Metrics, entanglement, and mixedness in the space of two-qubits

We revisit the problem of entanglement-distribution in the 15-dimensional space of two qubits, that has been earlier investigated, via Monte Carlo explorations, assuming that the concomitant states are randomly distributed according to the product measure introduced by Zyczkowski et al. [K. Zyczkowski, P. Horodecki, A. Sanpera, M. Lewenstein, Phys. Rev. A 58 (1998) 883]. In this Letter we consider the influence of the choice of (a) volume measures and (b) different ways of expressing distances between states, in determining some of the entanglement properties unveiled in the associated literature.