Characterizing the dynamics of entropic uncertainty for multi-measurement

Abstract

Uncertainty principle lies at the heart of quantum theory and is regarded as a vital property essentially differing from the rule in classical physics. We herein study the dynamics of the entropic uncertainty with regard to multi-measurement in the Markovian and non-Markovian regimes, respectively. We show that how non-Markovian and Markovian noises influence the dynamical evolutions of the measurement uncertainty and its bound. Moreover, we design a simple and valid method to decrease the uncertainty through pre-weak measurement and post-reversal measurement on the subsystems. Further, we offer the physical interpretations behind the uncertainty dynamics by the systemic quantum correlation. Finally, we apply the current observations on entanglement witness.

This is a preview of subscription content, access via your institution.

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

References

  1. 1.

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

    ADS  Google Scholar 

  2. 2.

    E.H. Kennard, Z. Phys. 44, 326 (1927)

    ADS  Google Scholar 

  3. 3.

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

    ADS  Google Scholar 

  4. 4.

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

    ADS  MathSciNet  Google Scholar 

  5. 5.

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

    ADS  MathSciNet  Google Scholar 

  6. 6.

    K. Kraus, Phys. Rev. D 35, 3070 (1987)

    ADS  MathSciNet  Google Scholar 

  7. 7.

    J.M. Renes, J.C. Boileau, Phys. Rev. Lett. 103, 020402 (2009)

    ADS  Google Scholar 

  8. 8.

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

    Google Scholar 

  9. 9.

    C.F. Li, J.S. Xu, X.Y. Xu, K. Li, G.C. Guo, Nat. Phys. 7, 752 (2011)

    Google Scholar 

  10. 10.

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

    ADS  Google Scholar 

  11. 11.

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

    ADS  Google Scholar 

  12. 12.

    M.L. Hu, H. Fan, Phys. Rev. A 87, 022314 (2013)

    ADS  Google Scholar 

  13. 13.

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

    ADS  Google Scholar 

  14. 14.

    F. Ming, D. Wang, A.J. Huang, W.Y. Sun, L. Ye, Quantum Inf. Process. 17, 9 (2018)

    ADS  Google Scholar 

  15. 15.

    D. Wang, F. Ming, A.J. Huang, W.Y. Sun, J.D. Shi, L. Ye, Laser Phys. Lett. 14, 055205 (2017)

    ADS  Google Scholar 

  16. 16.

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

    Google Scholar 

  17. 17.

    I. Bialynicki-Birula, AIP Conf. Proc. 889, 52 (2007)

    ADS  MathSciNet  Google Scholar 

  18. 18.

    M. Tomamichel, R. Renner, Phys. Rev. Lett. 106, 110506 (2011)

    ADS  Google Scholar 

  19. 19.

    P.J. Coles, R. Colbeck, L. Yu, M. Zwolak, Phys. Rev. Lett. 108, 210405 (2012)

    ADS  Google Scholar 

  20. 20.

    J. Zhang, Y. Zhang, C.S. Yu, Quantum Inf. Process. 14, 2239 (2015)

    ADS  MathSciNet  Google Scholar 

  21. 21.

    A.K. Pati, M.M. Wilde, A.R.U. Devi, A.K. Rajagopal, Sudha, Phys. Rev. A 86, 042105 (2012)

    ADS  Google Scholar 

  22. 22.

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

    ADS  Google Scholar 

  23. 23.

    P.J. Coles, M. Piani, Phys. Rev. A 89, 022112 (2014)

    ADS  Google Scholar 

  24. 24.

    J.L. Huang, W.C. Gan, Y.L. Xiao, F.W. Shu, M.H. Yung, Eur. Phys. J. C 78, 545 (2018)

    ADS  Google Scholar 

  25. 25.

    M. Yu, M.F. Fang, Quantum Inf. Process. 16, 21 (2017)

    ADS  Google Scholar 

  26. 26.

    Z.Y. Zhang, J.M. Liu, Z.F. Hu, Y.Z. Wang, Ann. Phys. (Berlin) 530, 1800208 (2018)

    ADS  Google Scholar 

  27. 27.

    Y. Lim, S. Lee, Phys. Rev. A 98, 012326 (2018)

    ADS  Google Scholar 

  28. 28.

    Y.H. Ji, Q. Ke, J.J. Hu, Phys. E 110, 140 (2019)

    Google Scholar 

  29. 29.

    P.F. Chen, L. Ye, D. Wang, Eur. Phys. J. D 73, 108 (2019)

    ADS  Google Scholar 

  30. 30.

    D. Wang, W.N. Shi, R.D. Hoehn, F. Ming, W.Y. Sun, S. Kais, L. Ye, Ann. Phys. (Berlin) 530, 1800080 (2018)

    ADS  Google Scholar 

  31. 31.

    M.N. Chen, D. Wang, L. Ye, Phys. Lett. A 383, 977 (2019)

    ADS  Google Scholar 

  32. 32.

    J. Zhang, Y. Zhang, C.S. Yu, Sci. Rep. 5, 11701 (2015)

    ADS  Google Scholar 

  33. 33.

    S. Liu, L.Z. Mu, H. Fan, Phys. Rev. A 91, 042133 (2015)

    ADS  Google Scholar 

  34. 34.

    A. Ketterer, O. Gühne, arXiv:1911.07533v1 (2019)

  35. 35.

    A.E. Rastegin, Open Sys. Inf. Dyn. 22, 1550005 (2015)

    Google Scholar 

  36. 36.

    N. Sönke, K. Matthias, O. Gühne, J. Math. Phys. 53, 012202 (2012)

    MathSciNet  Google Scholar 

  37. 37.

    S. Haseli, G. Karpat, S. Salimi, A.S. Khorashad, F.F. Fanchini, B. Cakmak, G.H. Aguilar, S.P. Waiborn, P.H. Souto Ribeiro, Phys. Rev. A 90, 052118 (2014)

    ADS  Google Scholar 

  38. 38.

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

    Google Scholar 

  39. 39.

    S. Maniscalco, F. Petruccione, Phys. Rev. A 73, 012111 (2006)

    ADS  MathSciNet  Google Scholar 

  40. 40.

    B.M. Garraway, Phys. Rev. A 55, 2290 (1997)

    ADS  Google Scholar 

  41. 41.

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

    Google Scholar 

  42. 42.

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

    ADS  Google Scholar 

  43. 43.

    M. Berta, S. Wehner, M.M. Wilde, New J. Phys. 18, 073004 (2016)

    ADS  Google Scholar 

  44. 44.

    G. Vallone, D.G. Marangon, M. Tomasin, P. Villoresi, Phys. Rev. A 90, 052327 (2014)

    ADS  Google Scholar 

  45. 45.

    S. Designolle, P. Skrzypczyk, F. Fröwis, N. Brunner, Phys. Rev. Lett. 122, 050402 (2019)

    ADS  Google Scholar 

  46. 46.

    S.J. Wu, S.X. Yu, K. Mølmer, Phys. Rev. A 79, 022104 (2009)

    ADS  MathSciNet  Google Scholar 

  47. 47.

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

    ADS  Google Scholar 

  48. 48.

    M.L. Hu, X.Y. Hu, J.C. Wang, Y. Peng, Y.R. Zhang, H. Fan, Phys. Rep. 762–764, 1 (2018)

    ADS  Google Scholar 

  49. 49.

    S. Golkar, M.K. Tavassoly, Eur. Phys. J. D 72, 184 (2018)

    ADS  Google Scholar 

  50. 50.

    M. Koashi, M. Ueda, Phys. Rev. Lett. 82, 2598–2601 (1999)

    ADS  Google Scholar 

  51. 51.

    Y.S. Kim, J.C. Lee, O. Kwon, Y.H. Kim, Nat. Phys. 8, 117 (2012)

    Google Scholar 

  52. 52.

    F. Adabi, S. Haseli, S. Salimi, Europhys. Lett. 115, 60004 (2016)

    ADS  Google Scholar 

  53. 53.

    D. Wang, A.J. Huang, A.J. Huang, Ross D. Hoehn, F. Ming, W.Y. Sun, J.D. Shi, L. Ye, S. Kais, Sci. Rep. 7, 1066 (2017)

    ADS  Google Scholar 

  54. 54.

    Y.Y. Yang, W.Y. Sun, W.N. Shi, F. Ming, D. Wang, L. Ye, Front. Phys. 14, 31601 (2019)

    ADS  Google Scholar 

  55. 55.

    Q.Q. Sun, M. Al-Amri, L. Davidovich, M.S. Zubairy, Phys. Rev. A 82, 052323 (2010)

    ADS  Google Scholar 

  56. 56.

    P.J. Coles, M. Berta, M. Tomamichel, S. Wehner, Rev. Mod. Phys. 89, 015002 (2017)

    ADS  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Science Foundation of China under Grant Nos. 61601002 and 11575001, and the fund from CAS Key Laboratory of Quantum Information (Grant No. KQI201701).

Author information

Affiliations

Authors

Corresponding author

Correspondence to Dong Wang.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zhou, AL., Wang, D., Ming, F. et al. Characterizing the dynamics of entropic uncertainty for multi-measurement. Eur. Phys. J. Plus 135, 489 (2020). https://doi.org/10.1140/epjp/s13360-020-00506-5

Download citation