Coherence measure of ensembles with nonlocality without entanglement

TL;DR

This paper introduces a coherence-based measure to quantify the quantum nature of orthogonal product state ensembles and relates it to their distinguishability via LOCC, revealing insights into nonlocality without entanglement.

Contribution

It proposes a novel coherence measure for ensembles of orthogonal product states and links it to LOCC distinguishability success probabilities.

Findings

Coherence measure effectively quantifies quantumness of ensembles.

Hierarchy established between coherence and LOCC discrimination success.

Framework connects coherence with nonlocality without entanglement.

Abstract

Irreversibility between preparation and discrimination processes is manifested in the indistinguishability of orthogonal product states via local operations and classical communication (LOCC). Characterizing quantum properties for sets of states according to their local distinguishing property is one of the avenues to explain the surprising results obtained in the LOCC indistinguishability domain. We propose a measure based on the $l_1$ norm of coherence to quantitatively assess the quantumness of ensembles composed of orthogonal product states. Furthermore, to establish a hierarchy among different product ensembles, we establish a relationship between the coherence-based measure of an ensemble and the optimal success probability of distinguishing states within the ensemble using LOCC, constrained by a limited amount of classical communication and projective measurements, in the framework of minimum error state discrimination.