随机纯态两体纠缠分布中的相变
Phase Transitions in the Distribution of Bipartite Entanglement of a Random Pure State
摘要：
利用库仑气体方法，我们解析地计算了一个大的二体量子系统的随机纯态的Renyi熵（纠缠的标准度量）的概率分布。我们表明，对于任意阶数q>1的Renyi熵，有两个临界值，在这两个临界值处熵的概率分布改变形状。这些临界点对应于库仑气体中相应电荷密度的两种不同跃迁：原点处可积奇点的消失和所有其他电荷的连续海中单个电荷滴的消失。这些转变分别控制熵的概率分布的左尾和右尾，这也由库仑气体平衡动力学的蒙特卡罗数值模拟所验证。
英文摘要：
Using a Coulomb gas method, we compute analytically the probability distribution of the Renyi entropies (a standard measure of entanglement) for a random pure state of a large bipartite quantum system. We show that, for any order q>1 of the Renyi entropy, there are two critical values at which the entropy's probability distribution changes shape. These critical points correspond to two different transitions in the corresponding charge density of the Coulomb gas: the disappearance of an integrable singularity at the origin and the detachement of a single-charge drop from the continuum sea of all the other charges. These transitions respectively control the left and right tails of the entropy's probability distribution, as verified also by Monte Carlo numerical simulations of the Coulomb gas equilibrium dynamics.
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