Conditions for separability in generalized Laplacian matrices and diagonally dominant matrices as density matrices

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 co...

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Bibliographic Details
Published inPhysics letters. A Vol. 351; no. 1; pp. 18 - 22
Main Author Wu, Chai Wah
Format Journal Article
LanguageEnglish
Published Elsevier B.V 20.02.2006
Subjects
Density matrix
Diagonally dominant matrix
Entanglement
Graph theory
Laplacian matrix
Non-negative matrix
Partial transpose
Diagonally dominant matrix
Partial transpose
02.10.Ud
03.65.Ud
03.65.-w
Density matrix
Entanglement
Graph theory
Laplacian matrix
02.10.Ox
Non-negative matrix
02.10.Yn
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Summary: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 condition is necessary and sufficient for separability in C 2 ⊗ C q . In addition, we present sufficient conditions for separability of generalized Laplacian matrices and diagonally dominant matrices.
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2005.10.049