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Theoretical and Mathematical Physics

, Volume 197, Issue 2, pp 1677–1689 | Cite as

Unnormalized Tomograms and Quasidistributions of Quantum States

  • V. I. Man’koEmail author
  • L. A. Markovich
Article
  • 13 Downloads

Abstract

We consider tomograms and quasidistributions, such as the Wigner functions, the Glauber–Sudarshan P-functions, and the Husimi Q-functions, that violate the standard normalization condition for probability distribution functions. We introduce special conditions for theWigner function to determine the tomogram with the Radon transform and study three different examples of states like the de Broglie plane wave, the Moshinsky shutter problem, and the stationary state of a charged particle in a uniform constant electric field. We show that their tomograms and quasidistribution functions expressed in terms of the Dirac delta function, the Airy function, and Fresnel integrals violate the standard normalization condition and the density matrix of the state therefore cannot always be reconstructed. We propose a method that allows circumventing this problem using a special tomogram in the limit form.

Keywords

quantum tomography quasidistribution normalization condition plane wave Moshinsky shutter particle in an electric field 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Lebedev Physical Institute, RASMoscowRussia
  2. 2.Moscow Institute of Physics and TechnologyDolgoprudnyRussia
  3. 3.Kharkevich Institute for Information Transmission ProblemsMoscowRussia
  4. 4.Trapeznikov Institute of Control SciencesMoscowRussia
  5. 5.International Center for Quantum Optics and Quantum Technologies (the Russian Quantum Center)MoscowRussia

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