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Journal Articles Quantum Information Processing Year : 2013

Distinguished three-qubit 'magicity' via automorphisms of the split Cayley hexagon

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 (18_{2}, 12_{3})-type of magic configurations, recently proposed by Waegell and Aravind (J. Phys. A: Math. Theor. 45 (2012) 405301), 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.
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Dates and versions

hal-00763975 , version 1 (12-12-2012)

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Michel Planat, Metod Saniga, Frédéric Holweck. Distinguished three-qubit 'magicity' via automorphisms of the split Cayley hexagon. Quantum Information Processing, 2013, 12, pp.2535-2549. ⟨10.1007/s11128-013-0547-3⟩. ⟨hal-00763975⟩
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