Certification of Maximum Confidence Quantum Measurements and Their Contextual Advantages

Abstract

Distinguishability is central to the foundations and applications of quantum information processing. An important task is to understand when quantum measurements are advantageous over their classical counterparts. We consider maximum confidence measurements, which include minimum-error and unambiguous state discrimination as special cases, in a semi-device-independent scenario, for which the state preparation is trusted but not the measurement. We show that maximum confidence measurements are certifiable and that the certified confidence can be greater in quantum theory than in noncontextual theories. A maximum confidence measurement for two states with inconclusive events, the most common experimental scenario, is analysed in detail. Our results relate contextual advantages of quantum distinguishability to the necessary assumptions behind them and may be used to devise quantum information protocols beyond the limitations of noncontextual theories.