多连续变量量子纯态研究中的凸刚性覆盖方法
Convex rigid cover method in studies of quantum pure-states of many continuous variables
摘要：
本文证明了N（N $\geqslant 3)$）个连续变量的每个纯态$Ψ^{(N)}$对应于连续维Hilbert-Schmidt空间中的一对凸刚性覆盖（CRC）结构.其次，我们严格定义了部分可分性和普通可分性的概念，并讨论了如何用CRC来描述各种可分性。本文讨论了$Ψ^{(N)}$的分类问题，并对作用于$Ψ^{(N)}$的局部幺正操作给出了运动学解释。第三，我们讨论了类的不变量，并给出了一个可能的物理解释。
英文摘要：
In this paper we prove that every pure-state $Ψ^{(N)}$ of N (N$\geqslant 3)$ continuous variables corresponds to a pair of convex rigid covers (CRCs) structures in the continuous-dimensional Hilbert-Schmidt space. Next we strictly define what are the partial separability and ordinary separability, and discuss how to use CRCs to describe various separability. We discuss the problem of the classification of $Ψ^{(N)}$ and give a kinematical explanation of the local unitary operations acting upon $Ψ^{(N)}$. Thirdly, we discuss the invariants of classes and give a possible physical explanation.
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