[HTML][HTML] Graphs whose normalized Laplacian matrices are separable as density matrices in quantum mechanics

CW Wu - Discrete Mathematics, 2016 - Elsevier
Discrete Mathematics, 2016Elsevier
Recently normalized Laplacian matrices of graphs are studied as density matrices in
quantum mechanics. Separability and entanglement of density matrices are important
properties as they determine the nonclassical behavior in quantum systems. In this note we
look at the graphs whose normalized Laplacian matrices are separable or entangled. In
particular, we show that the number of such graphs is related to the number of 0–1 matrices
that are line sum symmetric and to the number of graphs with at least one vertex of degree 1.
Abstract
Recently normalized Laplacian matrices of graphs are studied as density matrices in quantum mechanics. Separability and entanglement of density matrices are important properties as they determine the nonclassical behavior in quantum systems. In this note we look at the graphs whose normalized Laplacian matrices are separable or entangled. In particular, we show that the number of such graphs is related to the number of 0–1 matrices that are line sum symmetric and to the number of graphs with at least one vertex of degree 1.
Elsevier