  We consider explicitly two examples of d-dimensional quantum channels with
correlated noise and show that, in agreement with previous results on Pauli
qubit channels, there are situations where maximally entangled input states
achieve higher values of the output mutual information than product states. We
obtain a strong dependence of this effect on the nature of the noise
correlations as well as on the parity of the space dimension, and conjecture
that when entanglement gives an advantage in terms of mutual information,
maximally entangled states achieve the channel capacity.
