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Simple proof of Page’s conjecture on the average entropy of a subsystem
Phys. Rev. E 52, 5653 – Published 1 November, 1995
DOI: https://doi.org/10.1103/PhysRevE.52.5653
Abstract
It is shown that Page’s formula for the average entropy n of a subsystem of dimension m≤n of a quantum system of Hilbert space dimension mn in a pure state [Phys. Rev. Lett. 71, 1291 (1993)] can be written in terms of the one-point correlation function of a Laguerre ensemble of random matrices. This leads to a proof of Page’s conjecture, n=1/k-m-1/2n, which is simpler than that given by Foong and Kanno [Phys. Rev. Lett. 72, 1148 (1994)].
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