Abstract
The entropy HT (ρ) of a state with respect to a channel T and the Holevo capacity of the channel require the solution of difficult variational problems. For a class of 1-qubit channels, which contains all the extremal ones, the problem can be significantly simplified by attaching a unique Hermitian antilinear operator ϑ to every channel of the considered class. The channel's concurrence CT can be expressed by ϑ and turns out to be a flat roof. This allows to write down an explicit expression for HT. Its maximum would give the Holevo (one-shot) capacity.