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≤n is conjectured to be ${\mathit{S}}_{\mathit{m},\mathit{n}}$= ${\mathit{S}}_{\mathit{k}=\mathit{n}+1\mathrm{}}^{\mathit{mn}}$ 1/k-m-1/2n and is shown to be ≃lnm-m/2n for 1≪m≤n. 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.