Relative Entropy and Single Qubit Holevo-Schumacher-Westmoreland Channel Capacity
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چکیده
The relative entropy description of Holevo-Schumacher-Westmoreland (HSW) classical channel capacities is applied to single qubit quantum channels. A simple formula for the relative entropy of qubit density matrices in the Bloch sphere representation is derived. The formula is combined with the King-Ruskai-Szarek-Werner qubit channel ellipsoid picture to analyze several unital and non-unital qubit channels in detail. An alternate proof is presented that the optimal HSW signalling states for single qubit unital channels are those states with minimal channel output entropy. The derivation is based on symmetries of the relative entropy formula, and the King-Ruskai-SzarekWerner qubit channel ellipsoid picture. A proof is given that the average output density matrix of any set of optimal HSW signalling states for a ( qubit or non-qubit ) quantum channel is unique.
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تاریخ انتشار 2002