Conditions for separability in generalized Laplacian matrices and nonnegative matrices as density matrices

Details Conditions for separability in generalized Laplacian matrices and nonnegative matrices as density matrices Conditions for separability in generalized Laplacian matrices and nonnegative matrices as density matrices

2005-08-22

arxiv.org/abs/quant-ph/0508163v1

Expanded version in Physics Letters A, 251 (1-2), pp. 18-22, 2006

Physics

Quantum Physics

10 pages, 1 figure

Scientific paper

10.1016/j.physleta.2005.10.049

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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