  Explicit expressions for the concurrence of all positive and trace-preserving
("stochastic") 1-qubit maps are presented. By a new method we find the relevant
convex roof pattern. We conclude that two component optimal decompositions
always exist. Our results can be transferred to $2 \times n$-quantum systems
providing the concurrence for all rank two density operators as well as a lower
bound for their entanglement of formation.
