Local distinguishability of quantum states in bipartite systems

TL;DR

This paper establishes a necessary and sufficient condition for determining when bipartite quantum states can be distinguished using one-way LOCC, revealing minimal structures of indistinguishable sets and providing examples of distinguishable sets.

Contribution

It introduces a precise criterion for local distinguishability of bipartite states and characterizes minimal indistinguishable structures under one-way LOCC.

Findings

A necessary and sufficient condition for local distinguishability

Identification of minimal indistinguishable structures

Examples of distinguishable quantum state sets

Abstract

In this article, we show a sufficient and necessary condition for locally distinguishable bipartite states via one-way local operations and classical communication (LOCC). With this condition, we present some minimal structures of one-way LOCC indistinguishable quantum state sets. As long as an indistinguishable subset exists in a state set, the set is not distinguishable. We also list several distinguishable sets as instances.