High-dimensional Bell test for a continuous variable state in phase space and its robustness to detection inefficiency

TL;DR

This paper introduces a phase-space based scheme for high-dimensional Bell tests using quasiprobability functions, demonstrating violations with two-mode squeezed states and robustness to detection inefficiency.

Contribution

It presents a novel phase-space approach to high-dimensional Bell inequalities and analyzes their violation and robustness in continuous variable systems.

Findings

Violations increase with measurement outcome dimension

High-dimensional tests are robust against detection inefficiency

Applicable to two-mode squeezed states

Abstract

We propose a scheme for testing high-dimensional Bell inequalities in phase space. High-dimensional Bell inequalities can be recast into the forms of a phase-space version using quasiprobability functions with the complex-valued order parameter. We investigate their violations for two-mode squeezed states while increasing the dimension of measurement outcomes, and finally show the robustness of high-dimensional tests to detection inefficiency.