On 1-qubit channels

Details On 1-qubit channels On 1-qubit channels

2000-11-27

arxiv.org/abs/quant-ph/0011106v3

J. Phys. A: Math. Gen. 34 (2001) 7047 - 7055

Physics

Quantum Physics

12 pages, several printing or latex errors corrected

Scientific paper

10.1088/0305-4470/34/35/329

The entropy H_T(rho) of a state rho 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 associating an Hermitian antilinear operator theta to every channel of the considered class. The concurrence of the channel can be expressed by theta and turns out to be a flat roof. This allows to write down an explicit expression for H_T. Its maximum would give the Holevo (1-shot) capacity.

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