On Weyl-covariant channels

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.