Measurement compatibility in Bell nonlocality tests

TL;DR

This paper explores how measurement compatibility, traditionally seen as a limitation, can be leveraged to detect Bell nonlocality and certify entanglement, challenging conventional views on measurement incompatibility.

Contribution

It demonstrates that compatible measurements can still lead to Bell-like inequalities, offering new avenues for nonlocality detection and entanglement certification.

Findings

Compatible measurements can produce Bell-like inequalities.

Measurement compatibility can aid in device-independent entanglement certification.

Incompatibility is not strictly necessary for Bell nonlocality.

Abstract

Incompatibility of observables, or measurements, is one of the key features of quantum mechanics, related, among other concepts, to Heisenberg's uncertainty relations and Bell nonlocality. In this manuscript we show, however, that even though incompatible measurements are necessary for the violation of any Bell inequality, some relevant Bell-like inequalities may be obtained if compatibility relations are assumed between the local measurements of one (or more) of the parties. Hence, compatibility of measurements is not necessarily a drawback and may, however, be useful for the detection of Bell nonlocality and device-independent certification of entanglement.