The density matrix formalism is a fundamental tool in studying various problems in quantum information processing. In the space of density matrices, the most well-known measures are the Hilbert–Schmidt and Bures–Hall ensembles. In this work, the averages of quantum purity and von Neumann entropy for an ensemble that interpolates between these two major ensembles are explicitly calculated for finite-dimensional systems. The proposed interpolating ensemble is a specialization of the $𝜃$-deformed Cauchy–Laguerre two-matrix model and new results for this latter ensemble are given in full generality, including the recurrence relations satisfied by their associated bi-orthogonal polynomials when $𝜃$ assumes positive integer values.

密度矩阵形式是研究量子信息处理中各种问题的基本工具。在密度矩阵空间中，最著名的测度是 Hilbert–Schmidt 和 Bures–Hall 系综。在这项工作中，针对有限维系统明确计算了在这两个主要系综之间插值的系综的量子纯度和冯诺依曼熵的平均值。所提出的插值系综是$𝜃$-变形的 Cauchy–Laguerre 双矩阵模型和后一个系综的新结果完全具有一般性，包括它们相关联的双正交多项式满足的递归关系$𝜃$假定为正整数值。