Non-commutativity and Local Indistinguishability of Quantum States

TL;DR

This paper introduces a non-commutativity-based criterion for determining when a complete set of pure orthogonal product states cannot be distinguished locally, providing both theoretical insights and practical measurement procedures.

Contribution

It presents a necessary and sufficient criterion for local indistinguishability using non-commutativity and offers a constructive method for local state discrimination.

Findings

Non-commutativity effectively characterizes local indistinguishability.

A concrete procedure for local measurements and classical communication is provided.

Non-commutativity measures can quantify quantum correlations in classical-quantum states.

Abstract

We study the local indistinguishability problem of quantum states. By introducing an easily calculated quantity, non-commutativity, we present an criterion which is both necessary and sufficient for the local indistinguishability of a complete set of pure orthogonal product states. A constructive distinguishing procedure to obtain the concrete local measurements and classical communications is given. The non-commutativity of ensembles can be also used to characterize the quantumness for classical-quantum or quantum-classical correlated states.