Testing for a pure state with local operations and classical communication

TL;DR

This paper investigates the capability of local operations and classical communication (LOCC) to distinguish a known pure state from an unknown state, analyzing error bounds and asymptotic detection rates.

Contribution

It provides bounds on error probabilities and characterizes the asymptotic distinguishability of states using LOCC versus global measurements.

Findings

LOCC can asymptotically distinguish states as well as global measurements when overlap is large

The maximal Schmidt coefficient determines the asymptotic error rate in certain cases

Bounds on error probabilities are established for state discrimination using LOCC

Abstract

We examine the problem of using local operations and classical communication (LOCC) to distinguish a known pure state from an unknown (possibly mixed) state, bounding the error probability from above and below. We study the asymptotic rate of detecting multiple copies of the pure state and show that, if the overlap of the two states is great enough, then they can be distinguished asymptotically as well with LOCC as with global measurements; otherwise, the maximal Schmidt coefficient of the pure state is sufficient to determine the asymptotic error rate.