Optimal super dense coding over memory channels

We study the superdense coding capacity in the presence of quantum channels with correlated noise. We investigate both the cases of unitary and nonunitary encoding. Pauli channels for arbitrary dimensions are treated explicitly. The superdense coding capacity for some special channels and resource states is derived for unitary encoding. We also provide an example of a memory channel where nonunitary encoding leads to an improvement in the superdense coding capacity.