Quantum Mutual Entropy for a Multilevel Atom Interacting with a Cavity Field

  • M. Abdel-Aty
  • M. R. B. Wahiddin
  • A.-S. F. Obada
Article

Abstract

We derive an explicit formula for the quantum mutual entropy as a measure of the total correlations in a multi-level atom interacting with a cavity field. We describe its theoretical basis and discuss its practical relevance. The effect of the number of levels involved on the quantum mutual entropy is demonstrated via examples of three-, four- and five-level atom. Numerical calculations under current experimental conditions are performed and it is found that the number of levels present changes the general features of the correlations dramatically.

Keywords

multi-level systems mutual entropy 

References

  1. Abdel-Aty, M. (2000). Journal of Physics B (Atomic, Molecular and Optical Physics) 33, 2665.CrossRefADSGoogle Scholar
  2. Abdel-Aty, M., Furuichi, S., and Obada, A.-S. F. (2002). Journal of Optical B: Quantum and Semiclassical Optics 4, 37.CrossRefADSGoogle Scholar
  3. Abdel-Aty, M. and Obada, A.-S. F. (2003). European Journal of Physics D 23, 155.CrossRefGoogle Scholar
  4. Abdel-Hafez, A. M., Abu-Sitta, A. M. M., and Obada, A.-S. F. (1989). Physica A 156, 689.CrossRefADSMathSciNetGoogle Scholar
  5. Abdel-Hafez, A. M., Obada, A.-S. F., and Ahmed, M. M. A. (1987). Physica A 144, 530.CrossRefADSGoogle Scholar
  6. Acin, A., Durt, T., Gisin, N., and Latorre, J. I. (2002). Physical Review A 65, 052325.CrossRefADSGoogle Scholar
  7. Audenaert, K., Plenio, M. B., and Eisert, J. (2003). Physical Review Letters 90, 027901.CrossRefADSGoogle Scholar
  8. Belavkin, V. P. and Stratonovich, P. L. (1973). Journal of Radio Engineers and Electronics Physics 18(9), 1839–1844.Google Scholar
  9. Bennett, C. H., DiVincenzo, D. P., Smolin, J. A., and Wooters, W. K., et al. (1996). Physical Review A 54, 3824.CrossRefADSMathSciNetGoogle Scholar
  10. Bose, S., Fuentes-Guridi, Knight, P. L., and Vedral, V. (2001a) Physical Review Letters 87, 050401.CrossRefADSMathSciNetGoogle Scholar
  11. Bose, S., Fuentes-Guridi, Knight, P. L., and Vedral, V. (2001b) Physical Review Letters 87, 279901.CrossRefADSMathSciNetGoogle Scholar
  12. Bose, S., Fuentes-Guridi, Knight, P. L., and Vedral, V. (2001c). Physical Review Letters 87, 279901.CrossRefADSMathSciNetGoogle Scholar
  13. Bourennane, M., Karlsson, A., and Bjork, G. (2001). Physical Review A 64, 012306.CrossRefADSGoogle Scholar
  14. Braunstein, S. L. and Lo, H.-K., eds. (2001). Scalable Quantum Computers: Paving the Way to Realization. Wiley VCH, New York.Google Scholar
  15. Bruss, D. and Macchiavello, C. (2002). Physical Review Letters 88, 127901.CrossRefADSGoogle Scholar
  16. Braunstein, S. L. and Lo, H.-K., eds. (2001). Scalable Quantum Computers: Paving the Way to Realization. Wiley VCH, New York.Google Scholar
  17. Cerf, N. J., Bourennane, M., Karlsson, A., and Gisin, N. (2002). Physical Review Letters 88, 127902.CrossRefADSGoogle Scholar
  18. Durt, T., Cerf, N. J., Gisin, N., and Zukowski, M. (2003). Physical Review A 67, 012311.CrossRefADSGoogle Scholar
  19. Eisert, J. and Plenio, M. B. (1999). Journal of Modern Optics 46, 145.CrossRefADSGoogle Scholar
  20. Fichtner, K.-H. and Ohya, M. (2001). Communications in Mathematical Physics 222, 229.MATHCrossRefADSMathSciNetGoogle Scholar
  21. Furuichi, S. and Abdel-Aty, M. (2001). Journal of Physics A (Mathematical and General) 34, 6851.MATHCrossRefADSMathSciNetGoogle Scholar
  22. Furuichi, S. and Ohya, M. (1999). Letters in Mathematical Physics 49, 279.MATHCrossRefMathSciNetGoogle Scholar
  23. Gelfand, I. M. and Yaglom, A. M. (1959). Journal of Amercian Mathematical Society Translation 12, 199–246.MathSciNetGoogle Scholar
  24. Hill, S. and Wootters, W. K. (1997). Physical Review Letters 78, 5022.CrossRefADSGoogle Scholar
  25. Holevo, A. S. (1973). Problemy Peredachi Informacii 9, 3.MathSciNetMATHGoogle Scholar
  26. Horodecki, M., Horodecki, P., and Horodecki, R. (1997). Physical Review Letters 78, 574.CrossRefADSGoogle Scholar
  27. Ingarden, R. S. (1976). Reports on Mathematical Physics 10, 43.Google Scholar
  28. Kaszlikowski, D., Gnascinski, P., Zukowski, M., Miklaszewski, W., and Zeilinger, A. (2000). Physical Review Letters 85, 4418.CrossRefADSGoogle Scholar
  29. Kolmogorov, A. N. (1963). Journal of Amercian Mathematical Society Translation, Series 2 33, 291–321.Google Scholar
  30. Levitin, L. B. (1991). Physical Information Theory for 30 Years: Basic Concepts and Results, vol. 101, Springer Lect. Note in Phys., p. 378.Google Scholar
  31. Nielsen, M. A. and Chuang, I. L. (2000). Quantum Computation and Quantum Information. Cambridge University Press, Cambridge.MATHGoogle Scholar
  32. Nielsen, M. A. and Kempe, J. (2001). Physical Review Letters 86, 5184.CrossRefADSGoogle Scholar
  33. Ohya, M. (1983). IEEE Transactions Information Theory 29, 770.Google Scholar
  34. Ohya, M. and Petz, D. (1993). Quantum Entropy and Its Use. Springer-Verlag (TMP series).Google Scholar
  35. Phoenix, S. J. D. and Knight, P. L. (1991a). Physical Review A 44, 6023.CrossRefADSGoogle Scholar
  36. Phoenix, S. J. D. and Knight, P. L. (1991b). Physical Review A 66, 2833.ADSCrossRefGoogle Scholar
  37. Phoenix, S. J. D. and Knight, P. L. (1988). Annals of Physics 186, 381.MATHCrossRefADSGoogle Scholar
  38. Rekdal, P. K., Skagerstam, B.-S. K., and Knight, P. L. (2004). Journal of Modern Optics 51, 75.MATHCrossRefADSGoogle Scholar
  39. Scheel, S., Eisert, J., Knight, P. L., and Plenio, M. B. (2003). Journal of Modern Optics 50, 881.MATHCrossRefADSMathSciNetGoogle Scholar
  40. Song, K.-H., Zhang, W.-J., and Guo, G.-C. (2002). European Journal of Physics D 19, 267.CrossRefGoogle Scholar
  41. Vedral, V. and Plenio, M. B. (1998). Physical Review A 57, 1619.CrossRefADSGoogle Scholar
  42. Vedral, V. (2004a). New J. Phys. 6, 22.CrossRefADSGoogle Scholar
  43. Vedral, V. (2004b). New J. Phys. 6, 102.CrossRefADSGoogle Scholar
  44. Vogel, W. and de Matos Filho, R. L. (1995). Physical Review A 52, 4214.CrossRefADSGoogle Scholar
  45. Zheng, S. B. (1998). Quantum and Semiclassical Optics B 10, 691.CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  • M. Abdel-Aty
    • 1
  • M. R. B. Wahiddin
    • 1
  • A.-S. F. Obada
    • 2
  1. 1.Centre for Computational and Theoretical SciencesKulliyyah of Science, MalaysiaKuala LumpurMalaysia
  2. 2.Mathematics Department, Faculty of ScienceAl-Azhar UniversityNasr CityEgypt

Personalised recommendations