Phase space analysis of Bell inequalities for mixed Gaussian states

TL;DR

This paper introduces a phase space approach to evaluate Bell inequality violations in continuous variable systems, extending analysis from pure to mixed states and examining thermal noise effects.

Contribution

It develops a generalized phase space formalism for mixed Gaussian states, enabling analysis of Bell violations under thermal noise and optimal measurement strategies.

Findings

Thermal noise reduces Bell inequality violations in two-mode squeezed thermal states.

Bell violations show a non-monotonic relationship with entanglement.

Optimal pseudospin operators depend on the specific mixed state.

Abstract

We present a phase space formalism to evaluate Bell inequality violations in continuous variable systems. By doing so we can generalize previous analyses (which have dealt only with pure states) to arbitrary mixed states. We leverage these results to analyze the effect of temperature on violations of Bell inequalities in a two-mode squeezed thermal state, which can become useful in tests of local realism in the presence of thermal noise. We also explore the non-monotonic relationship between the violations of Bell inequalities and the amount of entanglement present in this family of mixed states. Additionally, we discuss the optimal choices of pseudospin operators for states beyond the two-mode squeezed vacuum.