  The classical product state capacity of a noisy quantum channel with memory
is investigated. A forgetful noise-memory channel is constructed by Markov
switching between two depolarizing channels which introduces non-Markovian
noise correlations between successive channel uses. The computation of the
capacity is reduced to an entropy computation for a function of a Markov
process. A reformulation in terms of algebraic measures then enables its
calculation. The effects of the hidden-Markovian memory on the capacity are
explored. An increase in noise-correlations is found to increase the capacity.
