All incompatible sets of measurements can generate Buscemi nonlocality

TL;DR

This paper demonstrates that all incompatible measurement sets can generate nonlocality in an extended quantum scenario, revealing a form of hidden nonlocality and establishing an upper bound related to their degree of incompatibility.

Contribution

It proves that all incompatible measurements can produce nonlocality with quantum inputs and introduces a new framework called generalized set of measurements.

Findings

All incompatible measurement sets can generate nonlocality with quantum inputs.

The maximum nonlocality generated is limited by the degree of measurement incompatibility.

A new concept called generalized set of measurements unifies the study of quantum input scenarios.

Abstract

The presence of Bell-nonlocality in the correlations arising from measuring spatially-separated systems guarantees that the sets of measurements used are necessarily incompatible. Not all sets of incompatible measurements can however lead to Bell-nonlocality, as there exist incompatible sets of measurements which can only produce local correlations. In this work we prove that all sets of incompatible measurements are nevertheless able to generate nonlocality in an extended Bell scenario where quantum, instead of classical, measurement inputs are considered. In particular, this holds true for all incompatible-local sets of measurements and, consequently, shows that these sets of measurements posses a form of hidden nonlocality which can be revealed in such a scenario. We furthermore prove that the maximum amount of nonlocality that can be extracted in such a way is limited by the degree of incompatibility of the given set of measurements, thus effectively establishing an achievable upper bound. In order to obtain these results, we introduce a new object which we term a \emph{generalised set of measurements}, which provides a unifying way to study any scenario involving quantum inputs.