Unitary-process discrimination with error margin

TL;DR

This paper explores a unified approach to discriminating between quantum unitary processes by introducing an error margin, analyzing cases with and without group symmetry, and highlighting the role of entanglement in improving discrimination success.

Contribution

It presents a novel discrimination scheme that interpolates between minimum-error and unambiguous discrimination, with solutions for processes with general priors and group symmetry.

Findings

Unambiguous discrimination success is either 0 or 1 under group symmetry.

Entanglement with an auxiliary system enhances discrimination performance.

The scheme provides a continuum between existing discrimination methods.

Abstract

We investigate a discrimination scheme between unitary processes. By introducing a margin for the probability of erroneous guess, this scheme interpolates the two standard discrimination schemes: minimum-error and unambiguous discrimination. We present solutions for two cases. One is the case of two unitary processes with general prior probabilities. The other is the case with a group symmetry: the processes comprise a projective representation of a finite group. In the latter case, we found that unambiguous discrimination is a kind of "all or nothing": the maximum success probability is either 0 or 1. We also closely analyze how entanglement with an auxiliary system improves discrimination performance.