Average entropy of a subsystem

If a quantum system of Hilbert space dimension mn is in a random pure state, the average entropy of a subsystem of dimension m is conjectured to be S₌, ₍= S₊=₍+₁^mn 1/k-m-1/2n and is shown to be -m/2n for 1. Thus there is less than one-half unit of information, on average, in the smaller subsystem of a total system in a random pure state.