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.
Similar content being viewed by others
References
Davies, E.B., Lewis, J.T.: Commun. math. Phys.17, 239–260 (1970)
von Neumann, J.: Mathematical foundations of quantum mechanics. Trans. by R.T. Beyer. Princeton: University Press 1955
Levitin, L.B.: Trudy IV Vsesoyuznoi Konfer. po Teorii Inform. i Kodirovaniya (English translation: Proceedings of the IV All-Union Conference on Theory of Information and Encoding) Tashkent 11172-115, 1969
Author information
Authors and Affiliations
Additional information
Communicated by R. Haag
Rights and permissions
About this article
Cite this article
Vainshtein, V.D., Tvorogov, S.D. Some problems on the measurement of quantum observables and determination of joint entropy in quantum statistics. Commun.Math. Phys. 43, 273–278 (1975). https://doi.org/10.1007/BF02345024
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02345024