Skip to main content
SpringerLink
Log in

On the Analytical Derivation of Quantum Fisher Information and Skew Information for two Qubit X States

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

Abstract

The quantum Fisher information defined via the symmetric logarithmic derivative and the skew information are two different aspects describing the information contents of quantum mechanical density operators. They are considered as natural generalizations of the classical Fisher information and constitute key ingredients in the emerging field of quantum metrology. In this paper, we give the analytical expression of quantum Fisher information and skew information for two-qubit system prepared in a two-qubit state of X type.

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

Similar content being viewed by others

References

  1. Einstein, A., Podolsky, B., Rosen, N.: Phys. Rev. 47, 777 (1935)

    Article  ADS  Google Scholar 

  2. Bell, J.S.: Physics 1, 195 (1964)

    Article  Google Scholar 

  3. Hill, S., Wootters, W.K.: Phys. Rev. Lett. 78, 5022 (1997)

    Article  ADS  Google Scholar 

  4. Daoud, M., Ahl Laamara, R., El Hadfi, H.: Inter. J. Quant. Inf. 12, 1450035 (2014)

    Article  Google Scholar 

  5. Daoud, M., Kaydi, W., El Hadfi, H.: Open Systems and Information Dynamics 22, 1550023 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  6. Daoud, M., Kaydi, W., El Hadfi, H.: Mod. Phys. Lett. B 29, 1550239 (2015)

    Article  ADS  Google Scholar 

  7. EL Hadfi, H., Ait Taleb, Y., Daoud, M.: Inter. J. Mod. Phys. B 30, 1750052 (2016)

    Google Scholar 

  8. Davide, G., et al.: Phys. Rev. Lett. 112, 210401 (2014)

    Article  Google Scholar 

  9. Modi, K., Cable, H., Williamson, M., Vedral, V.: Phys. Rev. X 1, 021022 (2011)

    Google Scholar 

  10. Girolami, D.: J. Phys. 626, 012042 (2015)

    Google Scholar 

  11. Jozsa, R., Abrams, D.S., Dowling, J.P., Williams, C.P.: Phys. Rev. Lett 85, 2010 (2000)

    Article  ADS  Google Scholar 

  12. Bollinger, J.J., Itano, W.M., Wineland, D.J., Heinzen, D.J.: Phys. Rev. A 54, 4649 (1996)

    Article  ADS  Google Scholar 

  13. Ma, J., Huang, Yi-X., Wang, X., Sun, C.P.: Phys. Rev. A 84, 022302 (2011)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  15. Tsang, M.: Phys. Rev. Lett. 108, 230401 (2012)

    Article  ADS  Google Scholar 

  16. Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic, New York (1976)

    MATH  Google Scholar 

  17. Holevo, A.S.: Probabilistic and Statistical Aspects of Quantum Theory. North-Holland (Amsterdam) (1982)

  18. Zhong, W., Sun, Z., Ma, J., Wang, X., Nori, F.: Phys. Rev. A 87, 022337 (2013)

    Article  ADS  Google Scholar 

  19. Pezzé, L, Smerzi, A: . Phys. Rev. Lett. 102, 100401 (2009). 20

    Article  ADS  MathSciNet  Google Scholar 

  20. Meyer, V., Rowe, M.A., Kielpinski, D., Sackett, C.A., Itano, W.M., Monroe, C., Wineland, D.: Phys. Rev. Lett. 86, 5870 (2001)

    Article  ADS  Google Scholar 

  21. Slaoui, A., Bakmou, L., Daoud, M., Ahl Laamara, R.: Phys. Lett. A 383, 2241–2247 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  22. Bakmou, L., Slaoui, A., Daoud, M., Ahl Laamara, R.: Quantum Inf Process 18, 163 (2019)

    Article  ADS  Google Scholar 

  23. Wigner, E.P., Yanase, M.M.: Proc. Nat. Acad. Sci 49, 910 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  24. Luo, S.L., Fu, S.S., Oh, C.H.: Phys. Rev. A 85, 032117 (2012)

    Article  ADS  Google Scholar 

  25. Luo, S.: Phys. Rev. Lett. 91, 180403 (2003)

    Article  ADS  Google Scholar 

  26. Luo, S.: Phys. Rev. A. 73, 022324 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  27. Liu, X., Cheng, W., Liu, J.M.: Sci. Rep. 6, 19359 (2016)

    Article  ADS  Google Scholar 

  28. Hayashi, M., et al.: New J. Phys. 8, 129 (2006)

    Article  ADS  Google Scholar 

  29. Fisher, R.A.: Proc. Camb. Phil. Soc. 22, 700 (1925)

    Article  ADS  Google Scholar 

  30. Prokopenko, M., et al.: Phys. Rev. E 84, 041116 (2011)

    Article  ADS  Google Scholar 

  31. Navarro, D.J.: Neural Comput. 16, 1763–1768 (2004)

    Article  Google Scholar 

  32. Yin, X., et al.: J. Phys. B: At. Mol. Opt. Phys. 44, 245502 (2011)

    Article  ADS  Google Scholar 

  33. Wang, X., Molmer, K.: Eur. Phys. J. D 18, 385 (2002)

    ADS  Google Scholar 

  34. Daoud, M., Ahl Laamara, R., Kaydi, W.: J. Phys. A: Math. Theor. 46, 395302 (2013)

    Article  Google Scholar 

  35. Daoud, M., Ahl Laamara, R.: Phys. Lett. A 376, 2361 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  36. Daoud, M., Ahl Laamara, R.: Int. J. Quantum Inform. 10, 1250060 (2012)

    Article  Google Scholar 

  37. Wang, X., Sanders, B.C.: Phys. Rev. A 65, 012303 (2001)

    Article  ADS  Google Scholar 

  38. Werner, R.F.: Phys. Rev. A 133, 4277 (1989)

    Article  ADS  Google Scholar 

  39. RAU, A. R. P.: J. Phys A: Math. Theor. 42, 412002 (2009)

    Article  Google Scholar 

  40. Plbnio, M.B., Virmani, S.S.: Quantum. Inf. Comput. 7, 1–51 (2007)

    MathSciNet  Google Scholar 

  41. Ali, M., Rau, A.R.P., Alber, G.: Phys. Rev. A 81, 042105 (2010)

    Article  ADS  Google Scholar 

  42. Liu, J., Chen, J., Jing, X.X., Wang, X.: J. Phys A: Math Theor. 49, 275302 (2016)

    Article  Google Scholar 

  43. Kaye, P., Laflamme, R., Mosca, M.: An introduction to quantum computing. Oxford University Press, Oxford (2007)

    MATH  Google Scholar 

  44. Ciccarello, F., Tufarelli, T., Giovannetti, V.: New J. Phys. 16, 013038 (2014)

    Article  ADS  Google Scholar 

  45. Braunstein, S.L., Caves, C.M.: Phys. Rev. Lett. 72, 3439 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  46. Toth, G., Apellaniz, L.: J. Phys. A: Math. Theor. 47, 424006 (1994)

    Article  Google Scholar 

  47. Luo, S., Zhang, Q.: Phys. Rev. A 69, 032106 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  48. Slaoui, A., Shaukat, M.I., Daoud, M., Ahl Laamara, R.: Eur. Phys. J. Plus 133, 413 (2018)

    Article  Google Scholar 

  49. Girolami, D.: Phys. Rev. Lett. 113, 170401 (2014)

    Article  ADS  Google Scholar 

  50. Slaoui, A., Daoud, M., Laamara, R.A.: Quant. Inf. Proc. 17, 178 (2018)

    Article  Google Scholar 

  51. Shaukat, M.I., Slaoui, A., Terças, H., Daoud, M.: Eur. Phys. J. Plus 135, 357 (2020)

    Article  Google Scholar 

  52. Slaoui, A., Salah, A., Daoud, M.: Physica A: Statistical Mechanics and its Applications 558, 124946 (2020)

    Article  MathSciNet  Google Scholar 

  53. Ay, N., Gibilisco, P., Matús̆, F.: Information Geometry and Its Applications, Springer Procedings in Mathematics and statistics, pp 252 (2016)

Download references

Author information

Authors and Affiliations

  1. LPMC, Department of Physics, Faculty of Sciences Ben M’Sick, University Hassan II, Casablanca, Morocco

    B. Maroufi

  2. LPHE-Modeling and Simulation, Faculty of Sciences, University Mohammed V, Rabat, Morocco

    B. Maroufi, R. Laghmach & H. EL Hadfi

  3. Department of Physics, Faculty of Sciences, University Ibn Tofail, Kenitra, Morocco

    B. Maroufi & M. Daoud

  4. Abdus Salam International Centre for Theoretical physics, Trieste,, Italy

    M. Daoud

Authors
  1. B. Maroufi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Laghmach
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. EL Hadfi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. Daoud
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. Maroufi.

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

Maroufi, B., Laghmach, R., EL Hadfi, H. et al. On the Analytical Derivation of Quantum Fisher Information and Skew Information for two Qubit X States. Int J Theor Phys 60, 3103–3114 (2021). https://doi.org/10.1007/s10773-021-04907-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-021-04907-9

Keywords

Search

Navigation