  In this paper we study quantum communication channels with correlated noise
effects, i.e., quantum channels with memory. We derive a model for correlated
noise channels that includes a channel memory state. We examine the case where
the memory is finite, and derive bounds on the classical and quantum
capacities. For the entanglement-assisted and unassisted classical capacities
it is shown that these bounds are attainable for certain classes of channel.
Also, we show that the structure of any finite memory state is unimportant in
the asymptotic limit, and specifically, for a perfect finite-memory channel
where no nformation is lost to the environment, achieving the upper bound
implies that the channel is asymptotically noiseless.
