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Quantum Speed Limit Under the Influence of Measurement-based Feedback Control

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Abstract

Quantum speed limit (QSL) represents the minimum evolution time of a quantum system. We investigate the QSL time of a two-level qubit in a phase-damping channel. By manipulating measurement-based feedback controls on the qubit, we show that the QSL time of the qubit can have an obvious decline when the measurement rate is high. We also study the effect from feedback and find that the QSL time can reach the largest value when the feedback angle is \({\pi \mathord{\left/ {\vphantom {\pi 2}} \right. \kern-0pt} 2}\) and it decreases symmetrically on both sides of the angle. Additionally, the QSL time of qubit in the whole dynamic process is calculated. High rate of measurement and control is helpful to drive the QSL time to a stable value at earlier time and the variation of the optimal evolution time can be witnessed by the purity of the qubit system.

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References

  1. Mandelstam, L., Tamm, I.: J. Phys. (USSR). 9, 249 (1945)

    Google Scholar 

  2. Margolus, N., Levitin, L.B., Physcia, D., Amsterdam: Neth.). 120, 188 (1998)

    Google Scholar 

  3. Taddei, M.M., Escher, B.M., Davidovich, L., de Matos, R.L., Filho: Phys. Rev. Lett. 110, 050402 (2013)

    Article  ADS  Google Scholar 

  4. Deffner, S., Lutz, E.: Phys. Rev. Lett. 111, 010402 (2013)

    Article  ADS  Google Scholar 

  5. Pires, D.P., Cianciaruso, M., Celeri, L.C., Adesso, G., Soares-Pinto, D.O.: Phys. Rev. X. 6, 021031 (2016)

    Google Scholar 

  6. Campaioli, F., Pollock, F.A., Binder, F.C., Modi, K.: Phys. Rev. Lett. 120, 060409 (2018)

    Article  ADS  Google Scholar 

  7. Campaioli, F., Pollock, F.A., Binder, F.C., Modi, K.: Quantum. 3, 168 (2019)

    Article  Google Scholar 

  8. del Campo, A., Egusquiza, I.L., Plenio, M.B., Huelga, S.F.: Phys. Rev. Lett. 110, 050403 (2013)

    Article  Google Scholar 

  9. Zhang, Y., Han, W., Xia, Y., Cao, J., Fan, H.: Sci. Rep. 4, 4890 (2014)

    Article  Google Scholar 

  10. Sun, S., Zheng, Y.J.: Phys. Rev. Lett. 123, 180403 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  11. Sun, S., Peng, Y., Hu, X., Zheng, Y.: Phys. Rev. Lett. 127, 100404 (2021)

    Article  ADS  Google Scholar 

  12. Ness, G., Alberti, A., Sagi, Y.: Phys. Rev. Lett. 129, 140403 (2022)

    Article  ADS  Google Scholar 

  13. Santos, A.C., Sarandy, M.S.: Sci. Rep. 5, 15775 (2015)

    Article  ADS  Google Scholar 

  14. Suzuki, K., Takahashi, K.:Phys. Rev. Res.2, 032016(R) (2020)

  15. Fogarty, T., Deffner, S., Busch, T., Campbell, S.: Phys. Rev. Lett. 124, 110601 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  16. Caneva, T., Murphy, M., Calaro, T., Fazio, R., Montangero, S., Giovannetti, V., Santoro, G.E.: Phys. Rev. Lett. 103, 240501 (2009)

    Article  ADS  Google Scholar 

  17. Hegerfeldt, G.C.: Phys. Rev. Lett. 111, 260501 (2013)

    Article  ADS  Google Scholar 

  18. Demkowicz-Dobrzanski, R., Kolodynski, J., Guta, M.: Nat. Commun. 3, 1063 (2012)

    Article  ADS  Google Scholar 

  19. Braun, D., Adesso, G., Benatti, F., Floreanini, R., Marzolino, U., Mitchell, M.W., Pirandola, S.: Rev. Mod. Phys. 90, 035006 (2018)

    Article  ADS  Google Scholar 

  20. Campaioli, F., Pollock, F., Binder, F., Celeri, L., Goold, J., Vinjanampathy, S., Modi, K.: Phys. Rev. Lett. 118, 150601 (2017)

    Article  ADS  Google Scholar 

  21. Garcia-Pintos, L., Hamma, A., del Campo, A.: Phys. Rev. Lett. 125, 040601 (2020)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  23. Hou, L., Shao, B., Zou, J.: Eur. Phys. J. D. 70, 35 (2016)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  25. Wang, Q., Perez-Bernal, F.: Phys. Rev. A. 100, 022118 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  26. de Campo, A.: Phys. Rev. Lett. 126, 180603 (2021)

    Article  Google Scholar 

  27. Funo, K., Shiraishi, N., Saito, K.: New. J. Phys. 21, 013006 (2019)

    Article  ADS  Google Scholar 

  28. Garcia-Pintos, L.P., de Campo, A.: New. J. Phys. 21, 033012 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  29. Breuer, H.P., Petruccione, F.: The Theory of Open Quantum Systems. Oxford University Press, Oxford (2007)

    Book  MATH  Google Scholar 

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

    MATH  Google Scholar 

  31. Barnett, S.M., Radmore, P.M.: Methods in Theoretical Quantum Optics. Oxford University Press, Oxford (1997)

    MATH  Google Scholar 

  32. Carmichael, H.: An Open Systems Approach to Quantum Optics. Springer Verlag, Berlin (1993)

    Book  MATH  Google Scholar 

  33. Jacobs, K., Steck, D.: Contemp. Phys. 47, 279 (2006)

    Article  ADS  Google Scholar 

  34. Cresser, J.D., Barnett, S.M., Jeffers, J., Pegg, D.T.: Opt. Commun. 264, 352 (2006)

    Article  ADS  Google Scholar 

  35. Yanagisawa, M.: Phys. Rev. Lett. 97, 190201 (2006)

    Article  ADS  Google Scholar 

  36. Gillett, G., Dalton, R.B., Lanyon, B.P., Almeida, M.P.: et. al. Phys. Rev. Lett. 104, 080503 (2010)

    Article  ADS  Google Scholar 

  37. Rossi, M., Mason, D., Chen, J.X., Tsaturyan, Y., Schliesser, A.: Nature. 563, 7729 (2018)

    Article  Google Scholar 

  38. Monteiro, T.S.: Nature. 595, 7867 (2021)

    Article  Google Scholar 

  39. Wiseman, H.M., Milburn, G.J.: Phys. Rev. Lett. 70, 548 (1993)

    Article  ADS  Google Scholar 

  40. Wiseman, H.M.: Phys. Rev. A. 49, 2133 (1994)

    Article  ADS  Google Scholar 

  41. Zhang, G., Zhu, H.: Opt. Lett. 41, 3932 (2016)

    Article  ADS  Google Scholar 

  42. Chen, L., Yan, D., Song, L.S., Zhang, S.: Chin. Phys. Lett. 36, 030302 (2019)

    Article  ADS  Google Scholar 

  43. Kato, Y., Nakao, H.: New. J. Phys. 23, 013007 (2021)

    Article  ADS  Google Scholar 

  44. Zhang, S., Martin, L.S., Whaley, K.B.: Phys. Rev. A. 102, 062418 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  45. Yu, M., Fang, M.F., Zou, H.M.: Chin. Phys. B. 27, 010303 (2018)

    Article  ADS  Google Scholar 

  46. Haseli, S.: Int. J. Theor. Phys. 59, 1927 (2020)

    Article  MathSciNet  Google Scholar 

  47. Awasthi, N., Joshi, D.K., Sachdev, S.: Int. J. Theor. Phys. 61, 123 (2022)

    Article  Google Scholar 

  48. Inoue, R., Tanaka, S.-I.-R., Namiki, R. 1, Sagawa, T., Takahashi, Y.: Phys. Rev. Lett. 110, 163602 (2013)

    Article  ADS  Google Scholar 

  49. Yan, Y., Zou, J., Xu, B.M., Li, J.G., Shao, B.: Phys. Rev. A. 88, 032320 (2013)

    Article  ADS  Google Scholar 

  50. Yan, Y., Zou, J., Wang, L., Xu, B.M., Wang, C.Q., Shao, B.: Commun. Theor. Phys. 63, 2 (2015)

    Article  Google Scholar 

  51. Lindblad, G.: Commun. Math. Phys. 48, 119 (1976)

    Article  ADS  Google Scholar 

  52. Stenholm, S., Suominen, K.A.: Quantum Approach to Informatics. Wiley, New York (2005)

    Book  MATH  Google Scholar 

  53. Barnett, S.M., Cresser, J.D.: Phys. Rev. A. 72, 022107 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  54. Barnett, S.M., Jeffffers, J., Cresser, J.D.: J. Phys. : Condens. Matter. 18, S401 (2006)

    ADS  Google Scholar 

  55. Wang, X.J., Chesi, S., Coish, W.A.: Phys. Rev. B. 92, 115424 (2015)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We sincerely acknowledge support from the National Nature Science Foundation of China under grants No. 12005182. This work is also sponsored by the Natural Science Research of Jiangsu Higher Education Institutions of China under grant No. 20KJB140003.

Author information

Authors and Affiliations

  1. Department of Information Engineering, Changzhou Vocational Institute of Industry Technology, 213164, Changzhou, Jiangsu, China

    Lu Hou

  2. School of Physical Science and Technology, Yangzhou University, 225009, Yangzhou, Jiangsu, China

    Lu Hou

  3. School of Physics, Beijing Institute of Technology, 100081, Beijing, People’s Republic of China

    Bin Shao

  4. Department of Physics, East China University of Technology, 330000, Nanchang, China

    Chaoquan Wang

Authors
  1. Lu Hou
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  2. Bin Shao
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  3. Chaoquan Wang
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Contributions

Lu Hou wrote the main manuscript text and gave mathematical calculation for Figs. 1, 2, 3, 4, 5 and 6.Bin Shao gave the software that is used in our paper and supervised the whole process of research.Chaoquan Wang is responsible for data curation and Investigation.All authors have reviewed the manuscript.

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Correspondence to Lu Hou.

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Hou, L., Shao, B. & Wang, C. Quantum Speed Limit Under the Influence of Measurement-based Feedback Control. Int J Theor Phys 62, 47 (2023). https://doi.org/10.1007/s10773-023-05318-8

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  • DOI: https://doi.org/10.1007/s10773-023-05318-8

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