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

Distinguished three-qubit ‘magicity’ via automorphisms of the split Cayley hexagon 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 45:405301, 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

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

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Springer US
Copyright © 2013 by Springer Science+Business Media New York
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
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