Quantum nonlocality without entanglement depending on nonzero prior probabilities in optimal unambiguous discrimination

TL;DR

This paper investigates how nonlocality without entanglement (NLWE) in quantum state discrimination depends on prior probabilities, revealing new conditions where NLWE can occur or be avoided in optimal unambiguous discrimination.

Contribution

It demonstrates that NLWE occurrence in unambiguous discrimination depends on prior probabilities, extending understanding beyond previous cases of minimum-error discrimination.

Findings

NLWE can depend on nonzero prior probabilities in unambiguous discrimination.

NLWE can occur even if only one state is locally distinguishable without error.

NLWE occurrence is independent of prior probabilities in some cases.

Abstract

Nonlocality without entanglement(NLWE) is a nonlocal phenomenon that occurs in quantum state discrimination of multipartite separable states. In the discrimination of orthogonal separable states, the term NLWE is used when the quantum states cannot be discriminated perfectly by local operations and classical communication. In this case, the occurrence of NLWE is independent of nonzero prior probabilities of quantum states being prepared. Recently, it has been found that the occurrence of NLWE can depend on nonzero prior probabilities in minimum-error discrimination of nonorthogonal separable states. Here, we show that even in optimal unambiguous discrimination, the occurrence of NLWE can depend on nonzero prior probabilities. We further show that NLWE can occur regardless of nonzero prior probabilities, even if only one state can be locally discriminated without error. Our results provide new insights into classifying sets of multipartite quantum states in terms of quantum state discrimination.