  This paper considers a class of qubit channels for which three states are
always sufficient to achieve the Holevo capacity. For these channels it is
known that there are cases where two orthogonal states are sufficient, two
non-orthogonal states are required, or three states are necessary. Here a
systematic theory is given which provides criteria to distinguish cases where
two states are sufficient, and determine whether these two states should be
orthogonal or non-orthogonal. In addition, we prove a theorem on the form of
the optimal ensemble when three states are required, and present efficient
methods of calculating the Holevo capacity.
