广义Laplacian矩阵和非负矩阵作为密度矩阵的可分性条件
Conditions for separability in generalized Laplacian matrices and nonnegative matrices as density matrices
摘要：
近年来，图的拉普拉斯矩阵作为密度矩阵在量子力学中得到了广泛的研究。我们继续这一研究，给出了单位迹赋权图的广义拉普拉斯矩阵可分性的条件。特别地，我们证明了Peres-Horodecki正的部分转置可分性条件对于${\mathbb C}^2\otimes {\mathbb C}^q$的可分性是充分必要的.另外，我们给出了广义Laplacian矩阵与对角占优非负矩阵可分性的一个充分条件。
英文摘要：
Recently, Laplacian matrices of graphs are studied as density matrices in quantum mechanics. We continue this study and give conditions for separability of generalized Laplacian matrices of weighted graphs with unit trace. In particular, we show that the Peres-Horodecki positive partial transpose separability condition is necessary and sufficient for separability in ${\mathbb C}^2\otimes {\mathbb C}^q$. In addition, we present a sufficient condition for separability of generalized Laplacian matrices and diagonally dominant nonnegative matrices.
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