Laboratoire de Physique Théorique et Modèles Statistiques (UMR 8626 du CNRS), Université Paris-Sud, Bâtiment 100, 91405 Orsay Cedex, France.
Phys Rev Lett. 2010 Mar 19;104(11):110501. doi: 10.1103/PhysRevLett.104.110501.
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 detachment 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.
使用库仑气体方法，我们分析地计算了大双量子系统的随机纯态的 Renyi 熵（一种标准的纠缠度量）的概率分布。我们表明，对于 Renyi 熵的任何阶 q>1，熵的概率分布都会在两个临界值处发生形状变化。这些临界点对应于库仑气体电荷密度中的两个不同跃迁：原点处可积奇点的消失以及单个电荷从所有其他电荷的连续海中断开。这些跃迁分别控制了熵的概率分布的左尾和右尾，这也通过库仑气体平衡动力学的蒙特卡罗数值模拟得到了验证。
