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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc73-0-4,
author = {Alberto Barchielli and Giancarlo Lupieri},
title = {Instruments and mutual entropies in quantum information},
journal = {Banach Center Publications},
volume = {72},
year = {2006},
pages = {65-80},
zbl = {1134.81310},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc73-0-4}
}
Alberto Barchielli; Giancarlo Lupieri. Instruments and mutual entropies in quantum information. Banach Center Publications, Tome 72 (2006) pp. 65-80. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc73-0-4/