无规Bures混合态及其纯度分布
Random Bures mixed states and the distribution of their purity
摘要：
分析了由各种概率测度确定的随机密度矩阵的集合。提出了一种简单有效的生成按Bures测度分布的随机密度矩阵的算法。该过程可以作为基于Bures先验对量子态估计执行贝叶斯方法的初始步骤。研究了随机混合态的纯度分布。纯度分布的时刻被确定为相对于Bures测量产生的量子态。该计算是基于可积性理论思想的“变形与研究”方法的一个典型应用。结果表明，潘勒韦方程是理论的一部分。
英文摘要：
Ensembles of random density matrices determined by various probability measures are analysed. A simple and efficient algorithm to generate at random density matrices distributed according to the Bures measure is proposed. This procedure may serve as an initial step in performing Bayesian approach to quantum state estimation based on the Bures prior. We study the distribution of purity of random mixed states. The moments of the distribution of purity are determined for quantum states generated with respect to the Bures measure. This calculation serves as an exemplary application of the "deform-and-study" approach based on ideas of integrability theory. It is shown that Painlevé equation appeared as a part of the presented theory.
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