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arXiv:1610.01928 · Physical Review A

Genuine multipartite nonlocality of permutationally invariant Gaussian states

Buqing Xu, Tommaso Tufarelli, Gerardo Adesso

Published Jan 18, 2017• 6 citations
arXivHTMLPDF

Abstract

We investigate genuine multipartite nonlocality of pure permutationally invariant multimode Gaussian states of continuous variable systems, as detected by the violation of Svetlichny inequality. We identify the phase space settings leading to the largest violation of the inequality when using displaced parity measurements, distinguishing our results between the cases of even and odd total number of modes. We further consider pseudospin measurements and show that, for three-mode states with asymptotically large squeezing degree, particular settings of these measurements allow one to approach the maximum violation of Svetlichny inequality allowed by quantum mechanics. This indicates that the strongest manifestation of genuine multipartite quantum nonlocality is in principle verifiable on Gaussian states.

DOI
10.1103/physreva.95.012124

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We investigate genuine multipartite nonlocality of pure permutationally invariant multimode Gaussian states of continuous variable systems, as detected by the violation of Svetlichny inequality. We identify the phase space settings leading to the largest violation of the inequality when using displaced parity measurements, distinguishing our results between the cases of even and odd total number of modes. We further consider pseudospin measurements and show that, for three-mode states with asymptotically large squeezing degree, particular settings of these measurements allow one to approach the maximum violation of Svetlichny inequality allowed by quantum mechanics. This indicates that the strongest manifestation of genuine multipartite quantum nonlocality is in principle verifiable on Gaussian states.
We investigate the genuine multipartite nonlocality of three-mode Gaussian states of continuous variable systems. For pure states, we present a simplified procedure to obtain the maximum violation of the Svetlichny inequality based on displaced parity measurements, and we analyze its interplay with genuine tripartite entanglement measured via Rényi-2 entropy. The maximum Svetlichny violation admits tight upper and lower bounds at fixed tripartite entanglement. For mixed states, no violation is possible when the purity falls below 0.86. We also explore a set of recently derived weaker inequalities for three-way nonlocality, finding violations for all tested pure states. Our results provide a strong signature for the nonclassical and nonlocal nature of Gaussian states despite their positive Wigner function, and lead to precise recipes for its experimental verification.
We demonstrate genuine three-mode nonlocality based on phase-space formalism. A Svetlichny-type Bell inequality is formulated in terms of the sss-parametrized quasiprobability function. We test such a tool using exemplary forms of three-mode entangled states, identifying the ideal measurement settings required for each state. We thus verify the presence of genuine three-mode nonlocality that cannot be reproduced by local or nonlocal hidden variable models between any two out of three modes. In our results, GHZ- and W-type nonlocality can be fully discriminated. We also study the behavior of genuine tripartite nonlocality under the effects of detection inefficiency and dissipation induced by local thermal environments. Our formalism can be useful to test the sharing of genuine multipartite quantum correlations among the elements of some interesting physical settings, including arrays of trapped ions and intracavity ultracold atoms.
Abstract Genuine multipartite nonlocality (GMN) has been recognized as the strongest form of multipartite quantum correlation. However, there exist states that cannot violate the Svetlichny inequality derived from the standard definition of GMN, even though they possess GMN properties. The reason is that the standard definition of GMN allows correlations that permit signalling among parties, which is inconsistent with an operational definition. Here, for the first time, we present an experimental test of GMN in the no-signalling scenario, with a three-photon pure state |ψs〉 and a noisy W state. The experimental results show that these states cannot violate the Svetlichny inequality. However, our results also demonstrate that they do violate a new inequality derived from the definition of GMN based on the no-signalling principle, i.e., these states can exhibit GMN under the requirement of no-signalling. Our results will be useful for the study and applications of GMN in quantum communications and quantum computation.
The structure of Bell-type inequalities detecting genuine multipartite nonlocality, and hence detecting genuine multipartite entanglement, is investigated. We first present a simple and intuitive approach to Svetlichny's original inequality, which provides a clear understanding of its structure and of its violation in quantum mechanics. Based on this approach, we then derive a family of Bell-type inequalities for detecting genuine multipartite nonlocality in scenarios involving an arbitrary number of parties and systems of arbitrary dimension. Finally, we discuss the tightness and quantum mechanical violations of these inequalities.
This thesis focuses on fundamental resources in quantum information theory with continuous variables and their applications to quantum optics and quantum thermodynamics. Our analysis mainly considers Gaussian states of continuous variable systems formed by two, three, or more modes, and adopts a variety of techniques to study their static and dynamical properties. Our original results include three main case studies: (i) quantifying genuine multipartite Bell nonlocality in permutationally invariant Gaussian states; (ii) characterising bipartite Einstein-Podolsky-Rosen (EPR) steering with non-Gaussian measurements; and (iii) benchmarking the reaction-coordinate mapping in non-equilibrium quantum harmonic chains. In project (i), we investigate genuine multipartite nonlocality of multimode Gaussian states, as detected by the violation of Svetlichny inequality. We consider both displaced parity and pseudospin measurements and identify the largest violation of the inequality on permutationally invariant states. In the pseudospin case, we show that the maximum violation of Svetlichny inequality allowed by quantum mechanics can be approached for asymptotically large squeezing. In project (ii) we study the detection of EPR steering (an asymmetric quantum correlation intermediate between entanglement and Bell nonlocality) in bipartite Gaussian states by pseudospin measurements. Our analysis reveals previously unexplored regimes where non-Gaussian measurements are more effective than Gaussian ones to witness steering of Gaussian states in the presence of local noise. Finally, in project (iii) we analyze the validity of the reaction-coordinate mapping to characterise heat transport in an exactly solvable model: a two-node linear "quantum wire" connecting two baths at different temperatures. We find surprisingly that the stationary state of the original problem can be reproduced accurately by a weak-coupling treatment even in the regime of very strong residual dissipation.
Measurement-based quantum correlation mimics several characteristics of multipartite quantum correlations and at the same time, it reduces the parent system to a smaller subsystem. On the other hand, genuine multipartite entanglement measures can capture certain features of a multisite composite system that are inaccessible via bipartite quantum correlation quantifiers. We merge these two concepts by introducing localizable genuine multimode entanglement for continuous variable systems, both for Gaussian and non-Gaussian multimode parent states. We report a compact form of localizable generalized geometric measure for multimode Gaussian states when Gaussian measurements are performed in some of the modes. We show that non-Gaussian measurements can concentrate more genuine multimode entanglement compared to the Gaussian ones. For non-Gaussian states with non-Gaussian measurements, we find that although four-mode squeezed vacuum state has permutation symmetry with respect to the exchange of first and third modes as well as the second and the fourth modes, the symmetry can be broken by performing measurements in one of the modes in case of addition while for subtraction, such symmetry is preserved, thereby providing a method for distinguishing multimode photon-added and -subtracted states via localizations.