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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 {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.
We investigate the separability of arbitrary dimensional tripartite sys- tems. By introducing a new operator related to transformations on the subsystems a necessary condition for the separability of tripartite systems is presented.
By combining a parameterized Hermitian matrix, the realignment matrix of the bipartite density matrix $rho$ and the vectorization of its reduced density matrices, we present a family of separability criteria, which are stronger than the computable cr
Separability is an important problem in theory of quantum entanglement. By using the Bloch representation of quantum states in terms of the Heisenberg-Weyl observable basis, we present a new separability criterion for bipartite quantum systems. It is
The correlation matrices or tensors in the Bloch representation of density matrices are encoded with entanglement properties. In this paper, based on the Bloch representation of density matrices, we give some new separability criteria for bipartite a
Starting with a set of conditions for bipartite separability of arbitrary quantum states in any dimension and expressed in terms of arbitrary operators whose commutator is a $c$-number, we derive a hierarchy of conditions for tripartite separability