We study the capacity of d-dimensional quantum channels with memory modeled by correlated noise. We show that, in agreement with previous results on Pauli qubit channels, there are situations where maximally entangled input states achieve higher values of mutual information than product states. Moreover, a strong dependence of this effect on the nature of the noise correlations as well as on the parity of the space dimension is found. We conjecture that when entanglement gives an advantage in terms of mutual information, maximally entangled states saturate the channel capacity.
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