{"paper":{"title":"The tripartite separability of density matrices of graphs","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Zhen Wang, Zhixi Wang","submitted_at":"2007-05-17T16:30:19Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.2561","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}