Skip to main content
SpringerLink
Log in

Tomographic and Improved Subadditivity Conditions for Two Qubits and a Qudit with j = 3/2

  • Published:
Journal of Russian Laser Research Aims and scope

Abstract

We obtain a new entropic inequality for quantum and tomographic Shannon information for systems of two qubits. We derive the inequality relating quantum information and spin-tomographic information for particles with spin j = 3/2. We recommend the method for obtaining new entropic and information inequalities for composite systems of qudits, as well as for one qudit.

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.

Similar content being viewed by others

References

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

    Article  ADS  MATH  Google Scholar 

  2. L. D. Landau and E. M. Lifshiz, Quantum Mechanics [in Russian], Nauka, Moscow (1963).

    Google Scholar 

  3. J. von Neumann, Nach. Ges. Wiss. G¨ottingen, 11, 245 (1927).

    Google Scholar 

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

    MATH  Google Scholar 

  5. V. N. Chernega and V. I. Man’ko, J. Russ. Laser Res., 30, 359 (2009).

    Article  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  7. E. H. Lieb and R. Seiringer, Phys. Rev. A, 71, 062329 (2005).

    Article  ADS  MathSciNet  Google Scholar 

  8. E. H. Lieb and M. B. Ruskai, J. Math. Phys., 14, 1938 (1973).

    Article  ADS  MathSciNet  Google Scholar 

  9. D. Petz, Rep. Math. Phys., 23, 57 (1986).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  10. E. Carlen and E. H. Lieb, Am. Math. Soc. Trans., 189, 59 (1999).

    MathSciNet  Google Scholar 

  11. A. Wehrl, Rep. Math. Phys., 16, 353 (1979).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  12. M. B. Ruskai, J. Math. Phys., 43, 4358 (2002).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  13. A. S. Holevo, Statistical Structure of Quantum Theory, Lecture Notes in Physics, Monographs, Springer (2001)

    Google Scholar 

  14. M. A. Man’ko and V. I. Man’ko, Found. Phys., 41, 330 (2011).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  15. M. A. Man’ko, V. I. Man’ko, and R. V. Mendes, J. Russ. Laser Res., 27, 507 (2006).

    Google Scholar 

  16. M. A. Man’ko and V. I. Man’ko, “Quantum correlations expressed as information and entropic inequalities for composite and noncomposite systems,” Symmetries in Science XVI, Proceedings of the International Symposium of Symmetries in Science (Bregenz, Austria, July 2013), J. Phys.: Conf. Ser. (2014, in press).

  17. M. A. Man’ko and V. I. Man’ko, “Quantum strong subadditivity condition for systems without subsystems,” Los Alamos arXiv:1312.6988 (2013); Phys. Scr. T (2014, in press).

  18. S. Mancini, V. I. Man’ko, and P. Tombesi, Phys. Lett. A, 213, 1 (1996).

    Google Scholar 

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

    Article  Google Scholar 

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

  21. M. A. Man’ko, V. I. Man’ko, G. Marmo, et al., “Introduction to tomography, classical and quantum,” Nuovo Cimento, Colloquia and Communications in Physics, Mathematical Structures in Quantum Systems and Applications (2013), Vol. 36, Ser. 3, p. 163.

  22. O. V. Man’ko, V. I. Man’ko, and G. Marmo, Phys. Scr., 62, 446 (2000).

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

    Google Scholar 

  24. O. V. Man’ko, V. I. Man’ko, and G. Marmo, “Tomographic map within the framework of starproduct quantization’,” in: E. Kapuschik and A. Horzela (Eds.), Proceedings of the Second International Symposium on Quantum Theory and Symmetries (Krakow, 2001), World Scientific, Singapore (2001), p. 126.

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

    Google Scholar 

  26. M. A. Man’ko, V. I. Man’ko, and R. V. Mendes, J. Phys. A: Math. Gen., 34, 8321 (2001).

    Google Scholar 

  27. O. V. Manko and V. N. Chernega, JETP Lett., 97, 557 (2013).

    Article  ADS  Google Scholar 

  28. V. N. Chernega, O. V. Man’ko, V. I. Man’ko, et al., J. Russ. Laser Res., 27, 132 (2006).

    Google Scholar 

  29. M. A. Man’ko and V. I. Man’ko, J. Russ. Laser Res., 34, 203 (2013).

    Article  Google Scholar 

  30. V. I. Man’ko and A. Yurkevich, J. Russ. Laser Res., 34, 463 (2013).

    Article  Google Scholar 

  31. I. H. Kim, Los Alamos arXiv:12105190 (2011).

    Google Scholar 

  32. V. N. Chernega and V. I. Man’ko, J. Russ. Laser Res., 28, 103 (2007).

    Article  Google Scholar 

  33. C. Lupo, V. I. Man’ko, and G. Marmo, J. Phys. A: Math. Theor., 40, 13091 (2007).

    Google Scholar 

  34. V. N. Chernega, O. V. Man’ko, and V. I. Man’ko, J. Russ. Laser Res., 34, 383 (2013).

    Google Scholar 

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

    Google Scholar 

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

    Article  ADS  Google Scholar 

  37. O. V. Man’ko, in: B. Gruber and H. Ramek (Eds.), Symmetries in Science X, Proceedings of the International Symposium of Symmetries in Science (Bregenz, Austria, 1997), Plenum Publishers, New York (1998), p. 207.

  38. O. V. Man’ko, J. Russ. Laser Res., 28, 483 (2007).

    Article  Google Scholar 

  39. V. A. Andreev, O. V. Man’ko, V. I. Man’ko, and S. S. Safonov, J. Russ. Laser Res., 19, 340 (1998).

    Google Scholar 

  40. A. B. Klimov, O. V. Man’ko, V. I. Man’ko, et al., J. Phys. A: Math. Gen, 35, 6101 (2002).

    Google Scholar 

  41. O. V. Man’ko, Acta Phys. Hung. A, Heavy Ion Phys. Ser., 19/3-4, 313 (2004).

  42. O. V. Man’ko and V. I. Man’ko, J. Phys.: Conf. Series, 36, 137 (2006).

    ADS  Google Scholar 

  43. O. V. Man’ko and V. I. Man’ko, Fortschr. Phys., 57, 1064 (2009).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Vladimir N. Chernega & Olga V. Man’ko

Authors
  1. Vladimir N. Chernega
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Olga V. Man’ko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Olga V. Man’ko.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chernega, V.N., Man’ko, O.V. Tomographic and Improved Subadditivity Conditions for Two Qubits and a Qudit with j = 3/2. J Russ Laser Res 35, 27–38 (2014). https://doi.org/10.1007/s10946-014-9397-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10946-014-9397-4

Keywords

Search

Navigation