Von Neumann entropy as information rate
type: Item
instance of: scholarly article
title: Von Neumann entropy as information rate
zbMATH Open document ID: 0563.60097
DOI: 10.1007/BF00672651
author: John F. Cyranski
published in: International Journal of Theoretical Physics
publication date: 1985-01-01T00:00:00Z
review text: 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 \(\hat W=\sum^{\infty}_{n=1}w_ n{\hat \Pi}_{E_ n}\) defines a set \({\mathcal M}_{\hat W}\) of probability measures such that \(\mu (E_ n)=w_ n\) (all n). Coding elements \(\psi\in H\) by subspaces \(E_ n\) entails distortion. We show that the von Neumann entropy \(S(\hat W)=-tr \hat W \ln \hat W\) equals the effective rate at which the Hilbert space produces information with zero expected distortion, and comment on the meaning of this.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 81P20
zbMATH DE Number: 3897993
zbMATH Keywords: hidden states
zbMATH Keywords: von Neumann entropy
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3897993