'Magic' Configurations of Three-Qubit Observables and Geometric Hyperplanes of the Smallest Split Cayley Hexagon
Recently Waegell and Aravind [J. Phys. A: Math. Theor. 45 (2012), 405301, 13 pages] have given a number of distinct sets of three-qubit observables, each furnishing a proof of the Kochen-Specker theorem. Here it is demonstrated that two of these sets/configurations, namely the 18₂−12₃ and 2₄14₂−4₃6₄...
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| Datum: | 2012 |
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| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2012
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/148670 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 'Magic' Configurations of Three-Qubit Observables and Geometric Hyperplanes of the Smallest Split Cayley Hexagon / M. Saniga, M. Planat, P. Pracna, P. Lévay // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 19 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | Recently Waegell and Aravind [J. Phys. A: Math. Theor. 45 (2012), 405301, 13 pages] have given a number of distinct sets of three-qubit observables, each furnishing a proof of the Kochen-Specker theorem. Here it is demonstrated that two of these sets/configurations, namely the 18₂−12₃ and 2₄14₂−4₃6₄ ones, can uniquely be extended into geometric hyperplanes of the split Cayley hexagon of order two, namely into those of types V₂₂(37;0,12,15,10) and V₄(49;0,0,21,28) in the classification of Frohardt and Johnson [Comm. Algebra 22 (1994), 773-797]. Moreover, employing an automorphism of order seven of the hexagon, six more replicas of either of the two configurations are obtained. |
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