Concurrence and foliations induced by some 1-qubit channels

We start with a short introduction to the roof concept. An elementary discussion of phase-damping channels shows the role of anti-linear operators in representing their concurrence. A general expression for some concurrences is derived. We apply it to 1-qubit channels of length two, getting induced foliations of the state space, the optimal decompositions, and the entropy of a state with respect to these channels. For amplitude-damping channels one obtains an expression for the Holevo capacity allowing for easy numerical calculations.