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

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.

7 pages, 1 figure

References in corpus (4)

• Separability Criterion for Density Matrices
• Some families of density matrices for which separability is easily tested
• Conditions for separability in generalized Laplacian matrices and nonnegative matrices as density matrices
• On graphs whose Laplacian matrix's multipartite separability is invariant under graph isomorphism

Cited by in corpus (1)

• Entanglement and other quantum correlations of a single qudit state as a resource for quantum technologies