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Tomographic characteristics of spin states

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Journal of Russian Laser Research Aims and scope

Abstract

Spin states are studied in the tomographic-probability representation. The standard probability distribution of spin projection onto a direction in space is used instead of the spinor or the density matrix to identify the quantum state. The Shannon entropy and information are associated with the spin tomographic probability. A short review of the probability-theory notions is presented. Analysis of tomographic entropy and tomographic information for the Werner state is considered. The probability representation is used to describe a spin-3/2 particle and two qubits. The connection of tomographic entropy with the von Neumann entropy is discussed.

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References

  1. E. Schrödinger, Ann. Phys. (Leipzig), 79, 489 (1926).

    MATH  Google Scholar 

  2. L. D. Landau, Z. Phys., 45, 430 (1927).

    Article  MATH  Google Scholar 

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

    Google Scholar 

  4. I. A. Malkin and V. I. Man’ko, Dynamical Symmetries and Coherent States of Quantum Systems [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  5. V. V. Dodonov and V. I. Man’ko, Invariants and Evolution of Nonstationary Quantum Systems, Proceedings of the P. N. Lebedev Physical Institute, Nauka, Moscow (1987), Vol. 183 [Nova Science, New York (1989)].

    Google Scholar 

  6. E. P. Wigner, Phys. Rev., 40, 749 (1932); E. P. Wigner, in: W. Yourgrau and A. van der Merwe (Eds.), Perspectives in Quantum Theory, Dover, New York (1979).

    Article  MATH  ADS  Google Scholar 

  7. K. Husimi, Proc. Phys. Math. Soc. Jpn, 23, 264 (1940).

    Google Scholar 

  8. Y. Kano, J. Math. Phys., 6, 1913 (1965).

    Article  MathSciNet  Google Scholar 

  9. E. C. G. Sudarshan, Phys. Rev. Lett., 10, 177 (1963).

    Article  MathSciNet  ADS  Google Scholar 

  10. R. J. Glauber, Phys. Rev. Lett., 10, 84 (1963); Phys Rev, 131, 2766 (1963).

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  13. E. Schrödinger, Naturwissenschaften, 23, 807; 823; 844 (1935).

    Article  MATH  Google Scholar 

  14. J. S. Bell, Physics, 1, 195 (1964).

    Google Scholar 

  15. S. Mancini, V. I. Man’ko, and P. Tombesi, Phys. Lett. A, 213, 1 (1996); Found. Phys., 27, 801 (1997).

    Article  MathSciNet  ADS  Google Scholar 

  16. V. V. Dodonov and V. I. Man’ko, Phys. Lett. A, 239, 335 (1997).

    Article  MathSciNet  ADS  Google Scholar 

  17. V. I. Man’ko and O. V. Man’ko, Zh. Éksp. Teor. Fiz., 112, 796 (1997) [JETP, 85, 430 (1997)].

    MathSciNet  Google Scholar 

  18. A. B. Klimov, O. V. Man’ko, V. I. Man’ko, Yu. F. Smirnov, and V. N. Tolstoy, J. Phys. A: Math. Gen., 35, 6101 (2002).

    Article  MathSciNet  ADS  Google Scholar 

  19. O. V. Man’ko, Acta Physica Hungarica B, Ser. Heavy Ion Phys., 19/3–4, 313 (2004).

    Article  Google Scholar 

  20. V. I. Man’ko and S. S. Safonov, Yad. Fiz., 4, 658 (1998).

    Google Scholar 

  21. O. V. Man’ko, V. I. Man’ko, and O. V. Pilyavets, J. Russ Laser Res., 26, 429 (2005).

    Article  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  23. V. I. Man’ko, G. Marmo, A. Simoni, A. Stern, E. C. G. Sudarshan, and F. Ventriglia, Open Systems & Inform. Dynam. (2006, in press).

  24. V. I. Man’ko, G. Marmo, A. Simoni, A. Stern, and F. Ventriglia, Phys. Lett. A, 343, 251 (2005).

    Article  ADS  Google Scholar 

  25. V. I. Man’ko and O. V. Pilyavets, J. Russ Laser Res., 26, 259 (2005).

    Article  Google Scholar 

  26. D. F. Styer, M. S. Balkin, K. M. Becker, et al., Am. J. Phys., 70, 288 (2002).

    Article  ADS  Google Scholar 

  27. C. E. Shannon, Bell Tech. J., 27, 379 (1948).

    MathSciNet  Google Scholar 

  28. Olga Man’ko and V. I. Man’ko, J. Russ. Laser Res., 18, 407 (1997).

    Google Scholar 

  29. M. A. Man’ko, J. Russ. Laser Res., 22, 168 (2001); S. De Nicola, R. Fedele, M. A. Man’ko, and V. I. Man’ko, Eur. Phys. J. B, 36, 385 (2003).

    Article  Google Scholar 

  30. O. V. Man’ko and V. I. Man’ko, J. Russ Laser Res., 25, 115 (2004); Olga V. Man’ko, On Entropy and Information of Quantum States, Contribution to the International Conference “New Trends in Quantum Mechanics. Fundamental Aspects and Applications” (University of Palermo, Italy, November 2005); Open Systems & Inform. Dynam. (2006, in press).

    Article  Google Scholar 

  31. Olga V. Man’ko and Vladimir I. Man’ko, Tomographic Entropy for Spin Systems, Contribution to the XII Central European Workshop on Quantum Optics (Bilkent University, Ankara, June 2005); J. Phys. Conf. Ser. (2006, in press).

  32. S. Mancini, V. I. Man’ko, E. V. Shchukin, and P. A. Tombesi, J. Opt. B: Quantum Semiclass. Opt., 5, S333 (2003).

    Article  ADS  Google Scholar 

  33. V. I. Man’ko, G. Marmo, E. C. G. Sudarshan, and F. Zaccaria, Phys. Lett. A, 327, 353 (2004).

    Article  MathSciNet  ADS  Google Scholar 

  34. S. V. Kuznetsov, A. V. Kusev, O. V. Man’ko, Acta Physica Hungarica B, Ser. Quantum Electron., 20/1, 11 (2004).

    Article  Google Scholar 

  35. S. V. Kuznetsov, A. V. Kusev, O. V. Man’ko, and N. V. Tcherniega, Izvestiya RAN, Ser. Fiz., 68, 1239 (2004); O. V. Man’ko and N. V. Tcherniega, Izvestiya RAN, Ser. Fiz., 70, 382; 514 (2006).

    Google Scholar 

  36. Olga V. Man’ko, V. I. Man’ko, G. Marmo, Anil Shaji, E. C. G. Sudarshan, and F. Zaccaria, Phys. Lett. A, 339, 194 (2005).

    Article  ADS  Google Scholar 

  37. R. F. Werner, Phys. Rev. A, 40, 4277 (1989).

    Article  ADS  Google Scholar 

  38. V. I. Man’ko, G. Marmo, E. C. G. Sudarshan, and F. Zaccaria, Phys. Lett. A, 327, 353 (2004).

    Article  MathSciNet  ADS  Google Scholar 

  39. L. D. Landau and E. M. Lifshits, Theoretical Physics [in Russian], Nauka, Moscow (1989), Vol. 3.

    Google Scholar 

  40. R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, New York (1985).

    Google Scholar 

  41. O. V. Man’ko, Talk at the International Workshop “Classical and Quantum Integrable Systems” (January 2005, Joint Institute for Nuclear Research, Dubna, Moscow Region, Russia); A. V. Andreev, V. I. Man’ko, O. V. Man’ko, and E. V. Shchukin, Theor. Math. Phys., 146, 140 (2006).

    Google Scholar 

  42. A. Peres, Phys. Rev. Lett., 77, 4277 (1996).

    Article  Google Scholar 

  43. P. Horodecki, Phys. Lett. A, 232, 333 (1997).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  44. M. A. Man’ko, V. I. Man’ko, and R. Vilela Mendes, A probabilistic operator symbol framework for quantum information, Los Alamos ArXiv quant-ph/0602189 (2006).

  45. Walter Rudin, Real and Complex Analysis, McGraw-Hill, New York (1987).

    Google Scholar 

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Authors and Affiliations

  1. Faculty of Physics, M. V. Lomonosov Moscow State University, Vorob’evy Gory, Moscow, 119992, Russia

    Vladimir N. Chernega

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

    Olga V. Man’ko & Vladimir I. Man’ko

  3. Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudny, Moscow Region, 141700, Russia

    Oleg V. Pilyavets & Vadim G. Zborovskii

Authors
  1. Vladimir N. Chernega
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  2. Olga V. Man’ko
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  3. Vladimir I. Man’ko
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  4. Oleg V. Pilyavets
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  5. Vadim G. Zborovskii
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Chernega, V.N., Man’ko, O.V., Man’ko, V.I. et al. Tomographic characteristics of spin states. J Russ Laser Res 27, 132–166 (2006). https://doi.org/10.1007/s10946-006-0006-z

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  • DOI: https://doi.org/10.1007/s10946-006-0006-z

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