Quantitative characterization of several entanglement detection criteria
- URL: http://arxiv.org/abs/2207.02049v2
- Date: Wed, 21 Sep 2022 18:13:30 GMT
- Title: Quantitative characterization of several entanglement detection criteria
- Authors: A. Sauer, J. Z. Bern\'ad
- Abstract summary: We show 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.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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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