'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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| Дата: | 2012 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2012
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | 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 |
| Цитувати: | '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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1486702019-02-19T01:26:28Z 'Magic' Configurations of Three-Qubit Observables and Geometric Hyperplanes of the Smallest Split Cayley Hexagon Saniga, M. Planat, M. Pracna, P. Lévay, P. 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. 2012 Article '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. 1815-0659 2010 Mathematics Subject Classification: 51Exx; 81R99 DOI: http://dx.doi.org/10.3842/SIGMA.2012.083 http://dspace.nbuv.gov.ua/handle/123456789/148670 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
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. |
| format |
Article |
| author |
Saniga, M. Planat, M. Pracna, P. Lévay, P. |
| spellingShingle |
Saniga, M. Planat, M. Pracna, P. Lévay, P. 'Magic' Configurations of Three-Qubit Observables and Geometric Hyperplanes of the Smallest Split Cayley Hexagon Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Saniga, M. Planat, M. Pracna, P. Lévay, P. |
| author_sort |
Saniga, M. |
| title |
'Magic' Configurations of Three-Qubit Observables and Geometric Hyperplanes of the Smallest Split Cayley Hexagon |
| title_short |
'Magic' Configurations of Three-Qubit Observables and Geometric Hyperplanes of the Smallest Split Cayley Hexagon |
| title_full |
'Magic' Configurations of Three-Qubit Observables and Geometric Hyperplanes of the Smallest Split Cayley Hexagon |
| title_fullStr |
'Magic' Configurations of Three-Qubit Observables and Geometric Hyperplanes of the Smallest Split Cayley Hexagon |
| title_full_unstemmed |
'Magic' Configurations of Three-Qubit Observables and Geometric Hyperplanes of the Smallest Split Cayley Hexagon |
| title_sort |
'magic' configurations of three-qubit observables and geometric hyperplanes of the smallest split cayley hexagon |
| publisher |
Інститут математики НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148670 |
| citation_txt |
'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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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