  We study the performance of a partially correlated amplitude damping channel
acting on two qubits. We derive lower bounds for the single-shot classical
capacity by studying two kinds of quantum ensembles, one which allows to
maximize the Holevo quantity for the memoryless channel and the other allowing
the same task but for the full-memory channel. In these two cases, we also show
the amount of entanglement which is involved in achieving the maximum of the
Holevo quantity. For the single-shot quantum capacity we discuss both a lower
and an upper bound, achieving a good estimate for high values of the channel
transmissivity. We finally compute the entanglement-assisted classical channel
capacity.
