Additivity for transpose depolarizing channels

TL;DR

This paper proves the additivity of the minimal output entropy for the entire family of transpose depolarizing quantum channels, resolving previously open cases using a method from earlier work.

Contribution

It extends the additivity proof to all parameter ranges of transpose depolarizing channels, completing the analysis of this channel family.

Findings

Additivity holds for all transpose depolarizing channels.

The method from previous work effectively addresses open cases.

The entire family of channels is now characterized by this additivity property.

Abstract

Additivity of the minimal output entropy for the family of transpose depolarizing channels introduced by Fannes et al. [quant-ph/0410195] is considered. It is shown that using the method of our previous paper [quant-ph/0403072] allows us to prove the additivity for the range of the parameter values for which the problem was left open in [quant-ph/0410195]. Together with the result of [quant-ph/0410195], this covers the whole family of transpose depolarizing channels.