论文标题
张量产品的随机子空间的浓度估计，并应用于量子信息理论
Concentration estimates for random subspaces of a tensor product, and application to Quantum Information Theory
论文作者
论文摘要
给定一个随机子空间$ h_n $在hilbert Spaces $ v_n \ otimes w $的张量产品中均匀地选择，我们考虑了$ h_n $的所有norm nord元素的所有单数值的集合$ k_n $相对于张量的结构。在$ w $固定的上下文中，已经获得了大量的法律，$ h_n $和$ v_n $的尺寸在贝林奇，柯林斯和尼基塔的论文中以相同的速度倾向于无穷大。在本文中，我们提供了衡量浓度估计值。 $ k_n $的概率研究是由量子信息理论中的重要问题激发的，并允许为尺寸提供最小的已知维度（184），一个ancilla空间允许最小输出熵（MOE）违规。根据我们的估计，作为一种应用，我们可以为发生MOE发生的空间的维度提供实际界限。
Given a random subspace $H_n$ chosen uniformly in a tensor product of Hilbert spaces $V_n\otimes W$, we consider the collection $K_n$ of all singular values of all norm one elements of $H_n$ with respect to the tensor structure. A law of large numbers has been obtained for this random set in the context of $W$ fixed and the dimension of $H_n$ and $V_n$ tending to infinity at the same speed in a paper of Belinschi, Collins and Nechita. In this paper, we provide measure concentration estimates in this context. The probabilistic study of $K_n$ was motivated by important questions in Quantum Information Theory, and allowed to provide the smallest known dimension (184) for the dimension an an ancilla space allowing Minimum Output Entropy (MOE) violation. With our estimates, we are able, as an application, to provide actual bounds for the dimension of spaces where violation of MOE occurs.
