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

We investigate the relation between the incompatibility of quantum measurements and quantum nonlocality. We show that a set of measurements is not jointly measurable (i.e., incompatible) if and only if it can be used for demonstrating Einstein-Podolsky-Rosen steering, a form of quantum nonlocality. 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 suggests the existence of incompatible quantum measurements which are Bell local, similarly to certain entangled states which admit a local hidden variable model.

Figure 1

The observation of EPR steering, a form of quantum nonlocality, implies the presence of both entanglement and incompatible measurements. Whether the converse links hold is an interesting question. Here we make progress in this direction by showing that any set of incompatible measurements can be used to demonstrate EPR steering (green arrow).