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Quadratic discrete Fourier transform and mutually unbiased bases

Abstract : 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.
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Contributor : Maurice Robert Kibler Connect in order to contact the contributor
Submitted on : Thursday, October 28, 2010 - 3:33:51 PM
Last modification on : Friday, September 10, 2021 - 1:50:07 PM
Long-term archiving on: : Saturday, January 29, 2011 - 2:47:11 AM


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  • HAL Id : in2p3-00530340, version 1
  • ARXIV : 1010.5964



Maurice Robert Kibler. Quadratic discrete Fourier transform and mutually unbiased bases. G. Nikolic. Fourier Transforms: Approach to Scientific Principles, InTech (Open access Publisher) Vienna, pp.103-138, 2010. ⟨in2p3-00530340⟩



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