Laplacian矩阵的多部可分性在图同构下不变的图
On graphs whose Laplacian matrix's multipartite separability is invariant under graph isomorphism
摘要：
图的正规化拉普拉斯矩阵作为量子系统的密度矩阵，近年来在量子力学的背景下得到了研究。特别感兴趣的是量子物理性质的密度矩阵和图形的基本图形的图论性质之间的关系。密度矩阵的一个重要方面是它们的纠缠特性，这是许多非直观物理现象的原因。归一化拉普拉斯矩阵的纠缠性质在图同构下一般不是不变的。在最近的论文中，确定了图的纠缠和可分性的同构下不变。本文的目的是刻画在图同构下可分离性不变的图的集合。特别是，我们表明，这个集合由$K_{2,2}$，$\overline{K_{2,2}}$和所有完全图。
英文摘要：
Normalized Laplacian matrices of graphs have recently been studied in the context of quantum mechanics as density matrices of quantum systems. Of particular interest is the relationship between quantum physical properties of the density matrix and the graph theoretical properties of the underlying graph. One important aspect of density matrices is their entanglement properties, which are responsible for many nonintuitive physical phenomena. The entanglement property of normalized Laplacian matrices is in general not invariant under graph isomorphism. In recent papers, graphs were identified whose entanglement and separability properties are invariant under isomorphism. The purpose of this note is to characterize the set of graphs whose separability is invariant under graph isomorphism. In particular, we show that this set consists of $K_{2,2}$, $\overline{K_{2,2}}$ and all complete graphs.
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