  We obtain a maximizer for the quantum mutual information for classical
information sent over the quantum qubit amplitude damping channel. This is
achieved by limiting the ensemble of input states to antipodal states, in the
calculation of the product-state capacity for the channel, the resulting
maximizing ensemble consisting of just two non-orthogonal states. We also
consider the product-state capacity of a convex combination of two memoryless
channels and demonstrate in particular that it is in general not given by the
minimum of the capacities of the respective memoryless channels.
