Study of universality in quantum entanglement and its application to quantum tomography and quantum control

研究了由二体系统动力学产生的量子纠缠统计的普适性。本文的研究主要有以下两点。(1)我们采用随机矩阵来模拟纠缠量子态，随机矩阵的元素都是统计随机的。为此，我们发展理论的随机矩阵在我们原来的方式。(2)我们对量子动力学进行了大规模模拟，得到了量子动力学产生的纠缠态的施密特本征值的精确的单体分布。我们将单体分布与（1）中导出的单体分布进行比较。这一比较揭示了量子混沌动力学表现出随机矩阵的统计特性。

We studied the universality of the statistics in the quantum entanglement generated by the dynamics of a bipartite system. The main points in our studies are two as follows. (1) We adopted the random matrices whose elements are all statistically random to model entangled quantum states. To this end, we developed theory of the random matrices in our original way. (2) We performed a large scale simulation of the quantum dynamics and obtained accurate one-body distribution of the Schmidt eigenvalues of entangled states generated by the quantum dynamics. We compared the one-body distribution with that derived in (1). This comparison revealed that the quantum chaotic dynamics shows the statistics of random matrices.