论文标题
总约束和自由纠缠的群岛。 ii
Archipelagos of Total Bound and Free Entanglement. II
论文作者
论文摘要
在上述预印本（i）中，我们在这里特别感兴趣的结果是某些三参数Qubit-ququart（$ 2 \ tims 4 $）和两分点（$ 4 \ times 4 $）分析。在其中，我们依靠Li和Qiao给出的纠缠约束。然而，对我们的进一步研究最终表明 - 使用众所周知的积极和足够的条件，以表明所有领先的未成年人（在这种情况下，可分离的成分）都是无负的 - 所给出的某些约束是有缺陷的，需要替换（较弱的）。这样做会导致一系列新的结果，在质上有些不同，并且在某些方面，本质上更简单。例如，$ \ frac {2} {2} {3} \ left（\ sqrt {2} -1 \ right）\大约0.276142 $，$ \ frac {1} {1} {4} {4 $ \ frac {1} {2} - \ frac {2} {3π^2} \大约0.432453 $和$ \ frac {1} {6} {6} $，以用于各种约束。我们还将Li-Qiao三参数框架采用到两参数的框架，并具有有趣的视觉结果。
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 $\frac{2}{3} \left(\sqrt{2}-1\right) \approx 0.276142$, $\frac{1}{4} \left(3-2 \log ^2(2)-\log (4)\right) \approx 0.1632$, $\frac{1}{2}-\frac{2}{3 π^2} \approx 0.432453$ 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.
