Conditions for separability in generalized Laplacian matrices and nonnegative matrices as density matrices
Chai Wah Wu
Abstract
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 C2 Cq. In addition, we present a sufficient condition for separability of generalized Laplacian matrices and diagonally dominant nonnegative matrices.
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