Local hypothesis testing between a pure bipartite state and the white noise state

TL;DR

This paper investigates the problem of local hypothesis testing between a pure bipartite state and white noise, deriving optimal measurements and error bounds for different classes of LOCC protocols.

Contribution

It analytically derives optimal error probabilities and measurements for one-way and separable LOCC, and compares the performance of simple two-way LOCC protocols.

Findings

Optimal type 2 error and POVM for one-way LOCC and separable POVM.

Two-way LOCC protocols outperform one-way LOCC in certain cases.

Simple three-step two-way LOCC protocols can surpass one-way LOCC performance.

Abstract

In this paper, we treat a local discrimination problem in the framework of asymmetric hypothesis testing. We choose a known bipartite pure state $\ket{\Psi}$ as an alternative hypothesis, and the completely mixed state as a null hypothesis. As a result, we analytically derive an optimal type 2 error and an optimal POVM for one-way LOCC POVM and Separable POVM. For two-way LOCC POVM, we study a family of simple three-step LOCC protocols, and show that the best protocol in this family has strictly better performance than any one-way LOCC protocol in all the cases where there may exist difference between two-way LOCC POVM and one-way LOCC POVM.