  The physically allowed quantum evolutions on a single qubit can be described
in terms of their geometry. From a simple parameterisation of unital
single-qubit channels, the canonical form of all such channels can be given.
The related geometry can be used to understand how to approximate positive maps
by completely-positive maps, such as in the case of optimal eavesdropping
strategies. These quantum channels can be generated by the appropriate network
or through dynamical means. The Str{\o}mer-Woronowisc result can also be
understood in terms of this geometry.
