Geodesic
The tripartite separability of density matrices of graphs
The electronic journal of combinatorics, Tome 14 (2007)

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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.
DOI : 10.37236/958
Classification : 81P68, 05C50 
Zhen Wang; Zhixi Wang. The tripartite separability of density matrices of graphs. The electronic journal of combinatorics, Tome 14 (2007). doi: 10.37236/958
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     author = {Zhen Wang and Zhixi Wang},
     title = {The tripartite separability of density matrices of graphs},
     journal = {The electronic journal of combinatorics},
     year = {2007},
     volume = {14},
     doi = {10.37236/958},
     zbl = {1116.81018},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/958/}
}
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