DI-UMONS : Dépôt institutionnel de l’université de Mons

Recherche transversale
Rechercher
(titres de publication, de périodique et noms de colloque inclus)
2008-01-01 - Article/Dans un journal avec peer-review - Anglais - page(s)

Massar S., Spindel Philippe , "Uncertainty Relation for the Discrete Fourier Transform" in Physical Review Letters, 100, 19

  • Edition : American Physical Society, Ridge (NY)
  • Codes CREF : Mécanique quantique classique et relativiste (DI1211), Théorie quantique des champs (DI1215)
  • Unités de recherche UMONS : Mécanique et gravitation (S884)
Texte intégral :

Abstract(s) :

(Anglais) We derive an uncertainty relation for two unitary operators which obey a commutation relation of the form UV ei VU. Its most important application is to constrain how much a quantum state can be localized simultaneously in two mutually unbiased bases related by a discrete fourier transform. It provides an uncertainty relation which smoothly interpolates between the well-known cases of the Pauli operators in two dimensions and the continuous variables position and momentum. This work also provides an uncertainty relation for modular variables, and could find applications in signal processing. In the finite dimensional case the minimum uncertainty states, discrete analogues of coherent and squeezed states, are minimum energy solutions of Harper’s equation, a discrete version of the harmonic oscillator equation.

Notes :
  • (Anglais) e-Print Archive: hep-th/0710.0723
Identifiants :
  • DOI : 0556-2821