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Purity loss and degradation of qubit-field correlations and entanglement due to phase noise in nonlinear interaction

  • Nonlinear and Quantum Optics
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Abstract

Numerical simulations and calculation of both the total entropy and the sub-entropies are used to investigate the purity loss in nonlinear interaction of a qubit with coherent field. While, the mutual entropy is used as a measure of the total correlations and the negativity as a measure to the entanglement. We show that the purity and entanglement behave different for standard energy dissipation as compared to an energy preserving phase noise coupling as introduced by Milburn. It is found that a very strong sensitivity of the degradation both total correlation with entanglement to the amount of phase damping and the chosen coupling. In particular for a coherent initial field state the maximum obtainable correlation is strongly reduced even for very weak noise.

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References

  1. S. M. Barnett and S. J. D. Phoenix, Phys. Rev. A 40, 2404 (1989).

    Article  MathSciNet  ADS  Google Scholar 

  2. B. Schumacher and M. D. Westmoreland, Phys. Rev. A 74, 042305 (2006).

    Article  ADS  Google Scholar 

  3. B. Groisman, S. Popescu, and A. Winter, Phys. Rev. A 72, 032317 (2005).

    Article  MathSciNet  ADS  Google Scholar 

  4. L. Henderson and V. Vedral, J. Phys. A 34, 6899 (2001).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  5. D. Yang, M. Horodecki, and Z. D. Wang, Phys. Rev. Lett. 101, 140501 (2008).

    Article  ADS  Google Scholar 

  6. M. Piani, M. Christandl, C. E. Mora, and P. Horodecki, Phys. Rev. Lett. 102, 250503 (2009).

    Article  ADS  Google Scholar 

  7. S. Luo, Phys. Rev. A 77, 022301 (2008); A.-B. A. Mohamed, J. Egytian Math. Soc. 21, 6874 (2013).

    Article  ADS  Google Scholar 

  8. A.-B. A. Mohamed, Quantum Inf. Process. 12, 1141 (2013); A.-S. F. Obade and A.-B. A. Mohamed, Opt. Commun. 309, 236 (2013).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  9. C. H. Bennett and D. P. Sicincenzo, Nature 404, 247 (2000).

    Article  ADS  Google Scholar 

  10. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, Cambridge, UK, 2000).

    MATH  Google Scholar 

  11. V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight, Phys. Rev. Lett. 78, 2275 (1997).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  12. C. H. Bennett, D. P. Di Vincenzo, J. A. Smolin, and W. K. Wootters, Phys. Rev. A 54, 3824 (1996).

    Article  MathSciNet  ADS  Google Scholar 

  13. L. Henderson and V. Vedral, Phys. Rev. Lett. 84, 2263 (2000); M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. Lett. 84, 2014 (2000).

    Article  ADS  Google Scholar 

  14. S. J. D. Phoenix and P. L. Knight, Ann. Phys. (New York) 186, 381 (1988); S. J. D. Phoenix and P. L. Knight, Phys. Rev. Lett. 66, 2833 (1991).

    Article  MATH  ADS  Google Scholar 

  15. V. Bu ek, H. Moya-Cessa, P. L. Knight, and S. J. D. Phoenix, Phys. Rev. A 45, 8190 (1992).

    Article  ADS  Google Scholar 

  16. S. J. D. Phienix and P. L. Knight, J. Opt. Soc. Am. B 7, 116 (1990).

    Article  ADS  Google Scholar 

  17. A.-S. F. Obada, H. A. Hessian, and A.-B. A. Mohamed, Internat. J. Quantum Information. 4, 871 (2006).

    Article  MATH  Google Scholar 

  18. Bin Zhang, Opt. Commun. 283, 4676 (2010).

    Article  ADS  Google Scholar 

  19. A.-B. A. Mohamed, Ann. Phys. 327, 3130 (2012); Phys. Scr. 85, 055013 (2012).

    Article  MATH  ADS  Google Scholar 

  20. G. Vidal and R. F. Werner, Phys. Rev. A 65, 032314 (2002).

    Article  ADS  Google Scholar 

  21. J. M. Raimond, M. Brune, and S. Haroche, Phys. Rev. Lett. 79, 1964 (1997).

    Article  ADS  Google Scholar 

  22. A.-S. F. Obada and H. A. Hessian, J. Opt. Soc. Am. B 21, 1535 (2004).

    Article  MathSciNet  ADS  Google Scholar 

  23. A.-B. A. Mohamed and H. A. Hessian, Physica E 44, 1552 (2012).

    Article  MathSciNet  ADS  Google Scholar 

  24. J. Q. You and F. Nori, Physica E 18, 33 (2003); G. Wendin, Roy Soc. London A 361, 1323 (2003).

    Article  ADS  Google Scholar 

  25. G. Burkard, D. Loss, and D. P. DiViencemzo, Phys. Rev. B 59, 2070 (1999).

    Article  ADS  Google Scholar 

  26. W. H. Zurek, Rev. Mod. Phys. 75, 715 (2003).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  27. A. Blais, R.-S. Huang, A. Wallraff, S. Girvin, and R. Schelkopf, Phys. Rev. A 69, 062320 (2004).

    Article  ADS  Google Scholar 

  28. D. F. Walls and G. J. Milburn, Quantum Optics (Springer, Berlin, 1994).

    Book  MATH  Google Scholar 

  29. H.-P. Breuer, U. Dorner, and F. Petrruccione, Comput. Phys. Commun. 132, 30 (2000).

    Article  MATH  ADS  Google Scholar 

  30. I. L. Chuang and Y. Yamamoto, Phys. Rev. A 55, 114 (1997); C. Massimo Palma, K. Suominen, and A. K. Ekert, Proc. Roy Soc. A 452, 567 (1996).

    Article  ADS  Google Scholar 

  31. D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Mekkhof, J. Res. Natl. Inst. Stand. Technol. 103, 259 (1998).

    Article  Google Scholar 

  32. B. Buck and C. V. Sukumar, Phys. Lett. A 81, 132 (1981); B. Buck and C. V. Sukumar, J. Phys. A: Math. Gen. 17, 885 (1984); G. S. Agarwal, J. Opt. Soc. Am. B 2, 480 (1985).

    Article  ADS  Google Scholar 

  33. S. S. Sharma, N. K. Sharma, and L. Zamick, Phys. Rev. A 56, 694 (1997); C. F. Lo and K. L. Liu, Phys. Rev. A 59, 3136 (1999).

    Article  ADS  Google Scholar 

  34. V. Man’ko, G. Marmo, A. Porzio, S. Solimeno, and F. Zaccaria, Phys. Rev. A 62, 053407 (2000).

    Article  ADS  Google Scholar 

  35. A. O. Caldeira and A. J. Leggett, Ann. Phys. (New York) 149, 374 (1983); A. J. Leggett, S. Chakravarty, A. T. Dorsey, Matthew P. A. Fisher, A. Garg, and W. Zwerger, Rev. Mod. Phys. 59, 1 (1987).

    Article  ADS  Google Scholar 

  36. C. Caves, K. Thorne, R. Drever, V. Sandberg, and M. Zimmermann, Rev. Mod. Phys. 52, 341 (1980).

    Article  ADS  Google Scholar 

  37. W. H. Louisell, Quantum Statistical Properties of Radiation (Wiley, New York, 1973).

    Google Scholar 

  38. G. J. Milburn, Phys. Rev. A 44, 540 (1991); G. J. Milburn, Phys. Rev. A 47, 2415 (1993).

    MathSciNet  ADS  Google Scholar 

  39. V. Bužek and I. Jex, Quantum Opt. 2, 147 (1989); V. Bužek, Phys. Rev. A 39, 3196 (1989).

    ADS  Google Scholar 

  40. H. Moya-Cessa, V. Bužek, M. S. Kim, and P. L. Knight, Phys. Rev. A 48, 3900 (1993).

    Article  ADS  Google Scholar 

  41. H. A. Hessian and H. Ritsch, J. Phys. B: At. Mol. Opt. Phys. 35, 4619 (2002).

    Article  ADS  Google Scholar 

  42. A.-S. F. Obada, A. M. Abdel-Hafez, and H. A. Hessian, J. Phys. B: At. Mol. Opt. Phys. 31, 5085 (1998).

    Article  ADS  Google Scholar 

  43. H. Araki and E. Lieb, Commun. Math. Phys. 18, 60 (1970).

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Faculty of Science, Assiut University, Assiut, Egypt

    H. A. Hessian & A. -B. A. Mohamed

  2. Faculty of Science, Al-Baha University, Al-Baha, Saudi Arabia

    H. A. Hessian

  3. Al-Aflaj Community College, Salman Bin Abdulaziz University, Al-Kharj, Saudi Arabia

    A. -B. A. Mohamed

Authors
  1. H. A. Hessian
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  2. A. -B. A. Mohamed
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Correspondence to A. -B. A. Mohamed.

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Hessian, H.A., Mohamed, A.B.A. Purity loss and degradation of qubit-field correlations and entanglement due to phase noise in nonlinear interaction. Opt. Spectrosc. 117, 474–479 (2014). https://doi.org/10.1134/S0030400X14080128

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  • DOI: https://doi.org/10.1134/S0030400X14080128

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