Finding optimal solutions for generalized quantum state discrimination problems

TL;DR

This paper introduces a method to find optimal quantum measurements for generalized state discrimination problems, including maximizing correct detection and Neyman-Pearson strategies, by transforming them into easier minimum error problems.

Contribution

The authors propose a novel approach that reduces complex quantum state discrimination problems to simpler minimum error problems, enabling easier computation of optimal measurements.

Findings

The approach effectively finds optimal measurements for various discrimination scenarios.

The relationship between original and modified problem solutions is clarified.

An algorithm for numerical solutions is demonstrated.

Abstract

We try to find an optimal quantum measurement for generalized quantum state discrimination problems, which include the problem of finding an optimal measurement maximizing the average correct probability with and without a fixed rate of inconclusive results and the problem of finding an optimal measurement in the Neyman-Pearson strategy. We propose an approach in which the optimal measurement is obtained by solving a modified version of the original problem. In particular, the modified problem can be reduced to one of finding a minimum error measurement for a certain state set, which is relatively easy to solve. We clarify the relationship between optimal solutions to the original and modified problems, with which one can obtain an optimal solution to the original problem in some cases. Moreover, as an example of application of our approach, we present an algorithm for numerically obtaining optimal solutions to generalized quantum state discrimination problems.