Quantitative characterization of several entanglement detection criteria

Abstract

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 Rényi-entropy-based criteria are very ineffective compared to the positive partial transpose. In the case of the Rényi-entropy-based criterion, we show that the ratio of detectable entanglement increases with the order of the Rényi entropy.

8 pages, 4 figures

References in corpus (5)

• Entanglement detection
• Bloch vectors for qudits
• Entanglement detection beyond the cross-norm or realignment criterion
• Majorization criterion for distillability of a bipartite quantum state
• Bell nonlocality and fully-entangled fraction measured in an entanglement-swapping device without quantum state tomography