Quantitative characterization of several entanglement detection criteria

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