Distribution of G-concurrence of random pure states

Cappellini, Valerio; Sommers, Hans-Juergen; Zyczkowski, Karol

Distribution of G-concurrence of random pure states

Authors

Cappellini, Valerio

Sommers, Hans-Juergen

Zyczkowski, Karol

Description

Average entanglement of random pure states of an N x N 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 N-th root of the determinant, called G-concurrence. We show that in the limit $N\to\infty$ this quantity becomes concentrated at a single point G=1/e. The position of the concentration point changes if one consider an arbitrary N x K bipartite system, in the joint limit $N,K\to\infty$, K/N fixed.
RevTeX4, 11 pages, 4 Encapsuled PostScript figures - Introduced new results, Section II and V have been significantly improved - To appear on PRA