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 antilinear operators in representing their concurrences. A general expression for some concurrences is derived. We apply it to 1-qubit channels of length 2, getting the 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.

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