A Fisher information-based incompatibility criterion for quantum channels

TL;DR

This paper introduces a Fisher information-based criterion to determine incompatibility of quantum channels, providing analytical conditions for Schur channels and analyzing depolarizing channels, advancing understanding of quantum channel incompatibility.

Contribution

It presents the first analytical incompatibility conditions for two Schur channels and explores the structure of depolarizing channels using the new criterion.

Findings

Analytical conditions for Schur channel incompatibility

Comparison of the criterion with quantum cloning results

Insights into depolarizing channel incompatibility

Abstract

We introduce a new incompatibility criterion for quantum channels, based on the notion of (quantum) Fisher information. Our construction is based on a similar criterion for quantum measurements put forward by H.~Zhu. We then study the power of the incompatibility criterion in different scenarios. Firstly, we prove the first analytical conditions for the incompatibility of two Schur channels. Then, we study the incompatibility structure of a tuple of depolarizing channels, comparing the newly introduced criterion with the known results from asymmetric quantum cloning.