Simple proof of Page’s conjecture on the average entropy of a subsystem

It is shown that Page’s formula for the average entropy S(m,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, Sm,n = tsum(k=n+1)mn1/k-m-1/2n, which is simpler than that given by Foong and Kanno [Phys. Rev. Lett. 72, 1148 (1994)].Publicad