论文标题
重新归一化的von Neumann熵，并在真实的无限尺寸系统中应用
Renormalized von Neumann entropy with application to entanglement in genuine infinite dimensional systems
论文作者
论文摘要
von Neumann量子熵的重新归一化版本（通常是有限的，一般是连续的，无限尺寸的情况），并遵守几种自然物理需求（如描述比比特派和无限尺寸系统的通用量子状态的“良好”范围的“良好”量度）。重新归一化的量子熵是通过明确使用弗雷霍尔姆决定因素理论来定义的。为了证明引入重新归一化的连续性和有限的主要结果，采用了基于无限的格拉斯曼代数理论的基本绿色方法。在本文中证明，在引入的重新归一化之下保留了多数化理论的几个特征。这一事实使我们能够将LOCC比较理论的大多数已知已知（主要是在两目标，有限维量子系统的背景下）扩展到真正的无限二维量子系统的情况下。
A renormalized version of the von Neumann quantum entropy (which is finite and continuous in general, infinite dimensional case) and which obeys several of the natural physical demands (as expected for a "good" measure of entanglement in the case of general quantum states describing bipartite and infinite-dimensional systems) is proposed. The renormalized quantum entropy is defined by the explicit use of the Fredholm determinants theory. To prove the main results on continuity and finiteness of the introduced renormalization the fundamental Grothendick approach, which is based on the infinite dimensional Grassmann algebra theory, is applied. Several features of majorization theory are preserved under then introduced renormalization as it is proved in this paper. This fact enables us to extend most of the known (mainly, in the context of two-partite, finite-dimensional quantum systems) results of the LOCC comparison theory to the case of genuine infinite-dimensional, two-partite quantum systems.
