Characterization of qutrit channels in terms of their covariance and symmetry properties

TL;DR

This paper analyzes qutrit channels by examining their covariance and symmetry properties, showing how these symmetries limit the channels' parameters, with a formalism applicable to higher-dimensional systems.

Contribution

It introduces a formalism for characterizing qutrit channels based on their covariance and symmetry, applicable to qudit channels, and details how symmetries constrain channel parameters.

Findings

Symmetry groups restrict channel parameters significantly.

Formalism applies to both discrete and continuous groups.

Results are generalizable to qudit channels.

Abstract

We characterize the completely positive trace-preserving maps on qutrits (qutrit channels) according to their covariance and symmetry properties. Both discrete and continuous groups are considered. It is shown how each symmetry group restricts arbitrariness in the parameters of the channel to a very small set. Although the explicit examples are related to qutrit channels, the formalism is sufficiently general to be applied to qudit channels.