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| HAL: hal-00002952, version 2 |
| arXiv: quant-ph/0409184 |
| Detailed view |  Export this paper |
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| Chaos, Solitons and Fractals 26 (2005) 1267 - 1270 |
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| Available versions: | v1 (2004-09-27) | v2 (2004-11-25) |
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| Sets of Mutually Unbiased Bases as Arcs in Finite Projective Planes? |
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| Metod Saniga 1Michel R. P. Planat 1 |
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| (2005) |
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| 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. |
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| 1: | Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (FEMTO-ST) |
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CNRS : UMR6174 – Université de Franche-Comté – Université de Technologie de Belfort-Montbeliard – Ecole Nationale Supérieure de Mécanique et des Microtechniques |
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| Subject | : | Physics/Quantum Physics Physics/Mathematical Physics |
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| Quantum Information – Mutually Unbiased Bases – Finite Geometries |
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| hal-00002952, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00002952 | |
| oai:hal.archives-ouvertes.fr:hal-00002952 | |
| From: Metod Saniga | |
| Submitted on: Thursday, 25 November 2004 11:31:57 | |
| Updated on: Tuesday, 7 June 2005 13:43:11 | |
