Distinguishability, Ensemble Steering, and the No-Signaling Principle

TL;DR

This paper develops a formalism for minimum-error state discrimination in generalized probabilistic theories, revealing that distinguishability depends on ensemble properties and is constrained by ensemble steering and no-signaling principles.

Contribution

It introduces a general convex optimization framework for state discrimination and demonstrates that distinguishability is governed by the interplay of ensemble steering and no-signaling, independent of state space structure.

Findings

Distinguishability is a global property of the ensemble.

Ensemble steering and no-signaling tightly constrain distinguishability.

The results are independent of the specific state space structure.

Abstract

We consider a fundamental operational task, distinguishing systems in different states, in the framework of generalized probabilistic theories and provide a general formalism of minimum-error discrimination of states in convex optimization. With the formalism established, we show that the distinguishability is generally a global property assigned to the ensemble of given states rather than other details of a given state space or pairwise relations of given states. Then, we consider bipartite systems where ensemble steering is possible, and show that show that with two operational tasks, ensemble steering and the no-signaling condition, the distinguishability is tightly determined. The result is independent to the structure of the state space. This concludes that the distinguishability is generally determined by the compatibility between two tasks, ensemble steering on states and the non-signaling principle on probability distributions of outcomes.