Vector Representations of Graphs and Distinguishing Quantum Product States with One-way LOCC

TL;DR

This paper introduces a graph-theoretic method using vector representations to analyze the problem of distinguishing quantum product states with one-way LOCC, providing new insights and examples in quantum information theory.

Contribution

It develops a novel graph-based framework for understanding quantum state distinguishability under one-way LOCC, linking graph properties to quantum measurement capabilities.

Findings

Graph-theoretic approach effectively characterizes distinguishability

Established connections between graph properties and quantum measurement outcomes

Provided illustrative examples demonstrating the framework's application

Abstract

Distinguishing sets of quantum states shared by two parties using only local operations and classical communication measurements is a fundamental topic in quantum communication and quantum information theory. We introduce a graph-theoretic approach, based on the theory of vector representations of graphs, to the core problem of distinguishing product states with one-way LOCC. We establish a number of results that show how distinguishing such states can be framed in terms of properties of the underlying graphs associated with a set of vector product states. We also present a number of illustrative examples.