Diagonal Unitary Covariant Superchannels

TL;DR

This paper fully characterizes diagonal unitary covariant superchannels, providing conditions for their physical validity, a canonical form, and applications to important quantum channels, advancing the understanding of symmetry-restricted quantum processes.

Contribution

It introduces a complete framework for diagonal unitary covariant superchannels, including conditions for complete positivity and trace preservation, and unifies various covariant quantum channels.

Findings

Derived necessary and sufficient conditions for superchannel complete positivity and trace preservation.

Provided a canonical decomposition for DU-covariant superchannels.

Applied framework to analyze amplitude-damping, bit-flip, and Pauli channels.

Abstract

We present a complete characterization of diagonal unitary covariant (DU-covariant) superchannels, i.e. higher-order transformations transforming quantum channels into themselves. Necessary and sufficient conditions for complete positivity and trace preservation are derived and the canonical decomposition describing DU-covariant superchannels is provided. The presented framework unifies and extends known families of covariant quantum channels and enables explicit analysis of their action on physically relevant examples, including amplitude-damping, bit-flip, and Pauli channels. Our results provide a practical toolbox for symmetry-restricted higher-order quantum processes and offer a setting for exploring open problems such as the celebrated PPT$^2$ conjecture.