Testing genuine multipartite nonlocality in phase space

Abstract

We demonstrate genuine three-mode nonlocality based on phase space formalism. A Svetlichny-type Bell inequality is formulated in terms of the $s$-parameterized quasiprobability function. We test such 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.

11 pages, 6 figures, RevTeX4

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• Theory of genuine tripartite nonlocality of Gaussian states
• Demonstrating nonclassicality and non-Gaussianity of single-mode fields: Bell-type tests using generalized phase-space distributions
• Enhanced multipartite quantum correlations by non-Gaussian operations
• Einstein-Podolsky-Rosen steering and Bell nonlocality of two macroscopic mechanical oscillators in optomechanical systems
• Violation of Bell inequalities in larger Hilbert spaces: robustness and challenges
• Verifying single-mode nonclassicality beyond negativity in phase space
• Genuine tripartite entanglement and nonlocality in Bose-Einstein condensates by collective atomic recoil
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• Beating the Clauser-Horne-Shimony-Holt and the Svetlichny games with Optimal States
• Noise-adaptive test of quantum correlations with quasiprobability functions