Profitable entanglement for channel discrimination

TL;DR

This paper analyzes when side entanglement improves the success probability in discriminating between two generic qubit channels, providing exact conditions and focusing on extremal and interior channels within the set of CPTP maps.

Contribution

It offers a detailed characterization of when entanglement enhances channel discrimination, including conditions for both beneficial and non-beneficial cases.

Findings

Entanglement can be profitable for channel discrimination under specific conditions.

Exact criteria are derived for extremal qubit channels.

The analysis covers channels both on the boundary and inside the set of CPTP maps.

Abstract

We investigate the usefulness of side entanglement in discriminating between two generic qubit channels, {\ up to unitary pre- and post-processing,} and determine exact conditions under which it does enhance (as well as conditions under which it does not) the success probability. This is done in a constructive way by first analyzing the problem for channels that are extremal in the set of completely positive and trace-preserving qubit linear maps and then for channels that are inside such a set.