'Magic' configurations of three-qubit observables and geometric hyperplanes of the smallest split Cayley hexagon

Metod Saniga, Michel Planat, Petr Pracna, P. Lévay

Research output: Contribution to journalArticle

3 Citations (Scopus)

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 furni- shing 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 John- son [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.

Original languageEnglish
Article number083
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume8
DOIs
Publication statusPublished - Nov 6 2012

Fingerprint

Cayley
Qubit
Hexagon
Hyperplane
Configuration
Replica
Automorphism
Distinct
Algebra
Theorem

Keywords

  • 'Magic' configurations of observables
  • Split cayley hexagon of order two
  • Three-qubit pauli group

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology
  • Mathematical Physics

Cite this

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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 furni- shing 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 John- son [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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