Lobachevskii Journal of Mathematics

, Volume 38, Issue 4, pp 595–599 | Cite as

On tomographic representation on the plane of the space of Schwartz operators and its dual



It is shown that the set of optical quantum tomograms can be provided with the topology of Frechet space. In such a case the conjugate space will consist of symbols of quantum observables including all polynomials of the position and momentum operators.

Keywords and phrases

Schwartz operator optical tomogram dual map 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    D. T. Smithey, M. Beck, and M. G. Raymer, “Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: application to squeezed states and the vacuum,” Phys. Rev. Lett. 70, 1244–1247 (1993).CrossRefGoogle Scholar
  2. 2.
    M. Keyl, J. Kiukas, and R. F. Werner, “Schwartz operators,” arXiv:1503.04086 (2015).MATHGoogle Scholar
  3. 3.
    G. G. Amosov, Ya. A. Korennoi, and V. I. Man’ko, “Calculating means of quantum observables in the optical tomography representation,” Theor. Math. Phys. 171, 832–838 (2012).MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    G. G. Amosov, Ya. A. Korennoy, and V. I. Man’ko, “Description and measurement of observables in the optical tomographic probability representation of quantum mechanics,” Phys. Rev. A 85, 052119 (2012).CrossRefMATHGoogle Scholar
  5. 5.
    G. G. Amosov and A. I. Dnestryan, “Towards a tomographic representation of quantum mechanics on the plane,” Phys. Scr. 90, 074025 (2015).CrossRefGoogle Scholar
  6. 6.
    L. M. Artiles, R. D. Gill, and M. I. Guta, “An invitation to quantum tomography,” J. R. Stat. Soc. B 67, 109–134 (2005).MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia

Personalised recommendations