Quantum computation and quantum information
Quantum computation and quantum information
Classical deterministic complexity of Edmonds' Problem and quantum entanglement
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Quantum Information: An Introduction to Basic Theoretical Concepts and Experiments
Quantum Information: An Introduction to Basic Theoretical Concepts and Experiments
Further Results on the Cross Norm Criterion for Separability
Quantum Information Processing
A matrix realignment method for recognizing entanglement
Quantum Information & Computation
An introduction to entanglement measures
Quantum Information & Computation
Quantifying Complexity in Networks: The von Neumann Entropy
International Journal of Agent Technologies and Systems
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The density matrices of graphs are combinatorial laplacians normalised to have trace one (Braunstein et al. 2006b). If the vertices of a graph are arranged as an array, its density matrix carries a block structure with respect to which properties such as separability can be considered. We prove that the so-called degree-criterion, which was conjectured to be necessary and sufficient for the separability of density matrices of graphs, is equivalent to the PPT-criterion. As such, it is not sufficient for testing the separability of density matrices of graphs (we provide an explicit example). Nonetheless, we prove the sufficiency when one of the array dimensions has length two (see Wu (2006) for an alternative proof). Finally, we derive a rational upper bound on the concurrence of density matrices of graphs and show that this bound is exact for graphs on four vertices.