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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