  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.
