  We consider generalizations of depolarizing channels to maps in which the
identity channel is replaced by a convex combinations of unitary conjugations.
  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.
