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 less-than-or-equal-to n is conjectured to be S(m, n) = SIGMA(k = n + 1)mn 1/k - m-1/2n and is shown to be congruent-to ln m - m/2n for 1 << m less-than-or-equal-to 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.