Operational Discriminability: From Noncontextuality Bounds to Bell Correlations

TL;DR

This paper introduces an operational discriminability measure using a two-copy comparison game, linking it to preparation contextuality and Bell correlations, and providing bounds within ontological models.

Contribution

It develops a new operational discriminability concept based on a two-copy comparison game and connects it to contextuality and Bell nonlocality bounds.

Findings

The game score $D_{op}$ is experimentally accessible and does not rely on minimum-error discrimination.

Within a preparation-noncontextual model, a sharp upper bound on the game score is derived and saturated in qubit realizations.

Discriminability constrains Bell correlations, establishing it as an operational resource.

Abstract

We investigate discriminability from an operational and contextuality-oriented perspective using a two-copy comparison game based on SWAP-type measurements. The resulting score $D_{\mathrm{op}}$ provides an experimentally accessible notion of distinguishability that does not rely on a minimum-error discrimination task. We first examine whether this discriminability game can directly witness preparation contextuality. Within a preparation-noncontextual ontological model, we derive a direct upper bound on the game score under a SWAP-like comparison rule and a sharp single-copy test, and show that this bound is saturated in the natural qubit realization. Thus, the direct game alone does not provide a contextuality witness in that regime. We then consider a Bell-coupled scenario in which two-copy comparison measurements are applied to Bob's conditional preparations. This yields a state-dependent upper bound on the CHSH value in terms of operational separation parameters, and hence in terms of the distinguishability of the conditional states. Our results establish a quantitative link between operational discriminability and the strength of nonclassical correlations, showing that discriminability can act as an operational resource constraining Bell-type nonclassical correlations.