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Parameterized multi-observable sum uncertainty relations

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Abstract

The uncertainty principle is one of the fundamental features of quantum mechanics and plays an essential role in quantum information theory. We study uncertainty relations based on variance for arbitrary finite N quantum observables. We establish a series of parameterized uncertainty relations in terms of the parameterized norm inequalities, which improve the exiting variance-based uncertainty relations. The lower bounds of our uncertainty inequalities are non-zero unless the measured state is a common eigenvector of all the observables. Detailed examples are provided to illustrate the tightness of our uncertainty relations.

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References

  1. W.Heisenberg, J. Zeitschrift für Physik. 43, 198 (1927)

    Google Scholar 

  2. M.A. Nielsen, I.Chuang, Am. J. Phys. 70, 558 (2002). https://doi.org/10.1119/1.1463744

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  4. E.Schrödinger, journalAcad. Wiss p. 296 (1930)

  5. L. Maccone, A.K. Pati, J. Phys. Rev. Lett. 113, 260401 (2014)

    Article  ADS  Google Scholar 

  6. E.H. Kennard, journalZeitschrift für Physik. 44, 326 (1927)

  7. E. Schrödinger, journalSitzungsberichte der Preussischen Akademie der Wissenschaften. Physikalisch-mathematische Klasse. 14, 296 (1930)

    Google Scholar 

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

    Article  ADS  Google Scholar 

  9. D. Mondal, S. Bagchi, A.K. Pati, J. Physi. Rev. A. 95, 052117 (2017)

    Article  ADS  Google Scholar 

  10. S.-H. Chiew, M. Gessner, J. Phys. Rev. Res. 4, 013076 (2022)

    Article  Google Scholar 

  11. G. Tóth, F. Fröwis, J. Phys. Rev. Res. 4, 013075 (2022)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  15. P. Busch, P. Lahti, R.F. Werner, J. Phys. Rev. Lett. 111, 160405 (2013)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  17. J. Distler, S. Paban, J. Phys. Rev. A. 87, 062112 (2013)

    Article  ADS  Google Scholar 

  18. Z. Puchała, Ł Rudnicki, K. Życzkowski, J. Phys. A Math. Theor. 46, 272002 (2013)

    Article  ADS  Google Scholar 

  19. S. Friedland, V. Gheorghiu, G. Gour, J. Phys. Rev. Lett. 111, 230401 (2013)

    Article  ADS  Google Scholar 

  20. S. Luo, J. Phys. Rev. Lett. 91, 180403 (2003)

    Article  ADS  Google Scholar 

  21. Q.-H. Zhang, J.-F. Wu, S.-M. Fei, J. Phys. Rev. Lett. 18, 095204 (2021)

    Google Scholar 

  22. Q.-H. Zhang, S.-M. Fei, J. Quantum Inf. Process. 20, 1 (2021)

    Article  ADS  Google Scholar 

  23. X. Ma, Q.-H. Zhang, S.-M. Fei, J. Laser Phys. Lett. 19, 055205 (2022)

    Article  ADS  Google Scholar 

  24. O.Gühne, J. Phys. Rev. Lett. 92, 117903 (2004)

  25. Q.-H. Zhang, S.-M. Fei, J. Phys. Lett. 17, 065202 (2020)

    ADS  Google Scholar 

  26. J.-B. Zhang, T. Li, Q.-H. Zhang, S.-M. Fei, Z.-X. Wang, J. Sci. Rep. 11, 1 (2021)

    Article  ADS  Google Scholar 

  27. V. Giovannetti, S. Lloyd, L. Maccone, J. Phys. Rev. Lett. 96, 010401 (2006)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  29. M.J. Hall, J. Gen. Relativ. Gravit. 37, 1505 (2005)

    Article  ADS  Google Scholar 

  30. C.A. Fuchs, A. Peres, J. Phys. Rev. A. 53, 2038 (1996)

    Article  ADS  Google Scholar 

  31. S. Kechrimparis, S. Weigert, J. Phys. Rev. A. 90, 062118 (2014)

    Article  ADS  Google Scholar 

  32. L. Dammeier, R. Schwonnek, R.F. Werner, J. New J. Phys. 17, 093046 (2015)

    Article  Google Scholar 

  33. W. Ma, B. Chen, Y. Liu, M. Wang, X. Ye, F. Kong, F. Shi, S.-M. Fei, J. Du, J. Phys. Rev. Lett. 118, 180402 (2017)

    Article  ADS  Google Scholar 

  34. B. Chen, N.-P. Cao, S.-M. Fei, G.-L. Long, J. Quantum Inf. Process. 15, 3909 (2016)

    Article  ADS  Google Scholar 

  35. B. Chen, S.-M. Fei, J. Sci. Rep. 5, 1 (2015)

    ADS  Google Scholar 

  36. Z.-X. Chen, H. Wang, J.-L. Li, Q.-C. Song, C.-F. Qiao, J. Sci. Rep. 9, 1 (2019)

    Article  ADS  Google Scholar 

  37. H.-H. Qin, S.-M. Fei, X. Li-Jost, J. Sci. Rep. 6, 1 (2016)

    Article  Google Scholar 

  38. Y. Xiao, N. Jing, J. Sci. Rep. 6, 1 (2016)

    Article  Google Scholar 

  39. Q.-C. Song, J.-L. Li, G.-X. Peng, C.-F. Qiao, J. Sci. Rep. 7, 1 (2017)

    Article  ADS  Google Scholar 

  40. Q.-H. Zhang, J.-F. Wu, X. Ma, S.-M. Fei, J. Quantum Inf. Process. 22, 1 (2023)

    ADS  Google Scholar 

  41. H.Li, T.Gao, F.Yan, J. Physica Scripta. 98, 015024 (2022)

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Acknowledgements

This work is supported by NSFC (Grant Nos. 12075159, 12171044), Beijing Natural Science Foundation (Z190005) and the Academician Innovation Platform of Hainan Province.

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Author notes

  1. Qing-Hua Zhang

    Present address: School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, 410114, China

Authors and Affiliations

  1. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China

    Jing-Feng Wu, Qing-Hua Zhang & Shao-Ming Fei

  2. Max-Planck-Institute for Mathematics in the Sciences, 04103, Leipzig, Germany

    Shao-Ming Fei

Authors
  1. Jing-Feng Wu
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Correspondence to Qing-Hua Zhang or Shao-Ming Fei.

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Wu, JF., Zhang, QH. & Fei, SM. Parameterized multi-observable sum uncertainty relations. Eur. Phys. J. Plus 138, 287 (2023). https://doi.org/10.1140/epjp/s13360-023-03873-x

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