Skip to main content
Log in

Statistical reconstruction of the quantum states of three-level optical systems

  • Nonlinear Dynamics
  • Published:
Journal of Experimental and Theoretical Physics Letters Aims and scope Submit manuscript

Abstract

The procedure of measurement followed by the reconstruction of the quantum state of a three-level optical system is implemented for a frequency-and spatially degenerate two-photon field. The method of statistical estimation of the quantum state from a solution to the likelihood equation and the analysis of the statistical properties of the obtained estimators is developed. Using the root method of estimating quantum states, the initial two-photon (qutrit) wave function is reconstructed from the measured fourth-order field moments.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. A. V. Burlakov and D. N. Klyshko, Pis’ma Zh. Éksp. Teor. Fiz. 69, 795 (1999) [JETP Lett. 69, 839 (1999)].

    Google Scholar 

  2. H. Bechmann-Pasquinucci and W. Tittel, Phys. Rev. A 61, 062308 (2000).

    Google Scholar 

  3. H. Bechmann-Pasquinucci and A. Peres, Phys. Rev. Lett. 85, 3313 (2000).

    Article  ADS  MathSciNet  Google Scholar 

  4. M. V. Chekhova, S. P. Kulik, G. A. Maslennikov, and A. A. Zhukov, quant-ph/0305115.

  5. D. N. Klyshko, Photons and Nonlinear Optics (Nauka, Moscow, 1980), p. 256.

    Google Scholar 

  6. A. V. Belinsky and D. N. Klyshko, Laser Phys. 4, 663 (1994).

    Google Scholar 

  7. A. V. Burlakov, M. V. Chekhova, D. N. Klyshko, et al., Phys. Rev. A 60, 4209 (1999).

    Article  ADS  Google Scholar 

  8. A. V. Burlakov and M. V. Chekhova, Pis’ma Zh. Éksp. Teor. Fiz. 75, 505 (2002) [JETP Lett. 75, 432 (2002)].

    Google Scholar 

  9. A. V. Burlakov, L. A. Krivitskii, S. P. Kulik, et al., Opt. Spektrosk. 94, 744 (2003) [Opt. Spectrosc. 94, 684 (2003)].

    Google Scholar 

  10. L. A. Krivitskii, S. P. Kulik, A. N. Penin, and M. V. Chekhova, Zh. Éksp. Teor. Fiz. 124(4), 943 (2003) [JETP 97, 846 (2003)].

    Google Scholar 

  11. D. N. Klyshko, Zh. Éksp. Teor. Fiz. 111, 1955 (1997) [JETP 84, 1065 (1997)].

    Google Scholar 

  12. Yu. I. Bogdanov, Fundamental Problem of Statistical Data Analysis: Root Approach (Mosk. Inst. Élektron. Tekh., Moscow, 2002); physics/0211109 (2002).

    Google Scholar 

  13. Yu. I. Bogdanov, Quantum Mechanical View of Mathematical Statistics, in Progress in Quantum Physics Research (Nova Science, New York, 2003); quant-ph/0303013 (2003).

    Google Scholar 

  14. Yu. I. Bogdanov, Root Estimator of Quantum States, in Progress in Quantum Physics Research (Nova Science, New York, 2003); quant-ph/0303014 (2003).

    Google Scholar 

  15. H. Cramer, Mathematical Methods of Statistics (Princeton Univ. Press, Princeton, N.J., 1946; Mir, Moscow, 1975).

    Google Scholar 

  16. M. G. Kendall and A. Stuart, The Advanced Theory of Statistics, 4th ed. (Griffin, London, 1977; Nauka, Moscow, 1973).

    Google Scholar 

  17. Optical Materials for Infrared Engineering (Mir, Moscow, 1965).

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Translated from Pis’ma v Zhurnal Éksperimental’no\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) i Teoretichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Fiziki, Vol. 78, No. 6, 2003, pp. 804–809.

Original Russian Text Copyright © 2003 by Bogdanov, Krivitsky, Kulik.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bogdanov, Y.I., Krivitsky, L.A. & Kulik, S.P. Statistical reconstruction of the quantum states of three-level optical systems. Jetp Lett. 78, 352–357 (2003). https://doi.org/10.1134/1.1630126

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/1.1630126

PACS numbers

Navigation