  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.
