Theory of genuine tripartite nonlocality of Gaussian states

TL;DR

This paper studies the genuine tripartite nonlocality of three-mode Gaussian states, providing bounds on Svetlichny inequality violations, analyzing the role of entanglement, and offering experimental verification methods.

Contribution

It introduces a simplified procedure to quantify Svetlichny inequality violations in Gaussian states and explores their relation with tripartite entanglement, including bounds and conditions for violation.

Findings

Maximum Svetlichny violation bounds at fixed entanglement

No violation for mixed states with purity below 0.86

Violations found for all tested pure states using weaker inequalities

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.