'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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2012 |
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2012
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| Онлайн доступ: | https://nasplib.isofts.kiev.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| _version_ | 1862706193360748544 |
|---|---|
| author | Saniga, M. Planat, M. Pracna, P. Lévay, P. |
| author_facet | Saniga, M. Planat, M. Pracna, P. Lévay, P. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T16:58:29Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148670 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T16:58:29Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Saniga, M. Planat, M. Pracna, P. Lévay, P. 2019-02-18T17:45:05Z 2019-02-18T17:45:05Z 2012 '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 https://nasplib.isofts.kiev.ua/handle/123456789/148670 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. This work was partially supported by the VEGA grant agency project 2/0098/10. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications 'Magic' Configurations of Three-Qubit Observables and Geometric Hyperplanes of the Smallest Split Cayley Hexagon Article published earlier |
| spellingShingle | 'Magic' Configurations of Three-Qubit Observables and Geometric Hyperplanes of the Smallest Split Cayley Hexagon Saniga, M. Planat, M. Pracna, P. Lévay, P. |
| title | '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_short | '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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148670 |
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