Contextual advantages and certification for maximum confidence discrimination

TL;DR

This paper explores how quantum advantages in state discrimination, including maximum confidence and unambiguous strategies, demonstrate contextual benefits over classical theories, especially in semi-device independent scenarios with undetected events.

Contribution

It introduces a unified approach to quantum state discrimination that reveals contextual advantages and extends these findings to semi-device independent certification scenarios.

Findings

Quantum advantages in discrimination tasks are rooted in contextuality.

Maximum confidence and unambiguous discrimination show contextual benefits.

Quantum theory's advantages persist even with undetected events in certification.

Abstract

One of the most fundamental results in quantum information theory is that no measurement can perfectly discriminate between non-orthogonal quantum states. In this work, we investigate quantum advantages for discrimination tasks over noncontextual theories by considering a maximum confidence measurement that unifies different strategies of quantum state discrimination, including minimum-error and unambiguous discrimination. We first show that maximum confidence discrimination, as well as unambiguous discrimination, contains contextual advantages. We then consider a semi-device independent scenario of certifying maximum confidence measurement. The scenario naturally contains undetected events, making it a natural setting to explore maximum confidence measurements. We show that the certified maximum confidence in quantum theory also contains contextual advantages. Our results establish how the advantages of quantum theory over a classical model may appear in a realistic scenario of a discrimination task.