Optimal measurement preserving qubit channels

TL;DR

This paper investigates conditions under which quantum channels preserve optimal measurements for qubit state discrimination, providing characterizations for specific channels and ensembles, and methods to construct such channels.

Contribution

It establishes a necessary and sufficient condition for measurement preservation by qubit channels and characterizes OMP channels for various ensembles and channels.

Findings

Derived a condition for measurement preservation in qubit channels

Characterized OMP channels for specific ensembles and channels

Provided methods to construct sets of OMP channels

Abstract

We consider the problem of discriminating qubit states that are sent over a quantum channel and derive a necessary and sufficient condition for an optimal measurement to be preserved by the channel. We apply the result to the characterization of optimal measurement preserving (OMP) channels for a given qubit ensemble, e.g., a set of two states or a set of multiple qubit states with equal a priori probabilities. Conversely, we also characterize qubit ensembles for which a given channel is OMP, such as unitary and depolarization channels. Finally, we show how the sets of OMP channels for a given ensemble can be constructed.