基于随机密度矩阵特征值联合分布的统一(r, s)相对微分熵

The Unified (r, s)-Relative Differential Entropy Based on Joint Distribution of Random Density Matrix

摘要: 采用Laplace变换和Laplace逆变换研究随机密度矩阵特征值联合分布的统一(r, s)相对微分熵。一方面，定义了在Haar分布的双体纯态上取部分迹所诱导的随机密度矩阵的特征值的联合分布相对于其对角元的联合分布(其对角元的联合分布相对于取部分迹所诱导的随机密度矩阵的特征值的联合分布)的统一(r, s)相对微分熵。另一方面，计算三种情形下的统一(r, s)相对微分熵，推广了微分熵的范围。

Abstract: The unified (r, s)-relative differential entropy of the joint distribution of eigenvalues of random density matrices is studied by Laplace transform and Laplace inverse transform. On the one hand, the unified (r, s)-relative differential entropy of the joint distribution of the eigenvalues to diagonal entries of random density matrices induced by partial tracing (the diagonal entries of random density matrices induced by partial tracing to joint distribution of the eigenvalues) over Haar-distributed bipartite pure states is defined. On the other hand, the unified (r, s)-relative differential entropy in the three cases is calculated. The range of differential entropy is generalized.