Skip to main content
SpringerLink
Log in

Dynamics of quantum discord based on linear entropy and negativity of qutrit-qubit system under classical dephasing environments

  • Regular Article - Quantum Information
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

A reliable analytical method to evaluate the non-classical correlations based on linear entropy for an arbitrary qudit-qubit quantum state is proposed. The linear entropy is used to overcome the difficulty encountered with the computability of quantum discord based on von Neumann entropy. The quantum discord based on linear entropy is employed to derive the quantum correlations for a qutrit-qubit system undergoing global (bilocal + collective) classical dephasing environment. Our studies were focused mainly on a particular initial qutrit-qubit state in thermal equilibrium at a temperature T. The obtained amount of quantum discord (QD) is then compared with the measurement-induced disturbance (MID) and logarithmic negativity (LN). The analysis shows that both QD and MID are more robust than entanglement (LN) against the decoherence effect. Besides, the system exhibits interesting behaviors. As for instance, freezing dynamics and entanglement sudden death (ESD). The method developed in this paper to quantify quantum correlations is reliable because it allows us to consider analytically the arbitrary qutrit-qubit quantum states in the classical dephasing environment.

Graphic abstract

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.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: Because all necessary information can be found in the original manuscript.]

References

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

    MATH  Google Scholar 

  2. R. Horodecki, P. Horodecki, M. Horodecki, K. Horodecki, Rev. Mod. Phys. 81, 865 (2009)

    Article  ADS  Google Scholar 

  3. C.H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, W.K. Wooters, Phys. Rev. Lett. 70, 1895–1899 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  4. T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, A. Zeilinger, Phys. Rev. Lett. 84, 4729–4732 (2000)

    Article  ADS  Google Scholar 

  5. M. Horodecki, J. Oppenheim, A. Winter, Nature 436, 673–676 (2005)

    Article  ADS  Google Scholar 

  6. A. Datta, A.T. Flammia, C.M. Caves, Phys. Rev. A 72, 042316 (2005)

    Article  ADS  Google Scholar 

  7. A. Datta, G. Vidal, Phys. Rev. A 75, 042310 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  8. A. Datta, A. Shaji, C.M. Caves, Phys. Rev. Lett. 100, 050502 (2008)

    Article  ADS  Google Scholar 

  9. B.P. Lanyon, M. Barbieri, M.P. Almeida, A.G. White, Phys. Rev. Lett. 101, 200501 (2008)

    Article  ADS  Google Scholar 

  10. J. Oppenheim, M. Horodecki, P. Horodecki, R. Horodecki, Phys. Rev. Lett. 89, 180402 (2002)

    Article  ADS  Google Scholar 

  11. A. Ferraro, D. Cavalcanti, F.M. Cucchietti, A. Acín, Phys. Rev. A 81, 052318 (2010)

    Article  ADS  Google Scholar 

  12. H. Ollivier, W.H. Zurek, Phys. Rev. Lett. 88, 017901 (2001)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  14. M. Daoud, R. Ahl Laamara, S. Seddik, Int. J. Mod. Phys. B 29, 1550124 (2015)

    Article  ADS  Google Scholar 

  15. A. Shabani, D.A. Lidar, Phys. Rev. Lett. 102, 100402 (2009)

    Article  ADS  Google Scholar 

  16. F. Galve, G.L. Giorgi, R. Zambrini, Phys. Rev. Lett. 83, 012102 (2011)

    ADS  Google Scholar 

  17. D. Girolami, G. Adesso, Phys. Rev. A 83, 052108 (2011)

    Article  ADS  Google Scholar 

  18. M. Daoud, R. Ahl Laamara, Int. J. Quantum Inf. 10, 1250060 (2012)

    Article  MathSciNet  Google Scholar 

  19. M. Daoud, R. Ahl Laamara, Phys. Lett. A 376, 2361 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  20. M. Daoud, R. Ahl Laamara, W. Kaydi, Phys. Lett. A 378, 3501 (2012)

    Article  ADS  Google Scholar 

  21. D. Girolami, T. Tufarelli, G. Adesso, Phys. Rev. Lett. 110, 240402 (2013)

    Article  ADS  Google Scholar 

  22. M. Horodecki, P. Horodecki, R. Horodecki, J. Oppenheim, A. Sen, U. Sen, B. Synak-Radtke, Phys. Rev. A 71, 062307 (2005)

    Article  ADS  Google Scholar 

  23. S. Luo, Phys. Rev. A 77, 022301 (2008)

    Article  ADS  Google Scholar 

  24. S. Luo, S. Fu, Phys. Rev. Lett. 106, 120401 (2011)

    Article  ADS  Google Scholar 

  25. T.J. Osborne, F. Verstraete, Phys. Rev. Lett. 96, 220503 (2006)

    Article  ADS  Google Scholar 

  26. Z. Ma, Z. Chen, F.F. Fanchini, S.M. Fei, Sci. Rep. 5, 10262 (2015)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  28. C.W. Gardiner, P. Zoller, Quantum Noise (Springer, Berlin, 2004)

    MATH  Google Scholar 

  29. H.M. Wiseman, G.J. Milburn, Quantum Measurement and Control (Cambridge University Press, Cambridge, 2009)

    Book  MATH  Google Scholar 

  30. T. Yu, J.H. Eberly, Phys. Rev. Lett. 93, 140404 (2004)

    Article  ADS  Google Scholar 

  31. T. Yu, J.H. Eberly, Opt. Commun. 264, 393 (2006)

    Article  ADS  Google Scholar 

  32. F.F. Fanchini, T. Werlang, C.A. Brasil, L.G.E. Arruda, A.O. Caldeira, Phys. Rev. A 81, 052107 (2010)

    Article  ADS  Google Scholar 

  33. B. Wang, Z.Y. Xu, M. Feng, Phys. Rev. A 81, 014101 (2010)

    Article  ADS  Google Scholar 

  34. F. Altintas, Opt. Commun. 283, 5264 (2010)

    Article  ADS  Google Scholar 

  35. T. Werlang, S. Souza, F.F. Fanchini, C.J.V. Boas, Phys. Rev. A 80, 024103 (2009)

    Article  ADS  Google Scholar 

  36. M.P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S.P. Walborn, Science 316, 579 (2007)

    Article  ADS  Google Scholar 

  37. G. Karpat, Z. Gedik, Phys. Lett. A 375, 4166–4171 (2011)

    Article  ADS  Google Scholar 

  38. T. Yu, J.H. Eberly, Phys. Rev. B 68, 165322 (2003)

    Article  ADS  Google Scholar 

  39. K. Ann, G. Jaeger, Phys. Rev. B 75, 115307 (2007)

    Article  ADS  Google Scholar 

  40. H.P. Breuer, F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002)

    MATH  Google Scholar 

  41. C.W. Gardiner, P. Zoller, Quantum Noise (Springer, Berlin, 2000)

    Book  MATH  Google Scholar 

  42. M.O. Scully, M.S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, 1997)

    Book  Google Scholar 

  43. A. Mazhar, Braz. J. Phys. 50(2), 124–135 (2020)

    Article  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  45. G.F. Zhang, Y.C. Hou, A.L. Ji, Solid State Commun. 151, 790 (2011)

    Article  ADS  Google Scholar 

  46. F. Benabdallah, A. Slaoui, M. Daoud, Quantum Inf. Process. 19, 252 (2020)

    Article  ADS  Google Scholar 

  47. K. Zyczkowski, P. Horodecki, A. Sanpera, M. Lewenstein, Phys. Rev. A 58, 883 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  48. S.L. Braunstein, C.M. Caves, R. Jozsa, N. Linden, S. Popescu, R. Schack, Phys. Rev. Lett. 83, 1054 (1999)

    Article  ADS  Google Scholar 

  49. J.Q. Li, J.Q. Liang, Phys. Lett. A 375, 1496 (2011)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LPHE-Modeling and Simulation, Faculty of Sciences, Mohammed V University in Rabat, Rabat, Morocco

    Fadwa Benabdallah

  2. Department of Physics, Faculty of Sciences, University Ibn Tofail, Kenitra, Morocco

    Mohammed Daoud

  3. Abdus Salam International Centre for Theoretical Physics, Miramare, Trieste, Italy

    Mohammed Daoud

Authors
  1. Fadwa Benabdallah
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohammed Daoud
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fadwa Benabdallah.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Benabdallah, F., Daoud, M. Dynamics of quantum discord based on linear entropy and negativity of qutrit-qubit system under classical dephasing environments. Eur. Phys. J. D 75, 3 (2021). https://doi.org/10.1140/epjd/s10053-020-00022-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/s10053-020-00022-2

Search

Navigation