Multipartite separability of Laplacian matrices of graphs

Details Multipartite separability of Laplacian matrices of graphs Multipartite separability of Laplacian matrices of graphs

2008-09-04

arxiv.org/abs/0809.0827v1

The Electronic Journal of Combinatorics, vol. 16, no.1, R61, 2009

Physics

Quantum Physics

13 pages, 1 figure

Scientific paper

Recently, Braunstein et al. [1] introduced normalized Laplacian matrices of graphs as density matrices in quantum mechanics and studied the relationships between quantum physical properties and graph theoretical properties of the underlying graphs. We provide further results on the multipartite separability of Laplacian matrices of graphs. In particular, we identify complete bipartite graphs whose normalized Laplacian matrix is multipartite entangled under any vertex labeling. Furthermore, we give conditions on the vertex degrees such that there is a vertex labeling under which the normalized Laplacian matrix is entangled. These results address an open question raised in [1]. Finally, we extend some of the results in [1,2] to the multipartite case and show that the Laplacian matrix of any product of graphs (strong, Cartesian, tensor, categorical, etc.) is multipartite separable.

Affiliated with

Also associated with

No associations

Rating

Multipartite separability of Laplacian matrices of graphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Multipartite separability of Laplacian matrices of graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Multipartite separability of Laplacian matrices of graphs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-142030