On characteristics of mixed unitary channels being additive or multiplicative with respect to taking tensor products

Abstract: We study mixed unitary channels generated by finite subgroups of the group of all unitary operators in a Hilbert space. Based on the majorization theory we introduce techniques allowing to calculate different characteristics of output states of channels. A class of channels has been allocated for which the use of entangled states doesn't give any advantage under taking supremum and infimum for output characteristics of channels. In particular, $l_p$-norms are multiplicative and the minimal entropy is additive with respect to taking tensor products of channels. As an important application of the obtained results the classical capacity of channel is calculated in the evident form. We compare our techniques with the informational characteristics of Boson quantum channels.