Skip to main content
SpringerLink
Log in

Polarization Tomography of Quantum Radiation: Theoretical Aspects and Operator Approach

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

We present theoretical foundations for the quantum tomography of polarization states of light fields as a method for measuring their polarization density operator \(\hat R\), which characterizes only the polarization degrees of freedom of the radiation. We mainly attend to the method in which the tomographic observables (the \(\hat R\) “measurement instruments”) are polarizable in nature. We show that the quantum nature of this method can be adequately expressed using the quasispectral tomographic decompositions of \(\hat R\) in special operator bases, which are finite sums of partially orthogonal projection operators determining the probability distributions of tomographic observables as the decomposition coefficients. We obtain the matrix versions of such “tomographic” representations of \(\hat R\), in particular, by projecting them on semiclassical operator bases determining the polarization quasiprobability functions. We briefly discuss the information aspects of the schemes considered in the paper.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. J. Bertrand and P. Bertrand, Found. Phys., 17, 397 (1987).

    Article  MathSciNet  Google Scholar 

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

    ADS  Google Scholar 

  3. D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, Phys. Rev. Lett., 70, 1244 (1993).

    Article  ADS  Google Scholar 

  4. H. Kuhn, D.-G. Welsh, and W. Vogel, Phys. Rev. A, 51, 4240 (1995).

    ADS  Google Scholar 

  5. U. Leonhardt, H. Paul, and G. M. D'Ariano, Phys. Rev. A, 52, 4899 (1995).

    Article  ADS  Google Scholar 

  6. K. Banaszek and K. Wodkiewicz, Phys. Rev. Lett., 76, 4344 (1996).

    Article  ADS  Google Scholar 

  7. V. Buzek, G. Adam, and G. Drobny, Ann. Phys., 245, 37 (1996).

    ADS  MathSciNet  Google Scholar 

  8. A. Wuensche, J. Modern Optics, 44, 2293 (1997).

    ADS  MATH  Google Scholar 

  9. V. P. Karasev and A. V. Masalov, JETP, 99, 51 (2004).

    Google Scholar 

  10. J. von Neumann, Mathematische Grundlagen der Quantenmechanik, Springer, Berlin (1932).

    Google Scholar 

  11. A. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory [in Russian], Nauka, Moscow (1980); English transl., North-Holland, Amsterdam (1982).

    Google Scholar 

  12. B. B. Kadomtsev, Phys. Usp., 37, 425 (1983); S. Ya. Kilin, Phys. Usp., 42, 435 (1999).

    Google Scholar 

  13. D. Bowmeester, A. K. Ekert, and A. Zeilinger, eds., The Physics of Quantum Information: Quantum Cryptography, Quantum Teleportation, Quantum Computation, Springer, Berlin (2000).

    Google Scholar 

  14. M. B. Menskii, Phys. Usp., 43, 585 (2000).

    Article  Google Scholar 

  15. I. V. Volovich, “Quantum information in space and time,” quant-ph/0108073 (2001); Quantum Computers, Teleportation, Cryptography: Lectures, Steklov Math. Inst., Moscow (2001–2002).

  16. B. A. Grishanin and V. N. Zadkov, Radiotekhn. Elektron., 47, 1029 (2002).

    Google Scholar 

  17. K. A. Valiev, Phys. Usp., 48, 1 (2005).

    Article  Google Scholar 

  18. R. L. Stratonovich, JETP, 4, 891 (1956).

    MATH  MathSciNet  Google Scholar 

  19. V. I. Tatarskii, Sov. Phys. Usp., 26, 311 (1983); M. Hillery, R. F. O'Connell, M. O. Scully, and E. P. Wigner, Phys. Rep., 106, 121 (1984).

    MathSciNet  Google Scholar 

  20. K. Banaszek, G. M. D'Ariano, M. G. A. Paris, and M. F. Sacchi, Phys. Rev. A, 61, 010304(R) (1999).

  21. A. B. Klimov, O. V. Man'ko, V. I. Man'ko, Yu. F. Smirnov, and V. N. Tolstoy, J. Phys. A, 35, 6101 (2002).

    ADS  MathSciNet  Google Scholar 

  22. V. P. Karasev, Bull. P. N. Lebedev Phys. Inst. (Allerton Press), no. 9, 31 (1999).

  23. M. G. Raymer, A. C. Funk, and D. F. McAlister, “Measuring the quantum polarization state of light,” in: Quantum Communications, Computing, and Measurement (P. Kumar et al., eds.), Vol. 2, Kluwer, New York (2000), p. 147.

    Google Scholar 

  24. P. A. Bushev, V. P. Karasev, A. V. Masalov, and A. A. Putilin, Optics Spectrosc., 91, 526 (2001).

    ADS  Google Scholar 

  25. V. P. Karassiov, J. Phys. A, 26, 4345 (1993); J. Rus. Laser Res., 15, 391 (1994); 21, 370 (2000).

    Article  ADS  MathSciNet  Google Scholar 

  26. A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev., 47, 777 (1935).

    Article  ADS  Google Scholar 

  27. V. P. Karassiov and A. V. Masalov, Laser Phys., 12, 948 (2002); J. Opt. B, 4, S366 (2002).

    Google Scholar 

  28. D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular Momentum [in Russian], Nauka, Leningrad (1975); English transl., World Scientific, Singapore (1988).

    Google Scholar 

  29. A. M. Perelomov, Generalized Coherent States and Their Applications [in Russian], Nauka, Moscow (1987); English version, Springer, Berlin (1986).

    Google Scholar 

  30. G. S. Agarwal, Phys. Rev. A, 57, 671 (1998).

    ADS  Google Scholar 

  31. Yu. V. Prokhorov and Yu. A. Rozanov, Probability Theory: Basic Concepts, Limit Theorems, Random Processes [in Russian] (2nd ed.), Nauka, Moscow (1973); English transl. prev. ed., Springer, Berlin (1969).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lebedev Physical Institute, RAS, Moscow, Russia

    V. P. Karassiov

Authors
  1. V. P. Karassiov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 145, No. 3, pp. 344–357, December, 2005.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Karassiov, V.P. Polarization Tomography of Quantum Radiation: Theoretical Aspects and Operator Approach. Theor Math Phys 145, 1666–1677 (2005). https://doi.org/10.1007/s11232-005-0189-4

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11232-005-0189-4

Keywords

Search

Navigation