Incompatibility of local measurements provide advantage in local quantum state discrimination

TL;DR

This paper explores how incompatible local measurements can provide an advantage in quantum state discrimination tasks, establishing bounds related to measurement incompatibility and showing the absence of nonlocality in optimal local discrimination.

Contribution

It connects local quantum state discrimination with measurement incompatibility, deriving bounds and demonstrating the optimality of local strategies without nonlocality.

Findings

The success probability ratio is bounded by a function of measurement incompatibility.

Every incompatible measurement pair has a local discrimination task achieving this bound.

Optimal local discrimination does not exhibit nonlocality in success probability ratios.

Abstract

The uncertainty principle may be considered as giving rise to the notion of incompatibility of observables. A pack of quantum measurements that cannot be measured simultaneously is said to form a set of incompatible measurements. Every set of incompatible measurements has an advantage over the compatible ones in a quantum state discrimination task where one prepares a state from an ensemble and sends it to another party, and the latter tries to detect the state using available measurements. Comparison between global and local quantum state discriminations is known to lead to a phenomenon of "nonlocality". In this work, we seal a connection between the domains of local quantum state discrimination and incompatible quantum measurements. We consider the local quantum state discrimination task where a sender prepares a bipartite state and sends the subsystems to two receivers. The receivers try to detect the sent state using locally incompatible measurements. We analyze the ratio of the probability of successfully guessing the state using incompatible measurements and the maximum probability of successfully guessing the state using compatible measurements. We find that this ratio is upper bounded by a simple function of robustnesses of incompatibilities of the local measurements. Interestingly, corresponding to every pair of sets of incompatible measurements, there exists at least one local state discrimination task where this bound can be achieved. We argue that the optimal local quantum state discrimination task does not present any "nonlocality", where the term is used in the sense of a difference between the ratios, of probabilities of successful detection via incompatible and compatible measurements, in global and local state discriminations. The results can be generalized to the regime of multipartite local quantum state distinguishing tasks.