Bures-Hall包络：谱密度和平均熵
Bures-Hall Ensemble: Spectral Densities and Average Entropies
摘要：
我们考虑一组随机密度矩阵按Bures测度分布。相应的联合概率密度的特征值描述的固定跟踪Bures-Hall合奏随机矩阵，反过来，是通过拉普拉斯变换与其无限制的跟踪对应。我们调查这两个合奏的谱统计，特别是，专注于水平密度，我们得到确切的封闭形式的结果涉及Pfavians。在固定迹的情况下，使用能级密度表达式来获得作为有限和的平均Havrda-Charvát-Tsallis（HCT）熵的精确结果。通过考虑平均HCT表达式中的适当限制，讨论了冯诺伊曼熵、线性熵和纯度。基于对平均冯诺伊曼熵和平均纯度的精确估计，我们还推测了类似于Hilbert-Schmidt系综的非常简单的公式。
英文摘要：
We consider an ensemble of random density matrices distributed according to the Bures measure. The corresponding joint probability density of eigenvalues is described by the fixed trace Bures-Hall ensemble of random matrices which, in turn, is related to its unrestricted trace counterpart via a Laplace transform. We investigate the spectral statistics of both these ensembles and, in particular, focus on the level density, for which we obtain exact closed-form results involving Pfaffians. In the fixed trace case, the level density expression is used to obtain an exact result for the average Havrda-Charvát-Tsallis (HCT) entropy as a finite sum. Averages of von Neumann entropy, linear entropy and purity follow by considering appropriate limits in the average HCT expression. Based on exact evaluations of the average von Neumann entropy and the average purity, we also conjecture very simple formulae for these, which are similar to those in the Hilbert-Schmidt ensemble.
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。
