Average Entropy of a Subsystem

Abstract

It was recently conjectured by D. Page that if a quantum system of Hilbert space dimension $nm$ is in a random pure state then the average entropy of a subsystem of dimension $m$ where $m\le n$ is $S_{mn}={\sum }_{k=n+1}^{mn}(1/k)-(m-1)/2n$. In this letter this conjecture is proved.

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• Average Entropy of a Subsystem

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