纠缠随机纯态的最小本征值分布
Exact Minimum Eigenvalue Distribution of an Entangled Random Pure State
摘要：
证明了最近关于随机复态约化密度矩阵最小特征值平均值的一个猜想。事实上，完全分布的最小特征值导出的情况下，一个随机的真实和随机的复杂的状态。我们的结果与随机矩阵理论和量子混沌系统的正交和酉系综的本征向量的纠缠特性有关。它们还为所有N值（而不仅仅是大N）的一组N { \em强相关}随机变量的最小值的分布提供了一种罕见的精确可解的情况。
英文摘要：
A recent conjecture regarding the average of the minimum eigenvalue of the reduced density matrix of a random complex state is proved. In fact, the full distribution of the minimum eigenvalue is derived exactly for both the cases of a random real and a random complex state. Our results are relevant to the entanglement properties of eigenvectors of the orthogonal and unitary ensembles of random matrix theory and quantum chaotic systems. They also provide a rare exactly solvable case for the distribution of the minimum of a set of N {\em strongly correlated} random variables for all values of N (and not just for large N).
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