We conduct a pair of quasirandom estimations of the separability probabilities with respect to 10 measures on the 15-dimensional convex set of two-qubit states, using its Euler-angle parametrization. The measures include the (nonmonotone) Hilbert–Schmidt one, plus nine others based on operator monotone functions. Our results are supportive of previous assertions that the Hilbert–Schmidt and Bures (minimal monotone) separability probabilities are 833≈0.242424 and 25341≈0.0733138, respectively, as well as suggestive of the Wigner–Yanase counterpart being 120. However, one result appears inconsistent (much too small) with an earlier claim of ours that the separability probability associated with the operator monotone (geometric-mean) function x is 1−25627π2≈0.0393251. But a seeming explanation for this disparity is that the volume of states for the x-based measure is infinite. So, the validity of the earlier conjecture — as well as an alternative one, 19(593−60π2)≈0.0915262, we now introduce — cannot be examined through the numerical approach adopted, at least perhaps not without some truncation procedure for extreme values.

中文翻译：

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基于双量子位算子-单调的可分概率的拟随机估计

我们使用其欧拉角参数化对两个量子位状态的 15 维凸集上的 10 个度量的可分离概率进行了一对拟随机估计。这些措施包括（非单调）希尔伯特施密特一项，以及其他九项基于算子单调函数的措施。我们的结果支持先前的断言，即 Hilbert-Schmidt 和 Bures（最小单调）可分性概率是833≈0.242424和25341≈0.0733138，分别，以及暗示 Wigner-Yanase 对应物是120. 然而，一个结果似乎与我们先前的主张不一致（太小），即与算子单调（几何平均）函数相关的可分离概率X是1-25627π2≈0.0393251. 但对这种差异的一个表面上的解释是X基于 - 的度量是无限的。所以，早期猜想的有效性——以及另一种猜想，19(593-60π2)≈0.0915262，我们现在介绍 - 不能通过所采用的数值方法来检查，至少在没有一些极值截断程序的情况下可能不会。