Contextuality in phase space

TL;DR

This paper develops a unified phase space framework for testing quantum contextuality using displacement operators, applicable to both continuous and discrete systems, facilitating experimental implementations.

Contribution

It introduces a general condition for displacement operators to construct contextuality tests like the Peres-Mermin square, bridging continuous and discrete phase space approaches.

Findings

Provides a geometric framework for contextuality in phase space.

Derives a condition applicable to both continuous and discrete systems.

Facilitates experimental testing of contextuality with modular variables.

Abstract

We present a general framework for contextuality tests in phase space using displacement operators. First, we derive a general condition that a single-mode displacement operator should fulfill in order to construct Peres-Mermin square and similar scenarios. This approach offers a straightforward scheme for experimental implementations of the tests via modular variable measurements. In addition to the continuous variable case, our condition can also be applied to finite-dimensional systems in discrete phase space, using Heisenberg-Weyl operators. This approach, therefore, offers a unified picture of contextuality with a geometric flavor.