On Weyl-covariant channels

TL;DR

This paper develops a formalism for discrete noncommutative Fourier transforms and applies it to analyze Weyl-covariant channels, extending bounds on their output norms and proving multiplicativity properties for certain classes.

Contribution

It introduces a new formalism for analyzing Weyl-covariant channels and proves multiplicativity of the maximal output 2-norm for specific classes of these channels.

Findings

Extended a bound on the maximal output 2-norm of Weyl-covariant channels.

Identified a class of channels that attain this bound.

Proved multiplicativity of the maximal output 2-norm for these channels.

Abstract

Formalism of discrete noncommutative Fourier transform is developed and applied to the study of Weyl-covariant channels. We then extend a result in quant-ph/0509126 concerning a bound of the maximal output 2-norm of a Weyl-covariant channel. A class of channels which attain the bound is introduced, for which the multiplicativity of the maximal output 2-norm is proven. Complementary channels are described which share the multiplicativity properties with the Weyl-covariant channels.