One-to-one mapping between steering and joint measurability problems

TL;DR

This paper establishes a universal equivalence between quantum steering and joint measurability, enabling new criteria and quantifiers for measurement incompatibility in quantum systems.

Contribution

It proves that steerability and joint measurability are always equivalent problems, extending previous results beyond pure states of maximal Schmidt rank.

Findings

Steerability can be formulated as a joint measurability problem for any assemblage.

Steering inequalities can be derived from joint measurability criteria.

New quantifiers for measurement incompatibility are introduced.

Abstract

Quantum steering refers to the possibility for Alice to remotely steer Bob's state by performing local measurements on her half of a bipartite system. Two necessary ingredients for steering are entanglement and incompatibility of Alice's measurements. In particular, it has been recently proven that for the case of pure states of maximal Schmidt rank the problem of steerability for Bob's assemblage is equivalent to the problem of joint measurability for Alice's observables. We show that such an equivalence holds in general, namely, the steerability of any assemblage can always be formulated as a joint measurability problem, and vice versa. We use this connection to introduce steering inequalities from joint measurability criteria and develop quantifiers for the incompatibility of measurements.