Distribution of G concurrence of random pure states

The average entanglement of random pure states of an NxN composite system is analyzed. We compute the average value of the determinant D of the reduced state, which forms an entanglement monotone. Calculating higher moments of the determinant, we characterize the probability distribution P(D). Similar results are obtained for the rescaled Nth root of the determinant, called the G concurrence. We show that in the limit N→∞ this quantity becomes concentrated at a single point G*=1/e. The position of the concentration point changes if one consider an arbitrary NxK bipartite system, in the joint limit N,K→∞, with K/N fixed