Verification of joint measurability using phase-space quasiprobability distributions

TL;DR

This paper introduces a phase-space quasiprobability distribution-based method to verify measurement incompatibility in quantum systems, linking non-classicality with measurement properties and analyzing effects of channels on measurement incompatibility.

Contribution

It establishes a novel approach connecting quasiprobability negativity with measurement incompatibility and derives practical conditions for bosonic and Gaussian channels.

Findings

Pure lossy channels with ≥50% losses break measurement incompatibility.

The method applies to all single-mode Gaussian channels.

Incompatibility-breaking conditions help assess errors in quantum measurements.

Abstract

Measurement incompatibility is a distinguishing property of quantum physics and an essential resource for many quantum information processing tasks. We introduce an approach to verify the joint measurability of measurements based on phase-space quasiprobability distributions. Our results therefore establish a connection between two notions of non-classicality, namely the negativity of quasiprobability distributions and measurement incompatibility. We show how our approach can be applied to the study of incompatibility-breaking channels and derive incompatibility-breaking sufficient conditions for bosonic systems and Gaussian channels. In particular, these conditions provide useful tools for investigating the effects of errors and imperfections on the incompatibility of measurements in practice. To illustrate our method, we consider all classes of single-mode Gaussian channels. We show that pure lossy channels with 50% or more losses break the incompatibility of all measurements that can be represented by non-negative Wigner functions, which includes the set of Gaussian measurements.