Operator and Graph Theoretic Techniques for Distinguishing Quantum States via One-Way LOCC

TL;DR

This paper integrates operator theory, operator algebras, and graph theory to analyze the distinguishability of quantum states under one-way LOCC, providing new theoretical insights and a graph-theoretic framework for single-qubit cases.

Contribution

It introduces a novel combination of mathematical techniques to study quantum state distinguishability and offers a new graph-theoretic description for single-qubit scenarios.

Findings

Unified framework for quantum state distinguishability

New graph-theoretic description for single-qubit cases

Enhanced understanding of one-way LOCC protocols

Abstract

We bring together in one place some of the main results and applications from our recent works in quantum information theory, in which we have brought techniques from operator theory, operator algebras, and graph theory for the first time to investigate the topic of distinguishability of sets of quantum states in quantum communication, with particular reference to the framework of one-way local quantum operations and classical communication (LOCC). We also derive a new graph-theoretic description of distinguishability in the case of a single qubit sender.