Structure of Optimal State Discrimination in Generalized Probabilistic Theories

TL;DR

This paper develops a general convex optimization approach to optimal state discrimination within generalized probabilistic theories, revealing shared properties with quantum state discrimination such as measurement non-uniqueness.

Contribution

It introduces a universal method for optimal discrimination in GPTs using convex optimization, independent of specific state-effect relations.

Findings

Optimal discrimination sometimes requires no measurement.

Optimal measurement is not unique in GPTs.

Properties of quantum state discrimination extend to GPTs.

Abstract

We consider optimal state discrimination in a general convex operational framework, so-called generalized probabilistic theories (GPTs), and present a general method of optimal discrimination by applying the complementarity problem from convex optimization. The method exploits the convex geometry of states but not other detailed conditions or relations of states and effects. We also show that properties in optimal quantum state discrimination are shared in GPTs in general: i) no measurement sometimes gives optimal discrimination, and ii) optimal measurement is not unique.