论文标题
所有密度矩阵上的均匀概率分布
Uniform Probability Distribution Over All Density Matrices
论文作者
论文摘要
令$ \ mathscr {h} $为有限维的希尔伯特空间，$ \ mathscr {d} $是$ \ mathscr {h} $上的密度矩阵集，即带有跟踪1的正面操作员。 $ \ mathscr {d} $。我们提出了对$ \ Mathscr {d} $的措施，认为它可以如此考虑，讨论其属性，并计算根据此度量分布的随机密度矩阵的特征值的联合分布。
Let $\mathscr{H}$ be a finite-dimensional complex Hilbert space and $\mathscr{D}$ the set of density matrices on $\mathscr{H}$, i.e., the positive operators with trace 1. Our goal in this note is to identify a probability measure $u$ on $\mathscr{D}$ that can be regarded as the uniform distribution over $\mathscr{D}$. We propose a measure on $\mathscr{D}$, argue that it can be so regarded, discuss its properties, and compute the joint distribution of the eigenvalues of a random density matrix distributed according to this measure.
