Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0508163 · Physics Letters A

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

Chai Wah Wu

Published Oct 27, 2005• 25 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2005.10.049

Related papers

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

Chai Wah Wu

arXiv:1407.5663•Discrete Mathematics•Dec 22, 2015•5 citations

The Laplacian of a Graph as a Density Matrix: A Basic Combinatorial Approach to Separability of Mixed States

Samuel L. Braunstein, Sibasish Ghosh, Simone Severini B

arXiv:quant-ph/0406165•Annals of Combinatorics•Dec 1, 2006•145 citations

Some families of density matrices for which separability is easily tested (10 pages)

Samuel L. Braunstein

Physical Review A•Jan 1, 2006•0 citations

The Tripartite Separability of Density Matrices of Graphs

Zhen Wang, Zhi‐Xi Wang

The density matrix of a graph is the combinatorial laplacian matrix of a graph normalized to have unit trace. In this paper we generalize the entanglement properties of mixed density matrices from combinatorial laplacian matrices of graphs discussed in Braunstein et al. [Annals of Combinatorics, 10 (2006) 291] to tripartite states. Then we prove that the degree condition defined in Braunstein et al. [Phys. Rev. A, 73 (2006) 012320] is sufficient and necessary for the tripartite separability of the density matrix of a nearest point graph.

arXiv:0705.2561•The Electronic Journal of Combinatorics•May 23, 2007•8 citations

Some families of density matrices for which separability is easily tested

Samuel L. Braunstein, Sibasish Ghosh A, Toufik Mansour +2 more

We reconsider density matrices of graphs as defined in quant-ph/0406165. The density matrix of a graph is the combinatorial Laplacian of the graph normalized to have unit trace. We describe a simple combinatorial condition (the ``degree condition'') to test the separability of density matrices of graphs. The condition is directly related to the Peres-Horodecki partial transposition condition. We prove that the degree condition is necessary for separability, and we conjecture that it is also sufficient. We prove special cases of the conjecture involving nearest-point graphs and perfect matchings. We observe that the degree condition appears to have a value beyond the density matrices of graphs. In fact, we point out that circulant density matrices and other matrices constructed from groups always satisfy the condition and indeed are separable with respect to any split. We isolate a number of problems and delineate further generalizations.

arXiv:quant-ph/0508020•Physical Review A•Jan 18, 2006•45 citations

Separability criteria based on Bloch representation of density matrices

Hui Zhao, Mei-Ming Zhang, Naihuan Jing +1 more

arXiv:2004.11525•Quantum Information Processing•Nov 26, 2019•16 citations
The density matrix of a graph is the combinatorial laplacian matrix of a graph normalized to have unit trace. In this paper we generalize the entanglement properties of mixed density matrices from combinatorial laplacian matrices of graphs discussed in Braunstein et al. [Annals of Combinatorics, 10 (2006) 291] to tripartite states. Then we prove that the degree condition defined in Braunstein et al. [Phys. Rev. A, 73 (2006) 012320] is sufficient and necessary for the tripartite separability of the density matrix of a nearest point graph.
We reconsider density matrices of graphs as defined in quant-ph/0406165. The density matrix of a graph is the combinatorial Laplacian of the graph normalized to have unit trace. We describe a simple combinatorial condition (the ``degree condition'') to test the separability of density matrices of graphs. The condition is directly related to the Peres-Horodecki partial transposition condition. We prove that the degree condition is necessary for separability, and we conjecture that it is also sufficient. We prove special cases of the conjecture involving nearest-point graphs and perfect matchings. We observe that the degree condition appears to have a value beyond the density matrices of graphs. In fact, we point out that circulant density matrices and other matrices constructed from groups always satisfy the condition and indeed are separable with respect to any split. We isolate a number of problems and delineate further generalizations.