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Quantum Information Processing

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01-07-2013

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

Authors: Michel Planat, Metod Saniga, Frédéric Holweck

Published in: Quantum Information Processing | Issue 7/2013

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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 45:405301, 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.

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Title: Distinguished three-qubit ‘magicity’ via automorphisms of the split Cayley hexagon
Authors: Michel Planat
Metod Saniga
Frédéric Holweck
Publication date: 01-07-2013
Publisher: Springer US
Published in: Quantum Information Processing / Issue 7/2013
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI: https://doi.org/10.1007/s11128-013-0547-3

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