Yingdong Lu, Mark S. Squillante, et al.
IFIP WG 7.3 Performance 2015
Normalized Laplacian matrices of graphs have recently been studied in the context of quantum mechanics as density matrices of quantum systems. Of particular interest is the relationship between quantum physical properties of the density matrix and the graph theoretical properties of the underlying graph. One important aspect of density matrices is their entanglement properties, which are responsible for many nonintuitive physical phenomena. The entanglement property of normalized Laplacian matrices is in general not invariant under graph isomorphism. In recent papers, graphs were identified whose entanglement and separability properties are invariant under isomorphism. The purpose of this note is to completely characterize the set of graphs whose separability is invariant under graph isomorphism. In particular, we show that this set consists of K2,2 and its complement, all complete graphs and no other graphs. © 2010 Elsevier B.V. All rights reserved.
Yingdong Lu, Mark S. Squillante, et al.
IFIP WG 7.3 Performance 2015
Chai Wah Wu
Physics Letters, Section A: General, Atomic and Solid State Physics
Chai Wah Wu
Linear and Multilinear Algebra
Andrew R. Conn, Paula K. Coulman, et al.
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems