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Instruments and mutual entropies in quantum information

Alberto Barchielli·Giancarlo Lupieri
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Abstract

General quantum measurements are represented by instruments. In this paper the mathematical formalization is given of the idea that an instrument is a channel which accepts a quantum state as input and produces a probability and an a posteriori state as output. Then, by using mutual entropies on von Neumann algebras and the identification of instruments and channels, many old and new informational inequalities are obtained in a unified manner. Such inequalities involve various quantities which characterize the performances of the instrument under study; in particular, these inequalities include and generalize the famous Holevo's bound.

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Alberto Barchielli, Giancarlo Lupieri. 2004-12-15. Instruments and mutual entropies in quantum information. https://arxiv.org/abs/quant-ph/0412116

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