Inclusion relations among separability criteria

Abstract

We revisit the application of different separability criteria by recourse to an exhaustive Monte Carlo exploration involving the pertinent state-space of pure and mixed states. The corresponding chain of implications of different criteria is in such a way numerically elucidated. We also quantify, for a bipartite system of arbitrary dimension, the proportion of states $\rho$ that can be distilled according to a definite criterion. Our work can be regarded as a complement to the recent review paper by B. Terhal [Theor. Comp. Sci. {\bf 287} (2002) 313]. Some questions posed there receive an answer here.