Device-independent quantification of measurement incompatibility

TL;DR

This paper establishes a direct link between Bell nonlocality and measurement incompatibility, providing new quantifiers and methods that generalize to various scenarios including semi-device-independent and prepare-and-measure settings.

Contribution

It introduces a novel framework connecting Bell nonlocality with measurement incompatibility quantification, applicable to multiple measurement scenarios and constraints.

Findings

Provides new incompatibility quantifiers for multipartite measurements

Generalizes methods to semi-device-independent and projective measurement scenarios

Offers improved bounds on measurement incompatibility quantifiers

Abstract

Incompatible measurements, i.e., measurements that cannot be simultaneously performed, are necessary to observe nonlocal correlations. It is natural to ask, e.g., how incompatible the measurements have to be to achieve a certain violation of a Bell inequality. In this work, we provide the direct link between Bell nonlocality and the quantification of measurement incompatibility. This includes quantifiers for both incompatible and genuine-multipartite incompatible measurements. Our method straightforwardly generalizes to include constraints on the system's dimension (semi-device-independent approach) and on projective measurements, providing improved bounds on incompatibility quantifiers, and to include the prepare-and-measure scenario.