# Compatibility of covariant quantum channels with emphasis on Weyl symmetry

## TL;DR

This paper investigates the compatibility conditions of covariant quantum channels, especially Weyl-covariant channels, simplifying the analysis by leveraging symmetry properties and examining both finite and non-compact phase spaces.

## Contribution

It provides new compatibility criteria for Weyl-covariant channels using symmetry considerations, including cases with finite and non-compact phase spaces.

## Key findings

- Derived compatibility conditions for Weyl-covariant channels
- Simplified compatibility analysis using covariance assumptions
- Analyzed compatibility in both finite and non-compact phase space scenarios

## Abstract

Compatibility conditions of quantum channels featuring symmetry through covariance are studied. Compatibility here means the possibility of obtaining two or more channels through partial trace out of a broadcasting channel. We see that covariance conditions can be used to simplify compatibility conditions as the broadcasting channel can be assumed to be covariant in a particular way. A particular emphasis is on Weyl covariance and in determining compatibility conditions for Weyl-covariant channels. The concrete examples studied include the case of a non-compact continuous phase space and the case of a finite phase space.