# Contextual advantage for state discrimination

## TL;DR

This paper establishes noncontextuality inequalities for quantum state discrimination, demonstrating quantum advantage over classical models, with robust, operationally testable violations that highlight fundamental quantum contextuality.

## Contribution

It introduces noncontextuality inequalities specific to quantum state discrimination, linking them to Bell scenarios and providing a framework for experimental validation of quantum contextuality.

## Key findings

- Quantum theory violates noncontextuality inequalities in state discrimination.
- The inequalities are robust to noise and operationally testable.
- A connection between state discrimination and Bell scenarios is demonstrated.

## Abstract

Finding quantitative aspects of quantum phenomena which cannot be explained by any classical model has foundational importance for understanding the boundary between classical and quantum theory. It also has practical significance for identifying information processing tasks for which those phenomena provide a quantum advantage. Using the framework of generalized noncontextuality as our notion of classicality, we find one such nonclassical feature within the phenomenology of quantum minimum error state discrimination. Namely, we identify quantitative limits on the success probability for minimum error state discrimination in any experiment described by a noncontextual ontological model. These constraints constitute noncontextuality inequalities that are violated by quantum theory, and this violation implies a quantum advantage for state discrimination relative to noncontextual models. Furthermore, our noncontextuality inequalities are robust to noise and are operationally formulated, so that any experimental violation of the inequalities is a witness of contextuality, independently of the validity of quantum theory. Along the way, we introduce new methods for analyzing noncontextuality scenarios, and demonstrate a tight connection between our minimum error state discrimination scenario and a Bell scenario.