Quantum measurements and entropic bounds on information transmission

Details Quantum measurements and entropic bounds on information transmission Quantum measurements and entropic bounds on information transmission

2005-05-12

arxiv.org/abs/quant-ph/0505090v1

Quantum Information and Computation 6 (2006) 16-45

Physics

Quantum Physics

29 pages, 2 figures, uses qic.sty

Scientific paper

While a positive operator valued measure gives the probabilities in a quantum measurement, an instrument gives both the probabilities and the a posteriori states. By interpreting the instrument as a quantum channel and by using the monotonicity theorem for relative entropies many bounds on the classical information extracted in a quantum measurement are obtained in a unified manner. In particular, it is shown that such bounds can all be stated as inequalities between mutual entropies. This approach based on channels gives rise to a unified picture of known and new bounds on the classical information (Holevo's, Shumacher-Westmoreland-Wootters', Hall's, Scutaru's bounds, a new upper bound and a new lower one). Some examples clarify the mutual relationships among the various bounds.

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