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Von neumann entropy as information rate

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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 set 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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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

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