Discrimination of symmetric states in operational probabilistic theory

TL;DR

This paper demonstrates that in operational probabilistic theories, symmetric state sets admit minimum-error measurements with the same symmetry, extending known quantum results to a broader theoretical framework and aiding measurement optimization.

Contribution

It proves the symmetry property of minimum-error measurements in general OPTs, generalizing quantum theory results and enabling measurement class restrictions for optimization.

Findings

Symmetric state sets have symmetric minimum-error measurements in OPTs.

The result applies to optimizing sequential and separable measurements.

Extends quantum symmetry results to operational probabilistic theories.

Abstract

A state discrimination problem in an operational probabilistic theory (OPT) is investigated in diagrammatic terms. It is well-known that, in the case of quantum theory, if a state set has a certain symmetry, then there exists a minimum-error measurement having the same type of symmetry. However, to our knowledge, it is not yet clear whether this property also holds in a more general OPT. We show that it also holds in OPTs, i.e., for a symmetric state set, there exists a minimum-error measurement that has the same type of symmetry. It is also shown that this result can be utilized to optimize over a restricted class of measurements, such as sequential or separable measurements.