bibkey: hildebrand2007graphconcurrence authors: Roland Hildebrand; Stefano Mancini; Simone Severini year: 2007 title: “Combinatorial Laplacians and positivity under partial transpose” doi: null url: https://arxiv.org/abs/cs/0607036v3 claim: “Section 3 bounds graph-state concurrence by the fraction of unmatched edges and lists its four-vertex values.” strata_touched:
- D5/S3/Quantum/Entanglement/GraphDensity/BraunsteinGhoshSeveriniStarRefutation license: citation-only triage: anchor
Verified locator
Source: https://arxiv.org/abs/cs/0607036v3
Statement and scope
Section 3, pp. 13–16 of arXiv:cs/0607036v3, defines concurrence and entanglement of formation of graph density matrices. If is the number of matched edges and the number of unmatched edges, its graph-state concurrence bound is . The table of entangled four-vertex graphs gives concurrence . At four vertices the three-edge star and path tie. This section does not determine the formation of stars of arbitrary order or settle the connected-graph maximum in BGS Conjecture 6.7.