hal-00692040, version 1
Finite Geometry Behind the Harvey-Chryssanthacopoulos Four-Qubit Magic Rectangle
Quantum Information and Computation 11 (2012) 1011-1016
Résumé : A ''magic rectangle" of eleven observables of four qubits, employed by Harvey and Chryssanthacopoulos (2008) to prove the Bell-Kochen-Specker theorem in a 16-dimensional Hilbert space, is given a neat finite-geometrical reinterpretation in terms of the structure of the symplectic polar space $W(7, 2)$ of the real four-qubit Pauli group. Each of the four sets of observables of cardinality five represents an elliptic quadric in the three-dimensional projective space of order two (PG$(3, 2)$) it spans, whereas the remaining set of cardinality four corresponds to an affine plane of order two. The four ambient PG$(3, 2)$s of the quadrics intersect pairwise in a line, the resulting six lines meeting in a point. Projecting the whole configuration from this distinguished point (observable) one gets another, complementary ''magic rectangle" of the same qualitative structure.
- 1 :
- Astronomical Institute, Slovak Academy of Sciences
- 2 :
- CNRS : UMR6174 – Université de Franche-Comté – Université de Technologie de Belfort-Montbeliard – Ecole Nationale Supérieure de Mécanique et des Microtechniques
- Domaine : Physique/Physique Quantique
Physique/Physique mathématiqueMathématiques/Physique mathématiqueMathématiques/Combinatoire - Mots-clés : Bell-Kochen-Specker Theorem – ''Magic Rectangle" of Observables – Four-Qubit Pauli Group – Finite Geometry
- Commentaire : 5 pages – 1 figure
- hal-00692040, version 1
- http://hal.archives-ouvertes.fr/hal-00692040
- oai:hal.archives-ouvertes.fr:hal-00692040
- Contributeur :
- Soumis le : Vendredi 27 Avril 2012, 16:58:54
- Dernière modification le : Lundi 30 Juillet 2012, 15:53:54
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