Joint Measurability, Einstein-Podolsky-Rosen Steering, and Bell Nonlocality

TL;DR

This paper explores the deep connection between measurement incompatibility, EPR steering, and Bell nonlocality, revealing that incompatible measurements can demonstrate EPR steering but may not always violate Bell inequalities, indicating their inequivalence.

Contribution

It establishes the equivalence between measurement incompatibility and EPR steering, and provides evidence that incompatible measurements can be Bell local, highlighting nuanced differences between these quantum phenomena.

Findings

Incompatible measurements can demonstrate EPR steering.

Some incompatible measurements do not violate Bell inequalities.

Measurement incompatibility and Bell nonlocality are not equivalent.

Abstract

We investigate the relation between the incompatibility of quantum measurements and quantum nonlocality. We show that any set of measurements that is not jointly measurable (i.e. incompatible) can be used for demonstrating EPR steering, a form of quantum nonlocality. This implies that EPR steering and (non) joint measurability can be viewed as equivalent. Moreover, we discuss the connection between Bell nonlocality and joint measurability, and give evidence that both notions are inequivalent. Specifically, we exhibit a set of incompatible quantum measurements and show that it does not violate a large class of Bell inequalities. This suggest the existence of incompatible quantum measurements which are Bell local, similarly to certain entangled states which admit a local hidden variable model.