Skip to main content
SpringerLink
Log in

Invariant and Freezing Dynamics of Quantum Correlations in Qubit-Qutrit Systems Under Collective Dephasing Colored Noise

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

We analyze in details the time-evolution of measurement-induced disturbance (MID) and local quantum uncertainty (LQU) in a qubit-qutrit system influenced by a collective dephasing pink or brown noise. We investigate the cases where each noise spectrum is generated by either a single two-states stochastic fluctuator, or a set of multiple ones. We further consider for our study, two non-equivalent classes of one-parameter qubit-qutrit initial states, namely the p-states and the x-states. We demonstrate that the initial state is particularly relevant for the future evolution of quantum correlations (QCs). In fact MID and LQU are less powerful against decoherence effects in x-states than in p-states, where we show the joint existence of time-invariant and freezing dynamics of QCs. In general, MID is always stronger than LQU, but we show that both measures can capture the same correlations (i.e. they are equal to each other) for carefully selected ranges of entanglement parameter in p-states. However, MID and LQU are more powerful in the system when subjected to brown noise than to pink noise no matter the initial state or the number of fluctuators generating the decoherent process. The relevance of separable states for the community is further reinforced by our results, as both QCs measures perfectly certify the existence of QCs without entanglement in ranges of separability for the selected input states.

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

Similar content being viewed by others

References

  1. Schrödinger, E.: Math. Proc. Camb. Philos. Soc. 31, 555 (1935)

    Article  ADS  Google Scholar 

  2. Buhrman, H., Cleve, R., Massar, S., de Wolf, R.: Rev. Mod. Phys. 82, 665 (2010)

    Article  ADS  Google Scholar 

  3. Brukner, Č., Żukowski, M., Pan, J.W., Zeilinger, A.: Phys. Rev. Lett. 92 (2004)

  4. Ekert, A.K.: Phys. Rev. Lett. 67, 661 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  5. Dakić, B., Lipp, Y.O., Ma, X., Ringbauer, M., Kropatschek, S., Barz, S., Paterek, T., Vedral, V., Zeilinger, A., Brukner, Č., et al.: Nat. Phys. 8, 666 (2012)

    Article  Google Scholar 

  6. Li, X., Pan, Q., Jing, J., Zhang, J., Xie, C., Peng, K.: Phys. Rev. Lett. 88 (2002)

  7. Masanes, L., Pironio, S., Acín, A.: Nat. Commun. 2 (2011)

  8. Giovannetti, V., Lloyd, S., Maccone, L.: Nat. Photonics 5, 222 (2011)

    Article  ADS  Google Scholar 

  9. Bennett, C.H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Phys. Rev. Lett. 70, 1895 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  10. Knill, E., Laflamme, R.: Phys. Rev. Lett. 81, 5672 (1998)

    Article  ADS  Google Scholar 

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

  12. Datta, A., Shaji, A., Caves, C.M.: Phys. Rev. Lett. 100 (2008)

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

    Article  ADS  Google Scholar 

  14. Ollivier, H., Zurek, W.H.: Phys. Rev. Lett. 88 (2001)

  15. Modi, K., Brodutch, A., Cable, H., Paterek, T., Vedral, V.: Rev. Mod. Phys. 84, 1655 (2012)

    Article  ADS  Google Scholar 

  16. Piani, M., Horodecki, P., Horodecki, R.: Phys. Rev. Lett. 100 (2008)

  17. Luo, S.: Phys. Rev. A 77 (2008)

  18. Dakić, B., Vedral, V., Brukner, Č.: Phys. Rev. Lett. 105 (2010)

  19. Luo, S., Fu, S.: Phys. Rev. A 82 (2010)

  20. Girolami, D., Tufarelli, T., Adesso, G.: Phys. Rev. Lett. 110 (2013)

  21. Yu, T., Eberly, J.H.: Phys. Rev. Lett. 93 (2004)

  22. Yu, T., Eberly, J.H.: Science 323, 598 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  23. Almeida, M.P., de Melo, F., Hor-Meyll, M., Salles, A., Walborn, S.P., Ribeiro, P.H.S., Davidovich, L.: Science 316, 579 (2007)

    Article  ADS  Google Scholar 

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

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

    Article  ADS  Google Scholar 

  26. Yu, T., Eberly, J.: Opt. Commun. 264, 393 (2006)

    Article  ADS  Google Scholar 

  27. López, C. E., Romero, G., Lastra, F., Solano, E., Retamal, J.C.: Phys. Rev. Lett. 101 (2008)

  28. Xu, J.S., Sun, K., Li, C.F., Xu, X.Y., Guo, G.C., Andersson, E., Franco, R.L., Compagno, G.: Nat. Commun. 4 (2013)

  29. Bellomo, B., Franco, R.L., Compagno, G.: Phys. Rev. Lett. 99 (2007)

  30. Paladino, E., Faoro, L., Falci, G., Fazio, R.: Phys. Rev. Lett. 88 (2002)

  31. Fujisawa, T., Hirayama, Y.: Appl. Phys. Lett. 77, 543 (2000)

    Article  ADS  Google Scholar 

  32. Ludviksson, A., Kree, R., Schmid, A.: Phys. Rev. Lett. 52, 950 (1984)

    Article  ADS  Google Scholar 

  33. Kogan, S., Nagaev, K.: Solid State Commun. 49, 387 (1984)

    Article  ADS  Google Scholar 

  34. Mooij, J.E.: Science 285, 1036 (1999)

    Article  Google Scholar 

  35. Falci, G., Fazio, R., Palma, G.M., Siewert, J., Vedral, V.: Nature 407, 355 (2000)

    Article  ADS  Google Scholar 

  36. Johanson, R.E., Güneş, M., Kasap, S.: J. Non Cryst. Solids 242, 266–269 (2000)

    Google Scholar 

  37. Raquet, B., Anane, A., Wirth, S., Xiong, P., von molnár, S.: Phys. Rev. Lett. 84, 4485 (2000)

    Article  ADS  Google Scholar 

  38. Jung, G., Paltiel, Y., Zeldov, E., Myasoedov, Y., Rappaport, M.L., Ocio, M., Bhattacharya, S., Higgins, M.J.: Noise in Vortex Matter. In: Weissman, M. B., Israeloff, N.E., Kogan, A.S. (eds.) Noise as a Tool for Studying Materials. (SPIE) (2003)

  39. Tsokeng, A.T., Tchoffo, M., Fai, L.C.: Quantum Inform. Process. 17 (2018)

  40. Tsokeng, A.T., Tchoffo, M., Fai, L.C.: J. Phys. Commun. 2, 035031 (2018)

    Article  Google Scholar 

  41. Arthur, T.T., Martin, T., Fai, L.C.: Quantum Inform. Process. 17 (2018)

  42. Arthur, T.T., Martin, T., Fai, L.C.: Int. J. Quantum Inform. 15, 1750047 (2017)

    Article  ADS  Google Scholar 

  43. Tsokeng, A.T., Tchoffo, M., Fai, L.C.: Quantum Inform. Process. 16 (2017)

  44. Javed, M., Khan, S., Ullah, S.A.: J. Russian Laser Res. 37, 562 (2016)

    Article  Google Scholar 

  45. Yang, Y., Wang, A.M.: Chin. Phys. Lett. 30, 080302 (2013)

    Article  ADS  Google Scholar 

  46. Girolami, D., Adesso, G.: Phys. Rev. A 83 (2011)

  47. Ciccarello, F., Giovannetti, V.: Phys. Rev. A 85 (2012)

  48. Koningsbruggen, P.J.V., Kahn, O., Nakatani, K., Pei, Y., Renard, J.P., Drillon, M., Legoll, P.: Inorg. Chem. 29, 3325 (1990)

    Article  Google Scholar 

  49. Ma, X., Zhang, J., Cong, H., Wang, A.: Sci. China Series G Phys. Mechan. Astron. 51, 1897 (2008)

    Article  ADS  Google Scholar 

  50. Ye, B.L., Liu, Y.M., Liu, X.S., Zhang, Z.J.: Chin. Phys. Lett. 30, 020302 (2013)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  52. Karpat, G., Gedik, Z.: Phys. Scr. T153, 014036 (2013)

    Article  ADS  Google Scholar 

  53. Guo, J.L., Li, H., Long, G.L.: Quantum Inf. Process 12, 3421 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  54. Yang, Y., Wang, A.M.: Chinese Phys. B 23, 020307 (2014)

    Article  ADS  Google Scholar 

  55. Yashodamma, K.O., Geetha, P.J.: Sudha, Quantum Inform. Process. 13, 2551 (2014)

    Article  ADS  Google Scholar 

  56. Guo, J.L., Wei, J.L., Qin, W.: Quantum Inf. Process 14, 1399 (2015)

    Article  ADS  Google Scholar 

  57. Basit, A., Ali, H., Badshah, F., Ge, G.Q.: Commun. Theor. Phys. 68, 29 (2017)

    Article  ADS  Google Scholar 

  58. Tchoffo, M., Tsokeng, A.T., Tiokang, O.M., Nganyo, P.N., Fai, L.C.: Phys. Lett. A 383, 1856 (2019)

    Article  ADS  Google Scholar 

  59. Hao, X.N., Hou, J.C., Li, J.Q.: Quantum Inf. Process 15, 2819 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  60. Benabdallah, F., Slaoui, A., Daoud, M.: Quantum Inform. Process. 19 (2020)

  61. Benabdallah, F., Daoud, M.: The European Phys. J. D 75 (2021)

  62. Ann, K., Jaeger, G.: Phys. Lett. A 372, 579 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  63. Jafarpour, M., Hasanvand, F.K., Afshar, D.: Commun. Theor. Phys. 67, 27 (2017)

    Article  ADS  Google Scholar 

  64. Bergli, J., Galperin, Y.M., Altshuler, B.L.: New J. Phys. 11, 025002 (2009)

    Article  ADS  Google Scholar 

  65. Ali, M.: Braz. J. Phys. 50, 124 (2019)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Research Unit of Condensed Matter, Electronics and Signal Processing, Department of Physics, Dschang School of Sciences and Technology, University of Dschang, P.O. Box 67, Dschang, Cameroon

    Tsamouo Tsokeng Arthur, Nguenang Nganyo Pernel, Kuate Fodouop Fabrice, Tchoffo Martin & Lukong Cornelius Fai

  2. Centre d’Etude et de Recherche en Agronomie et en Biodiversité, FASA, Université de Dschang, Dschang, Cameroon

    Tchoffo Martin

Authors
  1. Tsamouo Tsokeng Arthur
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nguenang Nganyo Pernel
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kuate Fodouop Fabrice
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Tchoffo Martin
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Lukong Cornelius Fai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tsamouo Tsokeng Arthur.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Arthur, T.T., Pernel, N.N., Fabrice, K.F. et al. Invariant and Freezing Dynamics of Quantum Correlations in Qubit-Qutrit Systems Under Collective Dephasing Colored Noise. Int J Theor Phys 60, 4078–4090 (2021). https://doi.org/10.1007/s10773-021-04957-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-021-04957-z

Keywords

Search

Navigation