The classical capacity of quantum channels with memory

TL;DR

This paper studies the classical capacity of specific quantum channels with memory, proving additivity and showing that entangled inputs are unnecessary for capacity achievement.

Contribution

It demonstrates the additivity of capacity for channels with memory and extends results to convex combinations of depolarizing channels.

Findings

Capacity is additive for the studied channels.

Entangled inputs are not needed to achieve capacity.

Results extend to other channels with additive capacity in the memoryless case.

Abstract

We investigate the classical capacity of two quantum channels with memory: a periodic channel with depolarizing channel branches, and a convex combination of depolarizing channels. We prove that the capacity is additive in both cases. As a result, the channel capacity is achieved without the use of entangled input states. In the case of a convex combination of depolarizing channels the proof provided can be extended to other quantum channels whose classical capacity has been proved to be additive in the memoryless case.