Instruments and mutual entropies in quantum information
Volume 73 / 2006
Banach Center Publications 73 (2006), 65-80
MSC: Primary 81P15; Secondary 94A17.
DOI: 10.4064/bc73-0-4
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.
