### 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 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 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 language | English |
---|---|

Article number | 083 |

Journal | Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) |

Volume | 8 |

DOIs | |

Publication status | Published - Nov 6 2012 |

### Fingerprint

### 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

**'Magic' configurations of three-qubit observables and geometric hyperplanes of the smallest split Cayley hexagon.** / Saniga, Metod; Planat, Michel; Pracna, Petr; Lévay, P.

Research output: Contribution to journal › Article

*Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)*, vol. 8, 083. https://doi.org/10.3842/SIGMA.2012.083

}

TY - JOUR

T1 - 'Magic' configurations of three-qubit observables and geometric hyperplanes of the smallest split Cayley hexagon

AU - Saniga, Metod

AU - Planat, Michel

AU - Pracna, Petr

AU - Lévay, P.

PY - 2012/11/6

Y1 - 2012/11/6

N2 - 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.

AB - 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.

KW - 'Magic' configurations of observables

KW - Split cayley hexagon of order two

KW - Three-qubit pauli group

UR - http://www.scopus.com/inward/record.url?scp=84869069320&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84869069320&partnerID=8YFLogxK

U2 - 10.3842/SIGMA.2012.083

DO - 10.3842/SIGMA.2012.083

M3 - Article

VL - 8

JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SN - 1815-0659

M1 - 083

ER -