We investigate separability of Laplacian matrices of graphs when seen as density matrices. This is a family of quantum states with many combinatorial properties. We firstly show that the well-known matrix realignment criterion can be used to test separability of this type of quantum states. The criterion can be interpreted as novel graph-theoretic idea. Then, we prove that the density matrix of the tensor product of N graphs is N-separable. However, the converse is not necessarily true. Additionally, we derive a sufficient condition for N-partite entanglement in star graphs and propose a necessary and sufficient condition for separability of nearest point graphs.
@article{10_37236_3092,
author = {Chen Xie and Hui Zhao and Zhixi Wang},
title = {Separability of density matrices of graphs for multipartite systems},
journal = {The electronic journal of combinatorics},
year = {2013},
volume = {20},
number = {4},
doi = {10.37236/3092},
zbl = {1295.05246},
url = {http://geodesic.mathdoc.fr/articles/10.37236/3092/}
}
TY - JOUR
AU - Chen Xie
AU - Hui Zhao
AU - Zhixi Wang
TI - Separability of density matrices of graphs for multipartite systems
JO - The electronic journal of combinatorics
PY - 2013
VL - 20
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/3092/
DO - 10.37236/3092
ID - 10_37236_3092
ER -
%0 Journal Article
%A Chen Xie
%A Hui Zhao
%A Zhixi Wang
%T Separability of density matrices of graphs for multipartite systems
%J The electronic journal of combinatorics
%D 2013
%V 20
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/3092/
%R 10.37236/3092
%F 10_37236_3092
Chen Xie; Hui Zhao; Zhixi Wang. Separability of density matrices of graphs for multipartite systems. The electronic journal of combinatorics, Tome 20 (2013) no. 4. doi: 10.37236/3092
