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Fourier Transforms: Approach to Scientific Principles, G. Nikolic (Ed.) (2010) 103-138
Quadratic discrete Fourier transform and mutually unbiased bases
Maurice Robert Kibler1

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.
1 :  IPNL - Institut de Physique Nucléaire de Lyon
Physique/Physique Quantique

Physique/Physique mathématique

Mathématiques/Physique mathématique
quadratic discrete Fourier transform – mutually unbiased bases – Weyl pairs – Pauli operators – Lie algebras
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