  We construct a class of quantum channels in arbitrary dimensions for which
entanglement improves the performance of the channel. The channels have
correlated noise and when the level of correlation passes a critical value we
see a sharp transition in the optimal input states (states which minimize the
output entropy) from separable to maximally entangled states. We show that for
a subclass of channels with some extra conditions, including the examples which
we consider, the states which minimize the output entropy are the ones which
maximize the mutual information.
