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Journal of Russian Laser Research

, Volume 35, Issue 1, pp 3–13 | Cite as

Wigner Functions and Spin Tomograms for Qubit States

  • Peter Adam
  • Vladimir A. Andreev
  • Iulia Ghiu
  • Aurelian Isar
  • Margarita A. Man’ko
  • Vladimir I. Man’ko
Article

Abstract

We establish the relation of the spin tomogram to the Wigner function on a discrete phase space of qubits. We use the quantizers and dequantizers of the spin tomographic star-product scheme for qubits to derive the expression for the kernel connecting Wigner symbols on the discrete phase space with the tomographic symbols.

Keywords

discrete Wigner function spin tomography star product quantizer dequantizer 

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References

  1. 1.
    J. Schwinger, Proc. Natl. Acad. Sci. U.S.A., 46, 570 (1960).ADSCrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    W. K. Wootters, IBM J. Res. Dev., 48, 99 (2004).CrossRefGoogle Scholar
  3. 3.
    A. Vourdas, Acta Appl. Math., 93, 197 (2006).CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    K. S. Gibbons, M. J. Hoffman, and W. K. Wootters, Phys. Rev. A 70, 062101 (2004).ADSCrossRefMathSciNetGoogle Scholar
  5. 5.
    A. B. Klimov, J. L. Romero, G. Bj¨ork, and L. L. S´anchez-Soto, J. Phys. A: Math. Theor., 40, 3987 (2007).ADSCrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    P. Stóvicék and J. Tolar, Rep. Math. Phys., 20, 157 (1984).ADSCrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    S. Chaturvedi, E. Ercolessi, G. Marmo, et al., J. Phys. A: Math. Gen., 39, 1405 (2006).ADSCrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    S. N. Filippov and V. I. Man’ko, Phys. Scr., T143, 014010 (2011).ADSCrossRefGoogle Scholar
  9. 9.
    I. D. Ivanović, J. Phys. A: Math. Gen., 14, 3241 (1981).ADSCrossRefGoogle Scholar
  10. 10.
    W. K. Wootters, Ann. Phys. (N.Y.), 176, 1 (1987).Google Scholar
  11. 11.
    V. V. Dodonov and V. I. Man’ko, Phys. Lett. A, 229 335 (1997).ADSCrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    V. I. Man’ko and O. V. Man’ko, J. Exp. Theor. Phys., 85, 430 (1997).ADSCrossRefGoogle Scholar
  13. 13.
    V. A. Andreev and V. I. Man’ko, J. Exp. Theor. Phys., 87, 239 (1998).ADSCrossRefGoogle Scholar
  14. 14.
    V. A. Andreev, O. V. Man’ko, V. I. Man’ko, and S. S. Safonov, J. Russ. Laser Res., 19, 340 (1998).Google Scholar
  15. 15.
    V. I. Man’ko, G. Marmo, A. Simoni, and F. Ventriglia, Phys. Lett. A, 372, 6490 (2004).Google Scholar
  16. 16.
    S. L. Stratonovich, Sov. Phys. JETP, 4, 891 (1957).MathSciNetGoogle Scholar
  17. 17.
    F. Bayen, M. Flato, C. Fronsdal, et al., Lett. Math. Phys., 1, 521 (1977).ADSCrossRefMathSciNetGoogle Scholar
  18. 18.
    E. Wigner, Phys. Rev., 40, 749 (1932).ADSCrossRefGoogle Scholar
  19. 19.
    O. V. Man’ko, V. I. Man’ko, and G. Marmo, J. Phys. A: Math. Gen., 35, 699 (2002).Google Scholar
  20. 20.
    W. K. Wootters, Found. Phys., 36, 112 (2006).ADSCrossRefMATHMathSciNetGoogle Scholar
  21. 21.
    I. Ghiu, J. Phys.: Conf. Ser., 338, 012008 (2012).ADSGoogle Scholar
  22. 22.
    G. Björk, J. L. Romero, A. B. Klimov, and L. L. Sánchez-Soto, J. Opt. Soc. Am. B, 24, 371 (2007).Google Scholar
  23. 23.
    I. Ghiu, Phys. Scr., T153, 014027 (2013).ADSCrossRefGoogle Scholar
  24. 24.
    A. B. Klimov, J. L. Romero, G. Björk, and L. L. S´anchez-Soto, Ann. Phys. (N.Y.), 324, 53 (2009).Google Scholar
  25. 25.
    T. Paterek, B. Dakic, and C. Brukner, Phys. Rev. A, 83, 036102 (2011).ADSCrossRefGoogle Scholar
  26. 26.
    T. Paterek, M. Pawlowski, M. Grassl, and C. Brukner, Phys. Scr., T140, 014031 (2010).ADSCrossRefGoogle Scholar
  27. 27.
    C. Ghiu and I. Ghiu, Cent. Eur. J. Math., 12, 337 (2014).Google Scholar
  28. 28.
    T. Durt, B.-G. Englert, I. Bengtsson, and K. Ż yczkowski, Int. J. Quantum Inform., 8, 535 (2010).Google Scholar
  29. 29.
    R. Asplund and G. Björk, Phys. Rev. A, 64, 012106 (2001).ADSCrossRefGoogle Scholar
  30. 30.
    R. Franco and V. Penna, J. Phys. A: Math. Gen., 39, 5907 (2006).ADSCrossRefMATHMathSciNetGoogle Scholar
  31. 31.
    A. Ibort, V. I. Man’ko, G. Marmo, et al., Phys. Scr., 79, 065013 (2009).Google Scholar
  32. 32.
    S. N. Filippov and V. I. Man’ko, J. Russ. Laser Res., 31, 32 (2010).CrossRefGoogle Scholar
  33. 33.
    M. O. Terra Cuñha, V. I. Man’ko, and M. O. Scully, Found. Phys. Lett., 14, 103 (2001).Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Peter Adam
    • 1
  • Vladimir A. Andreev
    • 2
  • Iulia Ghiu
    • 3
  • Aurelian Isar
    • 4
  • Margarita A. Man’ko
    • 2
  • Vladimir I. Man’ko
    • 2
  1. 1.Institute for Solid State Physics and Optics Wigner Research Centre for PhysicsHungarian Academy of SciencesBudapestHungary
  2. 2.P. N. Lebedev Physical InstituteRussian Academy of SciencesMoscowRussia
  3. 3.Centre for Advanced Quantum Physics Department of PhysicsUniversity of BucharestBucharest-MăgureleRomania
  4. 4.Horia Hulubei National Institute for Research and Development in Physics and Nuclear EngineeringBucharest-MăgureleRomania

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