Some families of density matrices for which separability is easily tested

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dc.creatorBraunstein, Samuel L.
dc.creatorGhosh, Sibasish
dc.creatorMansour, Toufik
dc.creatorSeverini, Simone
dc.creatorWilson, Richard C.
dc.date2005-08-02
dc.date2007-03-26
dc.date.accessioned2026-07-07T07:53:41Z
dc.date.available2026-07-07T07:53:41Z
dc.descriptionWe reconsider density matrices of graphs as defined in [quant-ph/0406165]. The density matrix of a graph is the combinatorial laplacian of the graph normalized to have unit trace. We describe a simple combinatorial condition (the "degree condition") to test separability of density matrices of graphs. The condition is directly related to the PPT-criterion. We prove that the degree condition is necessary for separability and we conjecture that it is also sufficient. We prove special cases of the conjecture involving nearest point graphs and perfect matchings. We observe that the degree condition appears to have value beyond density matrices of graphs. In fact, we point out that circulant density matrices and other matrices constructed from groups always satisfy the condition and indeed are separable with respect to any split. The paper isolates a number of problems and delineates further generalizations.
dc.description14 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/quant-ph/0508020
dc.identifierhttp://arxiv.org/abs/quant-ph/0508020
dc.identifierPhys. Rev. A 73, 012320 (2006)
dc.identifierdoi:10.1103/PhysRevA.73.012320
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/126314
dc.subjectQuantum Physics
dc.titleSome families of density matrices for which separability is easily tested
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