Some problems on the measurement of quantum observables and determination of joint entropy in quantum statistics

Abstract

In the paper the equivalency of a successive measurement of observablesa andb on the Hilbert spaceH and a specially organized measurement of the observablea⊗b on the Hilbert space ℋ=H⊗H is determined. The state, wherein the measurement on ℋ is performed, is shown to be an operator analog of classical joint density of probability distribution. The functionals such as joint and conventional entropy are constructed; the entropy defect of a quantum ensemble and the information quantity contained in quantum measurement are determined.