Skip to main content
Log in

Statistical reconstruction of optical quantum states based on mutually complementary quadrature quantum measurements

  • Atoms, Molecules, Optics
  • Published:
Journal of Experimental and Theoretical Physics Aims and scope Submit manuscript

Abstract

We describe a new method for reconstructing the quantum state of the electromagnetic field from the results of mutually complementary optical quadrature measurements. This method is based on the root approach and displaces squeezed Fock states are used as the basis. Theoretical analysis and numerical experiments demonstrate the considerable advantage of the developed tools over those described in the literature.

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. N. Bohr, in Albert Einstein, Philosopher–Scientist, Library of Living Philosophers, Ed. by P. A. Schilp (Evanston, Illinois, 1949), pp. 200–241.

  2. W. Pauli, General Principles of Quantum Mechanics (Springer, Berlin, Heidelberg, New York, 1980), p.212.

    Book  Google Scholar 

  3. Yu. I. Bogdanov, Fundamental Problem of Statistical Data Analysis: Root Approach (Mosk. Inst. Elektron. Tekh., Moscow, 2002) [in Russian]; arXiv:phys/0211109.

    Google Scholar 

  4. Yu. I. Bogdanov, Opt. Spectrosc. 96, 668 (2004).

    Article  ADS  Google Scholar 

  5. Yu. I. Bogdanov, Proc. SPIE, ed. by Yu. I. Ozhigov 6264, 62640E-1–68640E-15 (2006) Yu. I. Bogdanov, Quantum Mechanical View of Mathematical Statistics, New Topics in Quantum Physics Research (Nova Science, 2006), p. 1; arXiv:quant-ph/0303013.

    Google Scholar 

  6. H. P. Yuen and V. W. S. Chan, Opt. Lett. 8 (3), 177 (1983).

    Article  ADS  Google Scholar 

  7. B. L. Schumaker, Opt. Lett. 9 (5), 189 (1984).

    Article  ADS  MathSciNet  Google Scholar 

  8. K. Vogel and H. Risken, Phys. Rev. A 40, 2847 (1989).

    Article  ADS  Google Scholar 

  9. W. P. Schleich, Quantum Optics in Phase Space (Wiley-VCH, Berlin, 2001).

    Book  MATH  Google Scholar 

  10. Yu. I. Bogdanov and S. P. Kulik, Laser Phys. Lett. 10, 125202 (2013).

    Article  ADS  Google Scholar 

  11. A. I. Lvovsky and M. G. Raymer, Rev. Mod. Phys. 81, 299 (2009).

    Article  ADS  Google Scholar 

  12. E. U. Condon, Proc. Nat. Acad. Sci. USA 23, 158 (1937).

    Article  ADS  Google Scholar 

  13. S. Chountasis, A. Vourdas, and C. Bendjaballah, Phys. Rev. A 60, 3467 (1999).

    Article  ADS  MathSciNet  Google Scholar 

  14. G. M. D’Ariano, M. G. Paris, and M. F. Sacchi, Adv. Imag. Electron Phys. 128, 205 (2003); arXiv:quantph/0302028.

    Article  Google Scholar 

  15. A. Ibort, V. I. Man’ko, G. Marmo, et al., Phys. Scripta 79, 065013 (2009).

    Article  ADS  Google Scholar 

  16. M. Paris and J. Rehácek, Quantum State Estimation, Lect. Notes Phys. 649 (2004).

  17. Focus on Quantum Tomography, Ed. by K. Banaszek, M. Cramer, and D. Gross, New J. Phys. 15, 125020 (2013). http://iopscience.iop.org/1367-2630/page/Focus%20on%20Quantum%20Tomography.

  18. G. M. D’Ariano, C. Macchiavello, and M. G. Paris, Phys. Rev. A 50, 4298 (1994).

    Article  ADS  Google Scholar 

  19. A. I. Lvovsky, J. Opt. B: Quant. Semiclass. Opt. 6, S556 (2004).

    Article  ADS  Google Scholar 

  20. Yu. I. Bogdanov, M. V. Chekhova, S. P. Kulik, et al., Phys. Rev. A 70, 042303 (2004).

    Article  ADS  Google Scholar 

  21. Yu. I. Bogdanov, M. V. Chekhova, S. P. Kulik, et al., Phys. Rev. Lett. 93, 230503 (2004).

    Article  ADS  Google Scholar 

  22. Yu. I. Bogdanov and Yu. I. Bogdanov, J. Exp. Theor. Phys. 108, 928 (2009).

    Article  ADS  Google Scholar 

  23. Yu. I. Bogdanov, G. Brida, M. Genovese, et al., Phys. Rev. Lett. 105, 010404 (2010).

    Article  ADS  Google Scholar 

  24. Yu. I. Bogdanov, G. Brida, I. D. Bukeev, et al., Phys. Rev. A 84, 042108 (2011).

    Article  ADS  Google Scholar 

  25. I. Bengtsson and K. Zyczkowski, Geometry of Quantum States: An Introduction to Quantum Entanglement (Cambridge Univ. Press, Cambridge, 2006).

    Book  MATH  Google Scholar 

  26. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, et al., J. Chem. Phys. 21, 1087 (1953).

    Article  ADS  Google Scholar 

  27. M. E. J. Newman and G. T. Barkema, Monte Carlo Methods in Statistical Physics (Clarendon Press, 1999).

    MATH  Google Scholar 

  28. V. V. Dodonov, I. A. Malkin, and V. I. Man’ko, Physica 72, 597 (1974).

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yu. I. Bogdanov.

Additional information

Original Russian Text © Yu.I. Bogdanov, G.V. Avosopyants, L.V. Belinskii, K.G. Katamadze, S.P. Kulik, V.F. Lukichev, 2016, published in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2016, Vol. 150, No. 2, pp. 246–253.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bogdanov, Y.I., Avosopyants, G.V., Belinskii, L.V. et al. Statistical reconstruction of optical quantum states based on mutually complementary quadrature quantum measurements. J. Exp. Theor. Phys. 123, 212–218 (2016). https://doi.org/10.1134/S1063776116070025

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063776116070025

Navigation