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arXiv · 2207.02049

Quantitative characterization of several entanglement detection criteria

A. Sauer·J. Z. Bernád
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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 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.

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A. Sauer, J. Z. Bernád. 2022-07-05. Quantitative characterization of several entanglement detection criteria. https://doi.org/10.1103/physreva.106.032423

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