|
This article is cited in 3 scientific papers (total in 3 papers)
‘Magic’ configurations of three-qubit observables and geometric hyperplanes of the smallest split Cayley hexagon
Metod Sanigaa, Michel Planatb, Petr Pracnac, Péter Lévayd a Astronomical Institute, Slovak Academy of Sciences, SK-05960 Tatranská Lomnica, Slovak Republic
b Institut FEMTO-ST, CNRS, 32 Avenue de l'Observatoire, F-25044 Besançon Cedex, France
c J. Heyrovský Institute of Physical Chemistry, v.v.i., Academy of Sciences of the Czech Republic, Dolejškova 3, CZ-182 23 Prague 8, Czech Republic
d Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics, H-1521 Budapest, Hungary
Abstract:
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 $2_414_2-4_36_4$ ones, can uniquely be extended into geometric hyperplanes of the split Cayley hexagon of order two, namely into those of types $\mathcal V_{22}(37;0,12,15,10)$ and $\mathcal V_4(49;0,0,21,28)$ 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.
Keywords:
‘magic’ configurations of observables; three-qubit Pauli group; split Cayley hexagon of order two.
Received: June 22, 2012; in final form November 2, 2012; Published online November 6, 2012
Citation:
Metod Saniga, Michel Planat, Petr Pracna, Péter Lévay, “‘Magic’ configurations of three-qubit observables and geometric hyperplanes of the smallest split Cayley hexagon”, SIGMA, 8 (2012), 083, 9 pp.
Linking options:
https://www.mathnet.ru/eng/sigma760 https://www.mathnet.ru/eng/sigma/v8/p83
|
Statistics & downloads: |
Abstract page: | 564 | Full-text PDF : | 145 | References: | 73 |
|