Minimum error discrimination between similarity transformed quantum states

TL;DR

This paper develops a new approach to minimum error discrimination of quantum states, especially similarity transformed and symmetric states, by reformulating the conditions for optimal measurements and success probabilities.

Contribution

It introduces a convex combination method to simplify MED conditions and applies it to similarity transformed and symmetric quantum states.

Findings

Derived a convenient form for MED conditions using convex combinations.

Applied the method to similarity transformed quantum states.

Analyzed MED for group covariant or symmetric states.

Abstract

Using the known necessary and sufficient conditions for minimum error discrimination (MED), first it is shown that a Helstrom family of ensembles is equivalent to these conditions and then by a convex combination of the initial states (the states which we try to discriminate them) and the corresponding conjugate states, a more suitable and convenient form for the MED conditions is extracted, so that optimal set of measurements and corresponding optimal success probability of discrimination can be determined. Then, using the introduced identity, MED between N similarity transformed equiprobable quantum states is investigated. As a special case, MED between the so called group covariant or symmetric states is considered.