Quantum and classical informations are considered in quantum measurement processes described by pure operations. The quantum information is given by coherent information in the state change of the measured physical system, and the classical information represented by the Shannon mutual information is obtained from the measurement outcomes. It is shown that if the maximum classical information is obtained, the quantum information becomes zero and if any classical information is not obtained, all the quantum information that the physical system has can be transmitted.
Basic quantum information measures involved in the information analysis of quantum systems are considered. It is shown that the main quantum information measurement methods depend on whether the corresponding quantum events are compatible or incompatible. For purely quantum channels, the coherent and compatible information measures, which are qualitatively different, can be distinguished. A general information scheme is proposed for a quantum-physical experiment. In this scheme, informational optimization of an experimental setup is formulated as a mathematical problem.
Braunstein and Caves showed how quantum information can be used to define a metric for quantum states, relying on attainability of a quantum information bound. We show that the bound is not generally attainable. But a two-stage procedure of repeated measurements achieves the bound in the limit. We connect to the question of whether a generalised measurement on
n independent copies of a quantum system can yield more information than
n separate measurements. Separate measurements are in the limit as informative as joint, and measurement of classical observables suffices.