Testing genuine multipartite nonlocality in phase space

TL;DR

This paper introduces a phase space-based Bell inequality to detect genuine three-mode nonlocality in quantum states, distinguishing GHZ- and W-type nonlocality, and analyzes its robustness under realistic conditions.

Contribution

It formulates a Svetlichny-type Bell inequality in phase space and demonstrates its effectiveness in identifying genuine tripartite nonlocality in various entangled states.

Findings

Successfully discriminates GHZ- and W-type nonlocality.

Verifies genuine three-mode nonlocality beyond two-mode models.

Analyzes nonlocality robustness under detection inefficiency and dissipation.

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.