Joint measurability of generalized measurements implies classicality

TL;DR

This paper establishes that the inability to jointly measure certain generalized quantum measurements signifies their nonclassical nature, linking joint measurability to quantum steering and providing new criteria and inequalities.

Contribution

It proves that non-jointly measurable measurements are inherently nonclassical and connects this to quantum steering, offering new tools for analyzing quantum behavior.

Findings

Non-jointly measurable measurements enable quantum steering

Joint measurability characterizes classicality in quantum measurements

New steering inequalities and criteria for joint measurability are derived

Abstract

The fact that not all measurements can be carried out simultaneously is a peculiar feature of quantum mechanics and responsible for many key phenomena in the theory, such as complementarity or uncertainty relations. For the special case of projective measurements quantum behavior can be characterized by the commutator but for generalized measurements it is not easy to decide whether two measurements can still be understood in classical terms or whether they show already quantum features. We prove that generalized measurements which do not fulfill the notion of joint measurability are nonclassical, as they can be used for the task of quantum steering. This shows that the notion of joint measurability is, among several definitions, the proper one to characterize quantum behavior. Moreover, the equivalence allows to derive novel steering inequalities from known results on joint measurability and new criteria for joint measurability from known results on the steerability of states.