Theory of genuine tripartite nonlocality of Gaussian states

Abstract

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 Renyi-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.

5 pages, 2 figures. To appear in PRL

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• Demonstrating nonclassicality and non-Gaussianity of single-mode fields: Bell-type tests using generalized phase-space distributions
• Tight upper bound for the maximal quantum value of the Svetlichny operators
• Entanglement formation in continuous-variable random quantum networks
• Einstein-Podolsky-Rosen steering and Bell nonlocality of two macroscopic mechanical oscillators in optomechanical systems
• Efficient Test to Demonstrate Genuine Three Particle Nonlocality
• Multiphoton Bell-type inequality: a tool to unearth nonlocality of continuous variable quantum optical systems
• Verifying single-mode nonclassicality beyond negativity in phase space
• Experimental verification of time-order-dependent correlations in three-qubit Greenberger-Horne-Zeilinger-class states
• Genuine tripartite entanglement and nonlocality in Bose-Einstein condensates by collective atomic recoil
• Genuine multipartite nonlocality of permutationally invariant Gaussian states
• Tripartite separability conditions exponentially violated by Gaussian states
• Beating the Clauser-Horne-Shimony-Holt and the Svetlichny games with Optimal States