Contextuality-enhanced quantum state discrimination under fixed failure probability

TL;DR

This paper demonstrates how contextuality can enhance quantum state discrimination when considering a fixed failure probability, revealing a non-enhancement region dependent on state confusability and noise levels.

Contribution

It introduces a unified framework for quantum state discrimination that incorporates both error and failure probabilities, highlighting the conditions for contextuality enhancement and its dependence on noise.

Findings

Contextuality enhancement exists under fixed failure probability.

A non-enhancement region appears depending on state confusability.

Noise reduces the non-enhancement region, eventually eliminating it.

Abstract

Quantum state discrimination enables the accurate identification of quantum states, which are generally nonorthogonal. Among various strategies, minimum-error discrimination and unambiguous state discrimination exhibit contextuality-enhanced success probabilities that surpass classical bounds, offering significant advantages for quantum sensing and communication. However, in practice, both error and failure outcomes can occur, suggesting the need for a unified strategy that incorporates both aspects while exploring the potential for contextuality enhancement. In this work, we theoretically demonstrate contextuality enhancement in quantum state discrimination under a fixed failure probability. We show that this enhancement disappears within a certain intermediate range of failure probabilities--a phenomenon absent in conventional strategies, where both minimum-error and unambiguous discrimination consistently outperform the noncontextual bound for equal priors. Moreover, we analyze how the existence of this non-enhancement region depends on the confusability of the quantum states, which corresponds to their fidelity in a quantum model. We further extend the discussion to the noisy state discrimination, which even encompasses the maximal-confidence discrimination. In this extended discussion, we observe that the non-enhancement region tends to disappear with increasing noise strength.