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

TL;DR

This paper investigates mixed unitary channels generated by finite subgroups, establishing conditions under which certain output characteristics like $l_p$-norms and minimal entropy are multiplicative or additive when channels are combined via tensor products, and applies these results to compute classical capacities.

Contribution

It introduces techniques based on majorization theory to analyze output states of mixed unitary channels, identifying classes where entanglement offers no advantage and deriving explicit formulas for classical capacity.

Findings

$l_p$-norms are multiplicative for certain channels.

Minimal entropy is additive under tensor products.

Classical capacity can be explicitly calculated for these channels.

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.