Volume of the set of separable states. II

The problem of how many entangled or, respectively, separable states there are in the set of all quantum states is investigated. We study to what exte nt the choice of a measure in the space of density matrices Q describing N- dimensional quantum systems affects the results obtained. We demonstrate th at the link between the purity of the mixed states and the probability of e ntanglement is not sensitive to the measure chosen. Since the criterion of partial transposition is not sufficient to distinguish all separable states for N greater than or equal to 8, we develop an efficient algorithm to cal culate numerically the entanglement of formation of a given mixed quantum s tate, which allows us to compute the volume of separable states for N=8 and to estimate the volume of the bound entangled states in this case. [S1050- 2947(99)05110-0].