Information and entropy in quantum measurement processes

Quantum measurement processes of discrete and continuous observables are considered from the information-theoretic point of view. The information extracted from the results of quantum measurement performed on a physical system and the change of the Shannon entropy of the measured physical system are investigated in detail. It is shown that the amount of information about the intrinsic observable of the measured physical system can be expressed by the mutual information between the physical system and the measurement apparatus if the intrinsic observable commutes with the operational observable defined by the quantum measurement process. Furthermore, the condition can be obtained under which the amount of information extracted from the measurement outcomes becomes equal to the decrease of the entropy of the measured physical system. In addition, the change of the Shannon entropy is compared with that of the von Neumann entropy. The general results do not depend on whether the readout of the measurement outcome obeys the projection postulate or not. Several examples of quantum measurement processes are considered to examine the general results.