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SIGMA, 2012, Volume 8, 083, 9 pages (Mi sigma760)  

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.

DOI: https://doi.org/10.3842/SIGMA.2012.083

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ArXiv: 1206.3436
MSC: 51Exx; 81R99
Received: June 22, 2012; in final form November 2, 2012; Published online November 6, 2012
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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.

Citation in format AMSBIB
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\by Metod Saniga, Michel Planat, Petr Pracna, P{\'e}ter L{\'e}vay
\paper `Magic' configurations of three-qubit observables and geometric hyperplanes of the smallest split Cayley hexagon
\jour SIGMA
\yr 2012
\vol 8
\papernumber 083
\totalpages 9
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\crossref{https://doi.org/10.3842/SIGMA.2012.083}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Levay P. Planat M. Saniga M., “Grassmannian Connection Between Three- and Four-Qubit Observables, Mermin's Contextuality and Black Holes”, J. High Energy Phys., 2013, no. 9, 037  crossref  isi  scopus
    2. Planat M., Saniga M., Holweck F., “Distinguished Three-Qubit ‘Magicity’ via Automorphisms of the Split Cayley Hexagon”, Quantum Inf. Process., 12:7 (2013), 2535–2549  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. M. Saniga, F. Holweck, P. Pracna, “Veldkamp spaces: from (Dynkin) diagrams to (Pauli) groups”, Int. J. Geom. Methods Mod. Phys., 14:5 (2017), 1750080  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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