Abstract
Recently it has been shown that quantum theory can be viewed as a classical probability theory by treating Hilbert space as a measure space (H, B(H)) of “events” or “hidden states.” Each density operator\(\hat W = \sum _{n = 1}^\infty {\text{ }}w_n \hat \prod _{E_n } \) defines a setℳ ŵ of probability measures such thatμ(E n )=w n (alln). Coding elements ψεH by subspacesE n entails distortion. We show that the von Neumann entropyS(Ŵ) = -trŴInŴequals the effective rate at which the Hilbert space produces information with zero expected distortion, and comment on the meaning of this.
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References
Bach, A. (1980).J. Math. Phys.,21, 789–793.
Cyranski, J. F. (1982).J. Math. Phys.,23, 1074–1077.
Papoulis, A. (1965).Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York).
Werhl, A. (1978).Rev. Mod. Phys.,50, 221.
Jauch, J. M. (1968).Foundations of Quantum Mechanics (Addison-Wesley, Reading, Massachusetts).
Messiah, A. (1968).Quantum Mechanics (North-Holland, Amsterdam).
Berger, T. (1971).Rate Distortion Theory (Prentice-Hall, Englewood Cliffs, New Jersey).
Cyranski, J. F. (1981).Inform. Sci.,24, 217–227.
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Cyranski, J.F. Von neumann entropy as information rate. Int J Theor Phys 24, 175–178 (1985). https://doi.org/10.1007/BF00672651
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DOI: https://doi.org/10.1007/BF00672651