可分离态的体积是超双指数小的
The volume of separable states is super-doubly-exponentially small
摘要：
本文给出了N个量子比特上可分态集的体积的精确估计。特别是，在体积的意义上，该集合的“有效半径”的大小被确定为N的（小）幂的因子，并且因此精确地在其维度的幂的尺度上。此外，附录之一包含GUE随机矩阵的范数的期望值的尖锐估计（通过已知方法）。我们采用标准的工具，经典的凸性，高维概率和几何的Banach空间。
英文摘要：
In this note we give sharp estimates on the volume of the set of separable states on N qubits. In particular, the magnitude of the "effective radius" of that set in the sense of volume is determined up to a factor which is a (small) power of N, and thus precisely on the scale of powers of its dimension. Additionally, one of the appendices contains sharp estimates (by known methods) for the expected values of norms of the GUE random matrices. We employ standard tools of classical convexity, high-dimensional probability and geometry of Banach spaces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
