The Bures-Hall ensemble is a unique measure of density matrices that satisfies various distinguished properties in quantum information processing. In this work, we study the statistical behavior of entanglement over the Bures-Hall ensemble as measured by the simplest form of an entanglement entropy - the quantum purity. The main results of this work are the exact second and third moment expressions of quantum purity valid for any subsystem dimensions, where the corresponding results in the literature are limited to the scenario of equal subsystem dimensions. In obtaining the results, we have derived recurrence relations of the underlying integrals over the Cauchy-Laguerre biorthogonal polynomials that may be of independent interest.
翻译:Bures- Hall 组合体是一种独特的密度矩阵测量标准,它满足了量子信息处理中各种不同特性的特点。 在这项工作中,我们研究了以最简单的缠绕酶形式测量的Bures- Hall 组合体的纠缠的统计行为 -- -- 量子纯度。这项工作的主要结果是对任何子系统层面都有效的量子纯度的准确的第二和第三秒表达,文献中的相应结果仅限于等分子维维度的情景。在获得结果时,我们从Cauchy-Laguerre biorthogoal 多元体中产生了潜在组成部分的复发关系,而这种联系可能具有独立的兴趣。