Quantum nonlocality without entanglement and state discrimination measures

TL;DR

This paper explores how quantum nonlocality without entanglement varies with different state discrimination measures, revealing ensembles where LOCC fails for minimum-error but succeeds for unambiguous discrimination.

Contribution

It introduces a family of product state ensembles demonstrating measure-dependent nonlocality, highlighting the nuanced relationship between discrimination measures and nonlocality.

Findings

LOCC fails for minimum-error discrimination in the ensembles

LOCC succeeds for unambiguous discrimination in the same ensembles

Quantum nonlocality without entanglement depends on the discrimination measure

Abstract

An ensemble of product states is said to exhibit "quantum nonlocality without entanglement" if the states cannot be optimally discriminated by local operations and classical communication (LOCC). We show that this property can depend on the measure of state discrimination. We present a family of ensembles, each consisting of six linearly independent, equally probable product states for which LOCC fails to achieve optimal minimum-error discrimination but succeeds in achieving optimal unambiguous discrimination.