Distinguished three-qubit ‘magicity’ via automorphisms of the split Cayley hexagon View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2013-07

AUTHORS

Michel Planat, Metod Saniga, Frédéric Holweck

ABSTRACT

Disregarding the identity, the remaining 63 elements of the generalized three-qubit Pauli group are found to contain 12096 distinct copies of Mermin’s magic pentagram. Remarkably, 12096 is also the number of automorphisms of the smallest split Cayley hexagon. We give a few solid arguments showing that this may not be a mere coincidence. These arguments are mainly tied to the structure of certain types of geometric hyperplanes of the hexagon. It is further demonstrated that also an -type of magic configurations, recently proposed by Waegell and Aravind (J Phys A Math Theor 45:405301, 2012), seems to be intricately linked with automorphisms of the hexagon. Finally, the entanglement properties exhibited by edges of both pentagrams and these particular Waegell–Aravind configurations are addressed. More... »

PAGES

2535-2549

References to SciGraph publications

  • 2001-09. Generalized Flatland in THE MATHEMATICAL INTELLIGENCER
  • 2012-08. On small proofs of the Bell-Kochen-Specker theorem for two, three and four qubits in THE EUROPEAN PHYSICAL JOURNAL PLUS
  • 1989. Going Beyond Bell’s Theorem in BELL’S THEOREM, QUANTUM THEORY AND CONCEPTIONS OF THE UNIVERSE
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    http://scigraph.springernature.com/pub.10.1007/s11128-013-0547-3

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    http://dx.doi.org/10.1007/s11128-013-0547-3

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