  Quantitative characterization of different entanglement detection criteria
for bipartite systems is presented. We review the implication sequence of these
criteria and then numerically estimate volume ratios between criteria
non-violating quantum states and all quantum states. The numerical approach is
based on the hit-and-run algorithm, which is applied to the convex set of all
quantum states embedded into a Euclidean vector space of the Hilbert-Schmidt
inner product. We demonstrate that reduction, majorization, and the
R\'enyi-entropy-based criteria are very ineffective compared to the positive
partial transpose. In the case of the R\'enyi-entropy-based criterion, we show
that the ratio of detectable entanglement increases with the order of the
R\'enyi entropy.
