Archipelagos of Total Bound and Free Entanglement. II

• URL: http://arxiv.org/abs/2002.04084v2
• Date: Thu, 23 Jul 2020 00:55:39 GMT
• Title: Archipelagos of Total Bound and Free Entanglement. II
• Authors: Paul B. Slater
• Abstract summary: We use the well-known necessary and sufficient conditions for positive-semidefiniteness that all leading minors are nonnegative. bound-entanglement probabilities of $frac23 left(sqrt2-1right) approx 0.276142$, $frac14 left(3-2 log 2(2)-log (4)right) approx 0.1632$, $frac12-frac23pi 2 approx 0.432453$ and
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In the indicated preceding preprint (I), we reported the results of, in particular interest here, certain three-parameter qubit-ququart ($2 \times 4$) and two-ququart ($4 \times 4$) analyses. In them, we relied upon entanglement constraints given by Li and Qiao. However, further studies of ours conclusively show--using the well-known necessary and sufficient conditions for positive-semidefiniteness that all leading minors (of separable components, in this context) be nonnegative--that certain of the constraints given are flawed and need to be replaced (by weaker ones). Doing so, leads to a new set of results, somewhat qualitatively different and, in certain respects, simpler in nature. For example, bound-entanglement probabilities of $\frac{2}{3} \left(\sqrt{2}-1\right) \approx 0.276142$, $\frac{1}{4} \left(3-2 \log ^2(2)-\log (4)\right) \approx 0.1632$, $\frac{1}{2}-\frac{2}{3 \pi ^2} \approx 0.432453$ and $\frac{1}{6}$, are reported for various implementations of constraints. We also adopt the Li-Qiao three-parameter framework to a two-parameter one, with interesting visual results.

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