Maximal output purity and capacity for asymmetric unital qudit channels

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Abstract
We consider generalizations of depolarizing channels to maps which are convex combinations of unitary conjugations (rather than the identity) and the completely noisy map. We show that one can construct unital channels of this type for which the input which achieves maximal output purity is unique. We give conditions under which multiplicativity of the maximal p-norm and additivity of the minimal output entropy. We also show that the Holevo capacity need not equal log d - the minimal entropy as one might expect for a convex combination of unitary conjugations. Conversely, we give examples for which this condition holds, but the channel has no evident covariance properties.

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