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It is known that the partial entanglement/separability violates distributiverules with respect to the operations of taking convex hull and intersection. Inthis note, we give criteria for three qubit partially entangled states arisingfrom distributive rules, together with the corresponding witnesses. Thecriteria will be given in terms of diagonal and anti-diagonal entries. Theyactually characterize those partial entanglement completely when all theentries are zero except for diagonal and anti-diagonal entries. Importantstates like Greenberger-Horne-Zeilinger diagonal states fall down in thisclass.

Criteria for partial entanglement of three qubit states arising from distributive rules