HAL : in2p3-00530340, version 1
 arXiv : 1010.5964
 Fourier Transforms: Approach to Scientific Principles, G. Nikolic (Ed.) (2010) 103-138
 Quadratic discrete Fourier transform and mutually unbiased bases
 (2010)
 The present chapter [submitted for publication in "Fourier Transforms, Theory and Applications", G. Nikolic (Ed.), InTech (Open Access Publisher), Vienna, 2011] is concerned with the introduction and study of a quadratic discrete Fourier transform. This Fourier transform can be considered as a two-parameter extension, with a quadratic term, of the usual discrete Fourier transform. In the case where the two parameters are taken to be equal to zero, the quadratic discrete Fourier transform is nothing but the usual discrete Fourier transform. The quantum quadratic discrete Fourier transform plays an important role in the field of quantum information. In particular, such a transformation in prime dimension can be used for obtaining a complete set of mutually unbiased bases.
 Thème(s) : Physique/Physique QuantiquePhysique/Physique mathématiqueMathématiques/Physique mathématique
 Mot(s)-clé(s) : quadratic discrete Fourier transform – mutually unbiased bases – Weyl pairs – Pauli operators – Lie algebras
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 in2p3-00530340, version 1 http://hal.in2p3.fr/in2p3-00530340 oai:hal.in2p3.fr:in2p3-00530340 Contributeur : Maurice Robert Kibler <> Déposé pour le compte de : Maurice Kibler <> Soumis le : Jeudi 28 Octobre 2010, 15:33:51 Dernière modification le : Jeudi 5 Mai 2011, 14:01:19