Bures可分性函数的类Dyson指数行为
Dyson-Index-Like Behavior of Bures Separability Functions
摘要：
我们进行了一项研究的基础上Bures（最小单调）度量，类似于最近报道的希尔伯特-施密特（平坦或欧几里德）度量（arXiv：0704.3723v2）。在获得的有趣结果中，在实数、复数和四元数量子比特-量子比特情形下，分离函数S_{type}（μ）的四次、二次和一次幂之间存在比例关系--与随机矩阵理论的戴森指数β= 1、2、4完全对应。这里μ= \sqrt{\frac{ρ_{11} ρ_{44}}{ρ_{22} ρ_{33}}}，ρ是4 x 4密度矩阵。在密度矩阵的布卢尔（相关系数/非对角标度）参数化框架内，分离性函数已证明对计算分离性概率是有用的。我们发现-对于某些基本的简单场景（其中ρ的对角线项是不受限制的，并且一个或两个非对角线（实数，复数或四元数）项对是非零的）-这些比例不再严格地在Bures情况下成立，但确实非常接近。
英文摘要：
We conduct a study based on the Bures (minimal monotone) metric, analogous to that recently reported for the Hilbert-Schmidt (flat or Euclidean) metric (arXiv:0704.3723v2). Among the interesting results obtained there had been proportionalities--in exact correspondence to the Dyson indices β= 1, 2, 4 of random matrix theory--between the fourth, second and first powers of the separability functions S_{type}(μ) for real, complex and quaternionic qubit-qubit scenarios, Here μ=\sqrt{\frac{ρ_{11} ρ_{44}}{ρ_{22} ρ_{33}}}, with ρbeing a 4 x 4 density matrix. Separability functions have proved useful--in the framework of the Bloore (correlation coefficient/off-diagonal scaling) parameterization of density matrices--for the calculation of separability probabilities. We find--for certain, basic simple scenarios (in which the diagonal entries of ρare unrestricted, and one or two off-diagonal [real, complex or quaternionic] pairs of entries are nonzero) --that these proportionalities no longer strictly hold in the Bures case, but do come remarkably close to holding.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
