  The classical capacity of a quantum channel with arbitrary Markovian
correlated noise is evaluated. For the general case of a channel with long-term
memory, which corresponds to a Markov chain which does not converge to
equilibrium, the capacity is expressed in terms of the communicating classes of
the Markov chain. For an irreducible and aperiodic Markov chain, the channel is
forgetful, and one retrieves the known expression for the capacity.
