'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 18_2−12_3 and 2_4 14_2...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
National Academy of Science of Ukraine
2012-11-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.3842/SIGMA.2012.083 |
| Summary: | 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 18_2−12_3 and 2_4 14_2−4_3 6_4 ones, can uniquely be extended into geometric hyperplanes of the split Cayley hexagon of order two, namely into those of types V_{22}(37;0,12,15,10) and V_4(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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| ISSN: | 1815-0659 |