State discrimination with error margin and its locality

TL;DR

This paper explores quantum state discrimination with a finite error margin, providing optimal strategies for two pure states and demonstrating that local operations suffice for multipartite states.

Contribution

It introduces a unified framework for quantum state discrimination with arbitrary error margins and shows local operations are sufficient for optimal discrimination in multipartite cases.

Findings

Optimal discrimination probability for two pure states with arbitrary error margin

Discrimination strategies are achievable via local operations and classical communication for multipartite states

Unified approach bridging minimum-error and unambiguous discrimination

Abstract

There are two common settings in a quantum-state discrimination problem. One is minimum-error discrimination where a wrong guess (error) is allowed and the discrimination success probability is maximized. The other is unambiguous discrimination where errors are not allowed but the inconclusive result "I don't know" is possible. We investigate discrimination problem with a finite margin imposed on the error probability. The two common settings correspond to the error margins 1 and 0. For arbitrary error margin, we determine the optimal discrimination probability for two pure states with equal occurrence probabilities. We also consider the case where the states to be discriminated are multipartite, and show that the optimal discrimination probability can be achieved by local operations and classical communication.