experiments. Finally, I will discuss two
recent experiments where some of these ideas have been
implemented: one experiment aimed at the creation of an
eight-qubit W state with trapped ions, and in the other
experiment six-qubit graph states have been produced using
polarized photons.
- O. Gühne, Entanglement characterization in experiments, Universität Ulm (Ulm, Germany, 2006-11-03),
(2006), (ID: 417971) Toggle Abstract
Due to the rapid development of the experimental techniques
multi-particle entangled states of several ions or photons
are now generally available. To confirm the success of an
experiment, the analysis of the state has to verify that
genuine multipartite entanglement was indeed produced. This
means that entanglement must be present between all parties,
and not only between some of them.
In recent years, entanglement witnesses have turned out to
be one of the most powerful tools for this task. These are
linear inequalities for mean values of certain observables,
and violation indicates entanglement. In this talk, I will
present several ideas how these witnesses can be constructed
and measured in experiments. Finally, I will discuss two
recent experiments where some of these ideas have been
implemented: one experiment aimed at the creation of an
eight-qubit W state with trapped ions, and in the other
experiment six-qubit graph states have been produced using
polarized photons.
- O. Gühne, Entanglement detection in experiments, Kavli Institute of NanoScience (Delft, Netherlands, 2006-11-28),
(2006), (ID: 423140) Toggle Abstract
Due to the rapid development of experimental techniques multi-particle entangled states of several ions or photons are now generally available. To confirm the success of an experiment, the analysis of the state has to verify that genuine multipartite entanglement was indeed produced. This means that entanglement must be present between all parties, and not only between some of them.
In recent years, entanglement witnesses have turned out to be one of the most powerful tools for this task. These are linear inequalities for mean values of certain observables, and violation indicates entanglement. In this talk, I will present several ideas how these witnesses can be constructed and measured in experiments. Finally, I will discuss two recent experiments where some of these ideas have been implemented: one experiment aimed at the creation of an eight-qubit W state with trapped ions, and in the other experiment six-qubit graph states have been produced using polarized photons.
- P. Hyllus, O. Gühne, D. Bruss, M. Lewenstein, Relations between entanglement witnesses and Bell inequalities, Physical Review A (Atomic, Molecular, and Optical Physics) 72, 022340, (2005), URL doi:10.1103/PhysRevA.72.012321 (ID: 314176) Toggle Abstract
Bell inequalities, considered within quantum mechanics, can be regarded as nonoptimal witness operators. We discuss the relationship between such Bell witnesses and general entanglement witnesses in detail for the Bell inequality derived by Clauser, Horne, Shimony, and Holt (CHSH) [Phys. Rev. Lett. 23, 880 (1969)]. We derive bounds on how much an optimal witness has to be shifted by adding the identity operator to make it positive on all states admitting a local hidden variable model. In the opposite direction, we obtain tight bounds for the maximal proportion of the identity operator that can be subtracted from such a CHSH witness, while preserving the witness properties. Finally, we investigate the structure of CHSH witnesses directly by relating their diagonalized form to optimal witnesses of two different classes.
Alternative URL (local restricted copy) - M. Curty, O. Gühne, M. Lewenstein, N. Lütkenhaus, Detecting two-party quantum correlations in quantum-key-distribution protocols, Physical Review A (Atomic, Molecular, and Optical Physics) 71, 022306, (2005), URL doi:10.1103/PhysRevA.71.022306 (ID: 314544) Toggle Abstract
A necessary precondition for secure quantum key distribution is that sender and receiver can prove the presence of entanglement in a quantum state that is effectively distributed between them. In order to deliver this entanglement proof one can use the class of entanglement witness (EW) operators that can be constructed from the available measurements results. This class of EWs can be used to provide a necessary and sufficient condition for the existence of quantum correlations even when a quantum state cannot be completely reconstructed. The set of optimal EWs for two well-known entanglement-based (EB) schemes, the six-state and the four-state EB protocols, has been obtained recently [M. Curty et al., Phys. Rev. Lett. 92, 217903 (2004).] Here we complete these results, now showing specifically the analysis for the case of prepare and measure (PM) schemes. For this, we investigate the signal states and detection methods of the four-state and the two-state PM schemes. For each of these protocols we obtain a reduced set of EWs. More importantly, each set of EWs can be used to derive a necessary and sufficient condition to prove that quantum correlations are present in these protocols.
Alternative URL (local restricted copy) - G. Toth, O. Gühne, Detecting Genuine Multipartite Entanglement with Two Local Measurements, Physical Review Letters 94, 060501, (2005), URL doi:10.1103/PhysRevLett.94.060501 (ID: 314547) Toggle Abstract
We present entanglement witness operators for detecting genuine multipartite entanglement. These witnesses are robust against noise and require only two local measurement settings when used in an experiment, independent of the number of qubits. This allows detection of entanglement for an increasing number of parties without a corresponding increase in effort. The witnesses presented detect states close to Greenberger-Horne-Zeilinger, cluster, and graph states. Connections to Bell inequalities are also discussed.
Alternative URL (local restricted copy) - G. Toth, O. Gühne, Entanglement detection in the stabilizer formalism, Physical Review A (Atomic, Molecular, and Optical Physics) 72, 022340, (2005), URL doi:10.1103/PhysRevA.72.022340 (ID: 314172) Toggle Abstract
We investigate how stabilizer theory can be used for constructing sufficient conditions for entanglement. First, we show how entanglement witnesses can be derived for a given state, provided some stabilizing operators of the state are known. These witnesses require only a small effort for an experimental implementation and are robust against noise. Second, we demonstrate that also nonlinear criteria based on uncertainty relations can be derived from stabilizing operators. These criteria can sometimes improve the witnesses by adding nonlinear correction terms. All our criteria detect states close to Greenberger-Horne-Zeilinger states, cluster and graph states. We show that similar ideas can be used to derive entanglement conditions for states which do not fit the stabilizer formalism, such as the three-qubit W state. We also discuss connections between the witnesses and some Bell inequalities.
Alternative URL (local restricted copy) - O. Gühne, G. Toth, P. Hyllus, H. J. Briegel, Bell Inequalities for Graph States, Physical Review Letters 95, 120405, (2005), URL doi:10.1103/PhysRevLett.95.120405 (ID: 314624) Toggle Abstract
We investigate the nonlocal properties of graph states. To this aim, we derive a family of Bell inequalities which require three measurement settings for each party and are maximally violated by graph states. In turn, for each graph state there is an inequality maximally violated only by that state. We show that for certain types of graph states the violation of these inequalities increases exponentially with the number of qubits. We also discuss connections to other entanglement properties such as the positivity of the partial transpose or the geometric measure of entanglement.
Alternative URL (local restricted copy) - O. Gühne, G. Toth, H. J. Briegel, Multipartite entanglement in spin chains, New Journal of Physics 7, 229, (2005), URL doi:10.1088/1367-2630/7/1/229 (ID: 314198) Toggle Abstract
We investigate the presence of multipartite entanglement in macroscopic spin chains. We discuss the Heisenberg and the XY model and derive bounds on the internal energy for systems without multipartite entanglement. Based on this we show that in thermal equilibrium the above-mentioned spin systems contain genuine multipartite entanglement, even at finite modest temperatures.
Alternative URL (local restricted copy) - G. Toth, O. Gühne, M. Seevinck, J. Uffink, Addendum to ``Sufficient conditions for three-particle entanglement and their tests in recent experiments'', Physical Review A (Atomic, Molecular, and Optical Physics) 72, 022340, (2005), URL doi:10.1103/PhysRevA.72.014101 (ID: 314178) Toggle Abstract
A recent paper [M. Seevinck and J. Uffink, Phys. Rev. A 65, 012107 (2002)] presented a bound for the three-qubit Mermin inequality such that the violation of this bound indicates genuine three-qubit entanglement. We show that this bound can be improved for a specific choice of observables. In particular, if spin observables corresponding to orthogonal directions are measured at the qubits (e.g., X and Y spin coordinates), then the bound is the same as the bound for states with a local hidden variable model. As a consequence, it can straightforwardly be shown that in the experiment described by J.-W. Pan et al. [Nature 403, 515 (2000)], genuine three-qubit entanglement was detected.
Alternative URL (local restricted copy) - N. Kiesel, C. Schmid, U. Weber, G. Toth, O. Gühne, R. Ursin, H. Weinfurter, Experimental Analysis of a Four-Qubit Photon Cluster State, Physical Review Letters 72, 022340, (2005), URL doi:10.1103/PhysRevLett.95.210502 (ID: 314183) Toggle Abstract
Linear-optics quantum logic operations enabled the observation of a four-photon cluster state. We prove genuine four-partite entanglement and study its persistency, demonstrating remarkable differences from the usual Greenberger-Horne-Zeilinger (GHZ) state. Efficient analysis tools are introduced in the experiment, which will be of great importance in further studies on multiparticle entangled states.
- H. Häffner, W. Hänsel, C. Roos, J. Benhelm, D. Chek-al-Kar, M. Chwalla, T. Körber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Gühne, W. Dür, R. Blatt, Scalable multi-particle entanglement of trapped ions, Nature 438, 643, (2005), URL doi:10.1038/nature04279 (ID: 314190) Toggle Abstract
The generation, manipulation and fundamental understanding of entanglement lies at the very heart of quantum mechanics. Entangled particles are non-interacting but are described by a common wavefunction; consequently, individual particles are not independent of each other and their quantum properties are inextricably interwoven. The intriguing features of entanglement become particularly evident if the particles can be individually controlled and physically separated. However, both the experimental realization and characterization of entanglement become exceedingly difficult for systems with many particles. The main difficulty is to manipulate and detect the quantum state of individual particles as well as to control the interaction between them. So far, entanglement of four ions or five photons has been demonstrated experimentally. The creation of scalable multiparticle entanglement demands a non-exponential scaling of resources with particle number. Among the various kinds of entangled states, the 'W state' plays an important role as its entanglement is maximally persistent and robust even under particle loss. Such states are central as a resource in quantum information processing and multiparty quantum communication. Here we report the scalable and deterministic generation of four-, five-, six-, seven- and eight-particle entangled states of the W type with trapped ions. We obtain the maximum possible information on these states by performing full characterization via state tomography, using individual control and detection of the ions. A detailed analysis proves that the entanglement is genuine. The availability of such multiparticle entangled states, together with full information in the form of their density matrices, creates a test-bed for theoretical studies of multiparticle entanglement. Independently, 'Greenberger–Horne–Zeilinger' entangled states with up to six ions have been created and analysed in Boulder.
- O. Gühne, Multipartite entanglement in spin models, Universität Erlangen (Erlangen, Germany, 2005-09-21),
(2005-09-21), (ID: 351955) Toggle Abstract
In the last years the investigation of entanglement in condensed
matter systems has attracted an increasing interest. These studies
helped to understand quantum phase transitions and improved certain
simulation techniques.
In this talk we will dicuss the presence of multipartite entanglement
in spin models. After explaining some facts about multipartite
entanglement we develop a general method to compute energy bounds for
states without certain forms of multipartite entanglement. Violation
of these bounds (e.g. at low temperatures) implies the presence of these
types of multipartite entanglement. As examples, we investigate the
Heisenberg model in different dimensions, the Ising model and the XX
model in the presence of a magnetic field. Finally, by studying the
Heisenberg model on a triangular lattice, we demonstrate that our
techniques can be applied also to frustrated systems.
- O. Gühne, Multipartite entanglement in spin models, Universität Düsseldorf (Düsseldorf, Germany, 2005-09-13),
(2005-09-13), (ID: 351954) Toggle Abstract
In the last years the investigation of entanglement in condensed
matter systems has attracted an increasing interest. These studies
helped to understand quantum phase transitions and improved certain
simulation techniques.
In this talk we will dicuss the presence of multipartite entanglement
in spin models. After explaining some facts about multipartite
entanglement we develop a general method to compute energy bounds for
states without certain forms of multipartite entanglement. Violation
of these bounds (e.g. at low temperatures) implies the presence of these
types of multipartite entanglement. As examples, we investigate the
Heisenberg model in different dimensions, the Ising model and the XX
model in the presence of a magnetic field. Finally, by studying the
Heisenberg model on a triangular lattice, we demonstrate that our
techniques can be applied also to frustrated systems.
- O. Gühne, Characterizing Entanglement, Universität Konstanz (Konstanz, Germany, 2005-01-24),
(2005-01-24), (ID: 351953) Toggle Abstract
In the last years the phenomenon of entanglement enjoyed an
increasing attention, both from theoretical and from the
experimental point of view. But despite a lot of progress in
the last years, entanglement is still not fully understood.
For instance, for the simple question whether a given state
is entangled or not, no general answer is known.
In this talk I will explain some of the results and open problems
of entanglement theory. I will start with the theoretical
characterization and explain the different classes of entanglement,
entanglement criteria and their physical interpretation.
Then, I will turn to the experimental detection of entanglement
via entanglement witnesses. These are observables which allow for
an easy proof that entanglement is present in a physical system.
I will also shortly report on recent experiments, where this technique
has been applied to detect the entanglement of two-, three- and four-qubit
states of polarized photons.
- O. Gühne, Bell inequalities for graph states, MPI für Quantenoptik (Garching, Germany, 2005-03-04),
(2005-03-23), (ID: 351952) Toggle Abstract
In the last years graph states have attracted an increasing interest
in the field of quantum information theory. Graph states form a family
of multi-qubit states which comprises many popular states such as
the GHZ states and the cluster states. They also play an important role
in applications. For instance, measurement based quantum computation
uses graph states as resources. From a theoretical point of view, it is
remarkable that graph states allow for a simple description in terms of
stabilizing operators.
In this contribution, we investigate the non-local properties of graph
states. We derive a family of Bell inequalities which require three measurement
settings for each party and are maximally violated by graph
states. In turn, any graph state violates at least one of the inequalities.
We show that for certain types of graph states the violation of these
inequalities increases exponentially with the number of qubits. We also
discuss connections to other entanglement properties such as the positivity
of the partial transpose or the geometric measure of entanglement.
- O. Gühne, Bell inequalities for graph states, QUPON conference (Vienna, Austria, 2005-05-20),
(2005-05-20), (ID: 351979) Toggle Abstract
In the last years graph states have attracted an increasing interest
in the field of quantum information theory. Graph states form a family
of multi-qubit states which comprises many popular states such as
the GHZ states and the cluster states. They also play an important role
in applications. For instance, measurement based quantum computation
uses graph states as resources. From a theoretical point of view, it is
remarkable that graph states allow for a simple description in terms of
stabilizing operators.
In this contribution, we investigate the non-local properties of graph
states. We derive a family of Bell inequalities which require three measurement
settings for each party and are maximally violated by graph
states. In turn, any graph state violates at least one of the inequalities.
We show that for certain types of graph states the violation of these
inequalities increases exponentially with the number of qubits. We also
discuss connections to other entanglement properties such as the positivity
of the partial transpose or the geometric measure of entanglement.
- O. Gühne, Bell inequalities for graph states, IQING meeting (Paris, France, 2005-07-23),
(2005-07-23), (ID: 351978) Toggle Abstract
In the last years graph states have attracted an increasing interest
in the field of quantum information theory. Graph states form a family
of multi-qubit states which comprises many popular states such as
the GHZ states and the cluster states. They also play an important role
in applications. For instance, measurement based quantum computation
uses graph states as resources. From a theoretical point of view, it is
remarkable that graph states allow for a simple description in terms of
stabilizing operators.
In this contribution, we investigate the non-local properties of graph
states. We derive a family of Bell inequalities which require three measurement
settings for each party and are maximally violated by graph
states. In turn, any graph state violates at least one of the inequalities.
We show that for certain types of graph states the violation of these
inequalities increases exponentially with the number of qubits. We also
discuss connections to other entanglement properties such as the positivity
of the partial transpose or the geometric measure of entanglement.
- O. Gühne, Complete hierarchies of efficient approximations to problems in entanglement theory, DPG Frühjahrstagung (Berlin, Germany, 2005-03-04),
(2005-03-04), (ID: 351977) Toggle Abstract
In entanglement theory, many problems can be reduced to optimization
problems. Examples of these problems are the decision whether a
state is entangled or not and the minimization of expectation values of
witnesses with respect to product states. In this contribution, we investigate
this type of problems from the perspective of convex optimization.
We show that these problems can be formulated as certain optimization
problems: as optimization problems of a linear function with polynomial
constraints on the variables, employing polynomials of degree three or
less. We then apply known methods from the theory of semi-definite relaxations
to these problems, notably a method due to Lasserre. By this
we arrive at a hierarchy of efficiently solvable approximations to the solution,
approximating the exact solution as closely as desired, in a way
that is asymptotically complete. For example, this results in a hierarchy
of sufficient criteria for entanglement, such that every entangled state will
be detected in some step of the hierarchy. Finally, we present numerical
examples to demonstrate the practical accessibility of this approach.
- O. Gühne, Bell inequalities for graph states, DPG Frühjahrstagung (Berlin, Germany, 2005-03-04),
(2005-03-04), (ID: 351976) Toggle Abstract
In the last years graph states have attracted an increasing interest
in the field of quantum information theory. Graph states form a family
of multi-qubit states which comprises many popular states such as
the GHZ states and the cluster states. They also play an important role
in applications. For instance, measurement based quantum computation
uses graph states as resources. From a theoretical point of view, it is
remarkable that graph states allow for a simple description in terms of
stabilizing operators.
In this contribution, we investigate the non-local properties of graph
states. We derive a family of Bell inequalities which require three measurement
settings for each party and are maximally violated by graph
states. In turn, any graph state violates at least one of the inequalities.
We show that for certain types of graph states the violation of these
inequalities increases exponentially with the number of qubits. We also
discuss connections to other entanglement properties such as the positivity
of the partial transpose or the geometric measure of entanglement.
- O. Gühne, Detecting quantum correlations in quantum key distribution, DPG Frühjahrstagung (Berlin, Germany, 2005-03-04),
(2005-03-04), (ID: 351975) Toggle Abstract
Quantum key distribution (QKD) enables secure communication between
two parties. For practical implementations it is important to know
under which conditions a given QKD protocol is secure or not. It has
been shown that a necessary precondition for secure QKD is that sender
and receiver can prove the presence of entanglement in the quantum
state that is effectively distributed between them. In this contribution,
we demonstrate that entanglement witnesses (EW) are powerful tools in
order to deliver this entanglement proof. The class of EWs that can be
constructed from the available measurements results can be used to provide
a necessary and sufficient condition for the existence of quantum correlations.
First, we present the set of optimal EWs for two entanglement
based (EB) schemes, the 6-state and the 4-state EB protocols. Then, we
analyze prepare and measure (P and M) schemes. For this, we investigate the
4-state and the 2-state P and M schemes. For each of these protocols we obtain
a reduced set of EWs, yielding a necessary and sufficient condition
for the existence of quantum correlations.