关于多体随机量子态边缘的联合分布
On the joint distribution of the marginals of multipartite random quantum states
摘要：
研究了作用在张量积希尔伯特空间上的随机Wishart矩阵的所有边值之集的联合分布。我们计算了极限自由的混合累积量的边缘，我们表明，在平衡渐近制度，边缘是渐近自由的。我们连接的矩阵积分相关的研究张量积空间上的运营商与相应类别的组合地图，我们开发的组合机械必要的渐近研究。最后，我们介绍了随机量子态理论在量子信息论中的一些应用。
英文摘要：
We study the joint distribution of the set of all marginals of a random Wishart matrix acting on a tensor product Hilbert space. We compute the limiting free mixed cumulants of the marginals, and we show that in the balanced asymptotical regime, the marginals are asymptotically free. We connect the matrix integrals relevant to the study of operators on tensor product spaces with the corresponding classes of combinatorial maps, for which we develop the combinatorial machinery necessary for the asymptotic study. Finally, we present some applications to the theory of random quantum states in quantum information theory.
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