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Entanglement Theory Quantum Correlations Quantum State Preparation Representation Quantum Simulation

'Magic' Configurations of Three-Qubit Observables and Geometric Hyperplanes of the Smallest Split Cayley Hexagon

arXiv
Authors: Metod Saniga, Michel Planat, Petr Pracna, Péter Lévay

Year

2012

Paper ID

8581

Status

Preprint

Abstract Read

~2 min

Abstract Words

100

Citations

N/A

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 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 {cal V}22(37; 0, 12, 15, 10) and {cal 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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  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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  • Recently Waegell and Aravind [J.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1206.3436 [2] arXiv https://arxiv.org/abs/1206.3436 [3] Publisher https://arxiv.org/abs/1206.3436

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