  The relative entropy description of Holevo-Schumacher-Westmoreland (HSW)
classical channel capacity is applied to single qubit channels. A simple
formula for the relative entropy of qubit density matrices in the Bloch sphere
representation is derived. This formula is combined with the
King-Ruskai-Szarek-Werner qubit channel ellipsoid picture to analyze several
unital and non-unital qubit channels in detail. An alternate proof that the
optimal HSW signalling states for single qubit unital channels are those states
with the minimum channel output entropy is presented. The derivation is based
on the symmetries of the qubit relative entropy formula and the
King-Ruskai-Szarek-Werner qubit channel ellipsoid picture. A proof is given
that the average output density matrix of any set of optimal HSW signalling
states for a (qubit or non-qubit) quantum channel is unique.
