The tripartite separability of density matrices of graphs

Details The tripartite separability of density matrices of graphs The tripartite separability of density matrices of graphs

2007-05-17

arxiv.org/abs/0705.2561v2

The Electronic J. Combinatorics, 14(2007), R40

Physics

Quantum Physics

12 pages

Scientific paper

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 {\it et al.} Annals of Combinatorics, {\bf 10}(2006)291 to tripartite states. Then we proved that the degree condition defined in Braunstein {\it et al.} Phys. Rev. A {\bf 73}, (2006)012320 is sufficient and necessary for the tripartite separability of the density matrix of a nearest point graph.

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