Genuine multipartite nonlocality of permutationally invariant Gaussian states

TL;DR

This paper demonstrates that genuine multipartite nonlocality can be observed in permutationally invariant Gaussian states of continuous variables, using Svetlichny inequality violations with specific measurement settings.

Contribution

It identifies optimal measurement configurations for detecting maximal Svetlichny inequality violations in symmetric Gaussian states, including pseudospin measurements for large squeezing.

Findings

Maximal Svetlichny violation achieved with displaced parity measurements.

Pseudospin measurements approach maximum violation for large squeezing.

Genuine multipartite nonlocality is verifiable in Gaussian states.

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.