  We propose constructive approaches for the optimization of binary classical
communication over a general noisy qubit quantum channel, for both the error
probability and the classical capacity functionals. After showing that the
optimal measurements are always associated to orthogonal projections, we
construct a parametrization of the achievable transition probabilities via the
coherence vector representation. We are then able to rewrite the problem in a
form that can be solved by standard, efficient numerical algorithms and
provides insights on the form of the solutions.
