Theory of measurement of entangled states

Problem on reconstruction of state of finite-dimension quantum information transfer channel, pure or mixed, by results of measurements of needed number of observables, is considered. It is shown that in general case it is needed to measure incompatible observables in number exceeding by one dimension of space of vectors of state. Each of incompatible observables is measured in its statistically valuable series of measurements. In special case, when one of observables is a non-demolition observable, measurement of the other observables is needed for realization of control of property of non-demolition. In case of paired channel it is shown that results of measurements of observables that do not demolish states of sub-channels are characterized by mutual distribution of probabilities while results of measurement of over-classical observables are characterized by mutual correlation only. This correlation vanishes completely in case of pure unentangled states.