Operator Structures and Quantum One-Way LOCC Conditions

TL;DR

This paper explores the operator structures underlying quantum one-way LOCC, revealing new insights and equivalences in state distinguishability, and bridging concepts from operator theory and quantum information.

Contribution

It introduces a detailed analysis of operator structures in one-way LOCC, deriving new results and connecting operator theory with quantum information.

Findings

Operator structures naturally arise in one-way LOCC analysis

New equivalences in perfect distinguishability under different operations

Bridging operator theory and quantum information concepts

Abstract

We conduct the first detailed analysis in quantum information of recently derived operator relations from the study of quantum one-way local operations and classical communications (LOCC). We show how operator structures such as operator systems, operator algebras, and Hilbert C*-modules all naturally arise in this setting, and we make use of these structures to derive new results and new derivations of some established results in the study of LOCC. We also show that perfect distinguishability under one-way LOCC and under arbitrary operations is equivalent for several families of operators that appear jointly in matrix and operator theory and quantum information theory.