SIMPLE PROOF OF PAGES CONJECTURE ON THE AVERAGE ENTROPY OF A SUBSYSTEM

It is shown that Page's formula for the average entropy S-m,S-n of a s ubsystem of dimension m less than or equal to 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 P age's conjecture, S-m,S-n, = Sigma(k=n+1)(mn) 1/k - 2n/m-1, which is s impler than that given by Foong and Kanno [Phys. Rev. Lett. 72, 1148 ( 1994)].