Skip to main content
SpringerLink
Log in

The Dynamics of Quantum-Memory-Assisted Entropic Uncertainty of Two-Qubit System in the XY Spin Chain Environments with Dzyaloshinsky-Moriya Interaction

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

Abstract

We investigate the dynamical behaviors of quantum-memory-assisted (QMA) entropic uncertainty for the central two-qubit system coupled to the N-site spin XY chain environment with z-component Dzyaloshinsky-Moriya (DM) interaction and external magnetic field, asymmetrically. The results show that the dynamics of QMA entropic uncertainty for a pair of Pauli observables are oscillatory and ascending gradually with evolution time, which is anti-correlated to the entanglement of the two-qubit system. We also find that QMA entropic uncertainty exhibits sudden change phenomena near the critical point of quantum phase transform both in the case of weak and strong coupling regimes, which can act as a new witness of the critical point of quantum phase transition. Meanwhile, the DM interactions of the spin chain environment have non-equivalent effects on the QMA entropic uncertainty when the external magnetic field strength is far from the critical point. Furthermore, the asymmetricallity of the qubit-environment couplings has slightly effects on QMA entropic uncertainty in the case of strong coupling regime of the two-qubit system. While, in the weak coupling regime of the two-qubit system, QMA entropic uncertainty is very sensitive to the asymmetricallity of qubit-environment couplings. Finally, the larger the number of spin sites of the environment, the more quickly the QMA entropic uncertainty increases to the maximal value both in the weak and strong coupling regimes of the two-qubit system.

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

Similar content being viewed by others

References

  1. Heisenberg, W.: . Z. Phys. 43, 172 (1927)

    Article  ADS  Google Scholar 

  2. Robertson, H.P.: . Phys. Rev. 34, 163 (1929)

    Article  ADS  Google Scholar 

  3. Deutsch, D.: . Phys. Rev. Lett. 50, 631 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  4. Maassen, H., Uffink, J.B.: . Phys. Rev. Lett. 60, 1103 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  5. Wehner, S., Winter, A.J.: . New J. Phys. 12, 65 (2010)

    Article  Google Scholar 

  6. Oppenheim, J., Wehner, S.: . Science 330, 1072 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  7. Renes, J.M., Boilean, J.C.: . Phys. Rev. Lett. 103, 020402 (2009)

    Article  ADS  Google Scholar 

  8. Dressel, J., Nori, F.: . Phys. Rev. A 89, 022106 (2014)

    Article  ADS  Google Scholar 

  9. Berta, M., Christandl, M., Colbeck, R., Renes, J.M., Renner, M.: . Nat. Phys. 6, 659 (2010)

    Article  Google Scholar 

  10. Xu, Z.Y., Zhu, S.Q., Yang, W.L.: . Appl. Phys. Lett. 101, 172 (2012)

    Google Scholar 

  11. Prevedel, R., Hamel, D.R.: . Nat. Phys. 7, 757 (2011)

    Article  Google Scholar 

  12. Li, C.F., Xu, J.S., Xu, X.Y., Li, K., Guo, G.C.: . Nat. Phys. 7, 752 (2012)

    Article  Google Scholar 

  13. Xiang, Z.L., Ashhab, S., You, J.Q., Nori, F.: . Rev. Mod. Phys. 85, 623 (2013)

    Article  ADS  Google Scholar 

  14. Xing, J., Zhang, Y.R., Liu, S., Chang, Y.C., Yue, J.D., Fan, H., Pan, X.Y.: . Sci. Rep. 7, 2563 (2017)

    Article  ADS  Google Scholar 

  15. Berta, M., Coles, P.J., Wehner, S.: . Phys. Rev. A 90, 062127 (2014)

    Article  ADS  Google Scholar 

  16. Schneeloch, J., Broadbent, C.J., Walborn. S.P., Cavalcanti. E.G., Howell. J.C.: . Phys. Rev. A 87, 062103 (2013)

    Article  ADS  Google Scholar 

  17. Walborn, S.P., Salles, A., Gomes, R.M., Toscano, F., Souto Ribeiro, P.H.: . Phys. Rev. Lett. 106, 130402 (2011)

    Article  ADS  Google Scholar 

  18. Adabi, F., Salimi, S., Haseli, S.: . Phys. Rev. A 93, 062123 (2016)

    Article  ADS  Google Scholar 

  19. Pati, A.K., Wilde, M.M., Devi, A.R.U., et al.: . Phys. Rev. A 89, 042105 (2012)

    Article  ADS  Google Scholar 

  20. Zheng, X., Zhang, G.F.: . Quantum. Inf. Process. 1, 1 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  21. Li, J.Q., Bai, L., Liang, J.Q.: . Quantum. Inf. Process. 17, 206 (2018)

    Article  ADS  Google Scholar 

  22. Xu, Z.Y., Yang, W.L., Feng, M.: . Phys. Rev. A 86, 012113 (2012)

    Article  ADS  Google Scholar 

  23. Hu, M.L., Fan, H.: . Phys. Rev. A 86, 032338 (2012)

    Article  ADS  Google Scholar 

  24. Wang, D., Ming, F., Hu, M.L., Ye, L.: . Ann. Phys. (Berlin) 531, 1900124 (2019)

    Article  ADS  Google Scholar 

  25. Wang, D., Ming, F., Huang, A.J., Sun, W.Y., Shi, J.D., Ye, L.: . Sci. Rep. 7, 1066 (2017)

    Article  ADS  Google Scholar 

  26. Huang, A.J., Shi, J.D., Wang, D., Ye, L.: . Quantum. Inf. Process. 16, 46 (2017)

    Article  ADS  Google Scholar 

  27. Huang, Z.M.: . Quantum. Inf. Process. 17, 73 (2018)

    Article  ADS  Google Scholar 

  28. Huang, Z.M., Situ, H.: . Quantum Inf. Process. 18, 38 (2019)

    Article  ADS  Google Scholar 

  29. Huang, Z.M.: . Laser Phys. Lett. 15, 025203 (2018)

    Article  ADS  Google Scholar 

  30. Zou, H.M., Fang, M.F., Yang, B.Y., Guo, Y.N., He, W., Zhang, S.Y.: . Phys. Scr. 89, 115101 (2014)

    Article  ADS  Google Scholar 

  31. Fang, B.L., Shi, J.D., Wu, T.: . Int. J. Theor. Phys. 59, 763 (2020)

    Article  Google Scholar 

  32. Haseli, S., Ahmadi, F.: . Eur. Phys. J. D. 74, 170 (2020)

    Article  ADS  Google Scholar 

  33. Pourkarimi, R.M., Haseli, S.: . Laser Phys. Lett. 17, 2 (2020)

    Article  Google Scholar 

  34. Peng, X.H., Jiangfeng Du, J.F., Suter, D.: . Phys. Rev. A 71, 012307 (2005)

    Article  ADS  Google Scholar 

  35. Kuzyk, C.M., Wang, H.L.: . Phys. Rev. X 8, 041027 (2018)

    Google Scholar 

  36. Awschalom, D.D., Hanson, R., J Wrachtrup, J., Zhou, B.B.: . Nat. Photon. 12, 516 (2018)

    Article  ADS  Google Scholar 

  37. Huang, Z.M., Situ, H., Zhang, C.: . Int. J. Theor. Phys. 56, 2178 (2017)

    Article  Google Scholar 

  38. Yi, T.C., You, W.L., Wu, N., Oleś, M.A.: . Phys. Rev. B 100, 024423 (2019)

    Article  ADS  Google Scholar 

  39. Shi, X., Yuan, H., Mao, X., Ma, Y., Zhao, H.Q.: . Phys. Rev. B 95, 052332 (2017)

    Article  ADS  Google Scholar 

  40. Liu, B.Q., Shao, B., Zou, J.: . Phys. Rev. A 82, 062119 (2010)

    Article  ADS  Google Scholar 

  41. Liu, B.Q., Shao, B., Li, J.G., Zou, J., Wu, L.A.: . Phys. Rev. A 83, 052112 (2011)

    Article  ADS  Google Scholar 

  42. Wei, Y.B., Zou, J., Wang, Z.M., Shao, B.: . Sci. Rep. 6, 19308 (2016)

    Article  ADS  Google Scholar 

  43. Hu, M.L.: . Phys. Lett. A 374, 3520 (2010)

    Article  ADS  Google Scholar 

  44. Li, Y.C., Lin, H.Q., Xu, J.B.: . EPL. 100, 20002 (2012)

    Article  ADS  Google Scholar 

  45. Yin, S.Y., Song, J., Liu, S.T.: . Phys. Lett. A 383, 136 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  46. Cheng, W.W., Liu, J.M.: . Phys. Rev. A 79, 052320 (2009)

    Article  ADS  Google Scholar 

  47. Sachdev, S.: Quantum Phase Transition. Cambridge University Press, Cambridge (1999)

    Book  Google Scholar 

  48. Wootters, W.K.: . Phys. Rev. Lett. 80, 2245 (1998)

    Article  ADS  Google Scholar 

  49. Yuan, Z.G., Zhang, P., Li, S.S.: . Phys. Rev. A 76, 042118 (2007)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The work was supported by the National Natural Science Foundation of China under Grant No.11464015, the Scientific Project of Education Ministry of Hunan Province under Grant No.18C0579, the Science Research Foundation of Hunan Province under Grant No.2020JJ4496.

Author information

Authors and Affiliations

  1. School of Software, Jishou University, Zhangjiajie, 427000, People’s Republic of China

    Yanliang Zhang, Qingping Zhou & Guodong Kang

  2. Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, College of Physics and Information Science, Hunan Normal University, Changsha, 410081, People’s Republic of China

    Yanliang Zhang & Maofa Fang

Authors
  1. Yanliang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qingping Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Guodong Kang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Maofa Fang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yanliang Zhang.

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

Zhang, Y., Zhou, Q., Kang, G. et al. The Dynamics of Quantum-Memory-Assisted Entropic Uncertainty of Two-Qubit System in the XY Spin Chain Environments with Dzyaloshinsky-Moriya Interaction. Int J Theor Phys 60, 402–419 (2021). https://doi.org/10.1007/s10773-020-04708-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-020-04708-6

Keywords

Search

Navigation