Discrimination with error margin between two states - Case of general occurrence probabilities -

TL;DR

This paper introduces a unified framework for quantum state discrimination that interpolates between minimum-error and unambiguous discrimination by incorporating an error margin, providing analytic solutions for optimal success probabilities.

Contribution

It classifies optimal measurements into three types based on parameters and derives their domains and success probabilities analytically, also extending results to multipartite states and mixed states.

Findings

Optimal measurement types are classified into three categories.

Analytic expressions for success probabilities in each domain.

Multipartite states can achieve optimal success with local operations.

Abstract

We investigate a state discrimination problem which interpolates minimum-error and unambiguous discrimination by introducing a margin for the probability of error. We closely analyze discrimination of two pure states with general occurrence probabilities. The optimal measurements are classified into three types. One of the three types of measurement is optimal depending on parameters (occurrence probabilities and error margin). We determine the three domains in the parameter space and the optimal discrimination success probability in each domain in a fully analytic form. It is also shown that when the states to be discriminated are multipartite, the optimal success probability can be attained by local operations and classical communication. For discrimination of two mixed states, an upper bound of the optimal success probability is obtained.