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Purity of spin states in terms of tomograms

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Journal of Russian Laser Research Aims and scope

Abstract

The purity of spin-j states is expressed through measurable tomographic probabilities. Along with the general formula, we also establish particular relations for conventional spin tomography, spin tomography with a finite number of rotations, angular tomography, and some other types of fair tomographic-probability maps and quasidistributions.

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References

  1. G. Klose, G. Smith, and P. S. Jessen, Phys. Rev. Lett., 86, 4721 (2001).

    Article  ADS  Google Scholar 

  2. W. Rosenfeld, J. Volz, M. Weber, and H. Weinfurter, Phys. Rev. A, 84, 022343 (2011).

    Article  ADS  Google Scholar 

  3. V. I. Man’ko and O. V. Man’ko, J. Exp. Theor. Phys., 85, 430 (1997).

    Article  ADS  Google Scholar 

  4. V. V. Dodonov and V. I. Man’ko, Phys. Lett. A, 229, 335 (1997).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. O. V. Man’ko and V. I. Man’ko, Forschr. Phys., 57, 1064 (2009).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. M. A. Man’ko and V. I. Man’ko, AIP Conf. Proc., 1334, 217 (2011).

    Article  ADS  Google Scholar 

  7. R. L. Stratonovich, Sov. Phys. JETP, 4, 891 (1957).

    MathSciNet  Google Scholar 

  8. A. Vourdas, Rep. Prog. Phys., 67, 267 (2004).

    Article  MathSciNet  ADS  Google Scholar 

  9. K. S. Gibbons, M. J. Hoffman, and W. K. Wootters, Phys. Rev. A, 70, 062101 (2004).

    Article  MathSciNet  ADS  Google Scholar 

  10. A. Vourdas, J. Phys. A: Math. Gen., 39, R65 (2006).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. A. B. Klimov, C. Muñoz, and J. L. Romero, J. Phys. A: Math. Gen., 39, 14471 (2006).

    Article  ADS  MATH  Google Scholar 

  12. G. Björk, J. L. Romero, A. B. Klimov, and L. L. Sánchez-Soto, “The discrete Wigner function,” in: E. Wolf (ed.), Progress in Optics, Elsevier (2008), Vol. 51, Ch. 7, p. 469.

  13. F. A. Berezin, Math. USSR Izv., 6, 1117 (1972).

    Article  Google Scholar 

  14. O. V. Man’ko, V. I. Man’ko, and G. Marmo, J. Phys. A: Math. Gen., 35, 699 (2002).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. O. V. Man’ko, V. I. Man’ko, G. Marmo, and P. Vitale, Phys. Lett. A, 360, 522 (2007).

    Article  MathSciNet  ADS  Google Scholar 

  16. S. N. Filippov and V. I. Man’ko, J. Russ. Laser Res., 32, 56 (2011).

    Google Scholar 

  17. S. N. Filippov and V. I. Man’ko, J. Russ. Laser Res., 30, 129 (2009).

    Article  Google Scholar 

  18. G. M. D’Ariano, L. Maccone, and M. Paini, J. Opt. B: Quantum Semiclass. Opt., 5, 77 (2003).

    Article  ADS  Google Scholar 

  19. A. F. Nikiforov, S. K. Suslov, and V. B. Uvarov, Classical Orthogonal Polynomials of a Discrete Variable, Springer Verlag, Berlin, Heidelberg, New York (1991).

  20. S. N. Filippov, “Quantum states and dynamics of spin systems and electromagnetic field in the tomographic-probability representation,” Ph.D. Thesis, Moscow Institute of Physics and Technology [http://filippovsn.fizteh.ru/about/biography/Filippov-Abstract-Thesis.pdf (2012)].

  21. S. N. Filippov and V. I. Man’ko, J. Russ. Laser Res., 31, 32 (2010).

    Article  Google Scholar 

  22. I. D. Ivanović, J. Phys. A: Math. Gen., 14, 3241 (1981).

    Article  ADS  Google Scholar 

  23. W. K. Wootters, Ann. Phys. (N.Y.), 176, 1 (1987).

    Article  MathSciNet  ADS  Google Scholar 

  24. W. K. Wootters and B. D. Fields, Ann. Phys. (N.Y.), 191, 363 (1989).

    Article  MathSciNet  ADS  Google Scholar 

  25. S. N. Filippov and V. I. Man’ko, Phys. Scr., T143, 014010 (2011).

    Article  ADS  Google Scholar 

  26. H. F. Hofmann and S. Takeuchi, Phys. Rev. A, 69, 042108 (2004).

    Article  ADS  Google Scholar 

  27. R. G. Newton and B. Young, Ann. Phys., 49, 393 (1968).

    Article  ADS  Google Scholar 

  28. C. M. Caves, C. A. Fuchs, and R. Schack, Phys. Rev. A, 65, 022305 (2002).

    Article  MathSciNet  ADS  Google Scholar 

  29. J. M. Renes, R. Blume-Kohout, A. J. Scott, and C. M. Caves, J. Math. Phys., 45, 2171 (2004).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. S. Weigert, Int. J. Mod. Phys. B, 20, 1942 (2006).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  31. D. M. Appleby, S. T. Flammia, and C. A. Fuchs, J. Math. Phys., 52, 022202 (2011).

    Article  MathSciNet  ADS  Google Scholar 

  32. S. N. Filippov and V. I. Man’ko, J. Russ. Laser Res., 31, 211 (2010).

    Article  Google Scholar 

  33. J.-P. Amiet and S. Weigert, J. Phys. A: Math. Gen., 32, L269 (1999).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  34. J.-P. Amiet and S. Weigert, J. Opt. B: Quantum Semiclass. Opt., 2, 118 (2000).

    Article  MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology (State University), Institutskii Per. 9, Dolgoprudnyi, Moscow Region, 141700, Russia

    Sergey N. Filippov & Vladimir I. Man’ko

  2. Institute of Physics and Technology, Russian Academy of Sciences, Nakhimovskii Prospect 34, Moscow, 117218, Russia

    Sergey N. Filippov

  3. P. N. Lebedev Physical Institute, Russian Academy of Sciences, Leninskii Prospect 53, Moscow, 119991, Russia

    Vladimir I. Man’ko

Authors
  1. Sergey N. Filippov
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  2. Vladimir I. Man’ko
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Correspondence to Sergey N. Filippov.

Additional information

Manuscript submitted by the authors in English on November 20, 2012.

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Filippov, S.N., Man’ko, V.I. Purity of spin states in terms of tomograms. J Russ Laser Res 34, 14–21 (2013). https://doi.org/10.1007/s10946-013-9319-x

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  • DOI: https://doi.org/10.1007/s10946-013-9319-x

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