Contextual Advantages and Certification for Maximum-Confidence Discrimination

One of the most fundamental results in quantum information theory is that no measurement can perfectly discriminate between nonorthogonal 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 discrimi-nation, 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.

Automated summary

This work investigates the advantages of quantum discrimination tasks over noncontextual theories by considering a maximum-confidence measurement that unifies different strategies of quantum state discrimination. The study shows that maximum-confidence discrimination and unambiguous discrimination both possess contextual advantages, and that certified maximum confidence in quantum theory also contains contextual advantages.