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'Magic' Configurations of Three-Qubit Observables and Geometric Hyperplanes of the Smallest Split Cayley Hexagon
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8
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'Magic' Configurations of Three-Qubit Observables and Geometric Hyperplanes of the Smallest Split Cayley Hexagon
Інший ID:
2010 Mathematics Subject Classification: 51Exx; 81R99
DOI: http://dx.doi.org/10.3842/SIGMA.2012.083
DOI: http://dx.doi.org/10.3842/SIGMA.2012.083
Посилання:
'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.
Підтримка:
This work was partially supported by the VEGA grant agency project 2/0098/10.
Дата:
2012
Переглядів:
842
Завантажень:
265
Анотація:
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.
