New Classes of Facets of Cut Polytope and Tightness of I_{mm22} Bell Inequalities

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dc.creatorAvis, David
dc.creatorIto, Tsuyoshi
dc.date2005-05-09
dc.date.accessioned2026-07-07T05:19:42Z
dc.date.available2026-07-07T05:19:42Z
dc.descriptionThe Grishukhin inequality Gr_7 is a facet of CutP_7, the cut polytope on seven points, which is ``sporadic'' in the sense that its proper generalization has not been known. In this paper, we extend Gr_7 to an inequality I(G,H) valid for CutP_{n+1} where G and H are graphs with n nodes satisfying certain conditions, and prove a necessary and sufficient condition for I(G,H) to be a facet. This result combined with the triangular elimination theorem of Avis, Imai, Ito and Sasaki settles Collins and Gisin's conjecture in quantum theory affirmatively: the I_{mm22} Bell inequality is a facet of the correlation polytope CorP(K_{m,m}) of the complete bipartite graph K_{m,m} for all m>=1. We also extend the Gr_8 facet inequality of CutP_8 to an inequality I'(G,H,C) valid for CutP_{n+2}, and provide a sufficient condition for I'(G,H,C) to be a facet.
dc.descriptionThe part except for the appendices will appear in Proc. 4th Symp. Discrete Math. and Its Appl., June, 2005. 12 pages with 4 figures
dc.identifierhttps://arxiv.org/abs/math/0505143
dc.identifierhttp://arxiv.org/abs/math/0505143
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75117
dc.subjectCombinatorics
dc.subjectQuantum Physics
dc.subject52B12 (Primary) 05C99, 52B05 (Secondary)
dc.titleNew Classes of Facets of Cut Polytope and Tightness of I_{mm22} Bell Inequalities
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