2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/97547We 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.Quantum Composite systems 2002, Ustron, Poland, September 2002, talkQuantum Physicstext