Proposal for a macroscopic test of local realism with phase-space measurements

TL;DR

This paper introduces a phase-space based test of local realism using modular variables, demonstrating non-locality through violations of a derived inequality with entangled states in interferometric setups.

Contribution

It proposes a novel macroscopic test of local realism utilizing phase-space measurements and constructs entangled states that violate the inequality, revealing non-locality.

Findings

Entangled states violate the phase-space inequality.

Non-locality demonstrated through spatial correlation data.

Method applicable in space-like separated interferometric setups.

Abstract

We propose a new test of local realism based on correlation measurements of continuum valued functions of positions and momenta, known as modular variables. The Wigner representation of these observables are bounded in phase space, and therefore, the associated inequality holds for any state described by a non-negative Wigner function. This agrees with Bell's remark that positive Wigner functions, serving as a valid probability distribution over local (hidden) phase space coordinates, do not reveal non-locality. We construct a class of entangled states resulting in a violation of the inequality, and thus truly demonstrate non-locality in phase space. The states can be realized through grating techniques in space-like separated interferometric setups. The non-locality is verified from the spatial correlation data, collected from the screens.