Separability of Density Matrices of Graphs for Multipartite Systems

  • Chen Xie
  • Hui Zhao
  • Zhixi Wang
Keywords: density matrices of graphs, Laplacian matrices, separability


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 Number