Unifying contextual advantages in state discrimination

TL;DR

This paper unifies the understanding of contextual advantages in quantum state discrimination, deriving inequalities that reveal advantages across various discrimination strategies and figures of merit.

Contribution

It introduces a unified framework for contextual advantages in all state discrimination schemes, connecting different figures of merit and strategies.

Findings

Contextual advantages exist for confidence, guessing probability, and inconclusive outcomes.

Derived noncontextuality inequalities for multiple discrimination strategies.

Unified perspective on contextual advantages across all state discrimination methods.

Abstract

Quantum state discrimination, alongside its other applications, has recently found use as a tool for witnessing generalised contextuality. In this article, we derive noncontextuality inequalities for both conclusive and inconclusive outcomes across various guessing strategies. For minimum- error discrimination, the advantage is in terms of the confidences of individual outcomes, while for unambiguous state discrimination, it is in terms of the average guessing probability. For maximum- confidence discrimination, we show that contextual advantages occur not only for the confidence but also their average, the guessing probability, as well as the inconclusive outcome rate. Our results unify the contextual advantages across all state discrimination schemes and figures of merit. We envisage that various quantum information applications based on state discrimination may offer advantages over non-contextual theories.