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Taxonomy of Three-Qubit Mermin Pentagrams

by Metod Saniga 1,*,†, Frédéric Holweck 2,† and Hamza Jaffali 3,†
1
Astronomical Institute of the Slovak Academy of Sciences, SK-05960 Tatranská Lomnica, Slovakia
2
Laboratoire Interdisciplinaire Carnot de Bourgogne, ICB/UTBM, UMR 6303 CNRS, Université Bourgogne Franche-Comté, F-90010 Belfort, France
3
Institut FEMTO-ST, Université Bourgogne Franche-Comté, UTBM, F-90010 Belfort, France
*
Author to whom correspondence should be addressed.
All authors contributed equally to this work.
Symmetry 2020, 12(4), 534; https://doi.org/10.3390/sym12040534
Received: 21 February 2020 / Revised: 14 March 2020 / Accepted: 19 March 2020 / Published: 3 April 2020
Given the fact that the three-qubit symplectic polar space features three different kinds of observables and each of its labeled Fano planes acquires a definite sign, we found that there are 45 distinct types of Mermin pentagrams in this space. A key element of our classification is the fact that any context of such pentagram is associated with a unique (positive or negative) Fano plane. Several intriguing relations between the character of pentagrams’ three-qubit observables and ‘valuedness’ of associated Fano planes are pointed out. In particular, we find two distinct kinds of negative contexts and as many as four positive ones. View Full-Text
Keywords: Mermin pentagrams; three-qubit symplectic polar space; valued Fano planes Mermin pentagrams; three-qubit symplectic polar space; valued Fano planes
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Saniga, M.; Holweck, F.; Jaffali, H. Taxonomy of Three-Qubit Mermin Pentagrams. Symmetry 2020, 12, 534.

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