 |
|
|
|
| HAL : hal-00002952, version 2 |
| arXiv : quant-ph/0409184 |
| Fiche détaillée |  Récupérer au format |
|
|
| Chaos, Solitons and Fractals 26 (2005) 1267 - 1270 |
|
|
| Versions disponibles : | v1 (27-09-2004) | v2 (25-11-2004) |
|
|
|
|
| Sets of Mutually Unbiased Bases as Arcs in Finite Projective Planes? |
|
|
| Metod Saniga 1Michel R. P. Planat 1 |
|
|
| (2005) |
|
|
|
| This note is a short elaboration of the conjecture of Saniga et al (J. Opt. B: Quantum Semiclass. 6 (2004) L19-L20) by regarding a set of mutually unbiased bases (MUBs) in a d-dimensional Hilbert space, d being a power of a prime, as an analogue of an arc in a (Desarguesian) projective plane of order d. Complete sets of MUBs thus correspond to (d+1)-arcs, i.e., ovals. The existence of two principally distinct kinds of ovals for d even and greater than four, viz. conics and non-conics, implies the existence of two qualitatively different groups of the complete sets of MUBs for the Hilbert spaces of corresponding dimensions. |
|
|
|
|
|
|
|
|
|
|
|
| 1 : | Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (FEMTO-ST) |
|
|
|
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 mathématique |
|
|
| Quantum Information – Mutually Unbiased Bases – Finite Geometries |
|
|
|
| Liste des fichiers attachés à ce document : | ||||||||||
|
||||||||||
|
|
|
| hal-00002952, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00002952 | |
| oai:hal.archives-ouvertes.fr:hal-00002952 | |
| Contributeur : Metod Saniga | |
| Soumis le : Jeudi 25 Novembre 2004, 11:31:57 | |
| Dernière modification le : Mardi 7 Juin 2005, 13:43:11 | |
