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Average Entropy of a Subsystem
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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 $m \leq n$ is $ S_{mn} = \sum^{mn}_{k=n+1}(1/k) - (m-1)/2n$. In this letter this conjecture is proved.
Forward citations
Cited by 3 Pith papers
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Revisiting the Page curve and its moments. A combinatorial approach
Derives closed expressions for power moments of entanglement entropy of random states via Schur-Weyl duality and S_N character theory.
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The Maximal Entanglement Limit in Statistical and High Energy Physics
Quantum systems reach a Maximal Entanglement Limit where entanglement geometry produces thermal reduced density matrices and probabilistic behavior in statistical and high-energy physics.
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Modifications of the Page Curve from correlations within Hawking radiation
For a qubit model of Bell-pair Hawking emission, the per-step change in radiation entanglement entropy is bounded between (1-4*epsilon2^2-sqrt(1-gamma^2))*log2 and sqrt(1-4*epsilon2^2)*log2, yielding an early Page-cur...
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