Skip to main content
SpringerLink
Log in

Sudden change of local quantum uncertainty and geometry for arbitrary two-qubit X-states

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

Local quantum uncertainty (LQU) as a reliable measure of nonclassical correlations has been recently proposed by Girolami et al. (Phys Rev Lett 110:240402, 2013). In this paper, we have derived an explicit analytical expression of LQU and presented the level surfaces of constant LQU for a class of two-qubit X-states beyond Bell-diagonal states. The dynamical behavior of quantum correlations via the LQU under decoherence environment is studied, and the phenomenon of a sudden change of LQU is demonstrated. Our results are illustrated through the action of different noisy environments individually on a single qubit of quantum system where there is a necessary condition for the occurrence of sudden change of LQU.

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.

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Nielsen, I.L., Nielsen, M.A.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  2. Groisman, B., Popescu, S., Winter, A.: Quantum, classical, and total amount of correlations in a quantum state. Phys. Rev. A 72, 032317 (2005)

    ADS  MathSciNet  Google Scholar 

  3. Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009)

    ADS  MathSciNet  MATH  Google Scholar 

  4. Barnum, H., Linden, N.: Monotones and invariants for multi-particle quantum states. J. Phys. A Math. Gen. 34, 6787 (2001)

    ADS  MathSciNet  MATH  Google Scholar 

  5. Niset, J., Cerf, N.J.: Multipartite nonlocality without entanglement in many dimensions. Phys. Rev. A 74, 052103 (2006)

    ADS  Google Scholar 

  6. Lanyon, B.P., Barbieri, M., Almeida, M.P., White, A.G.: Experimental quantum computing without entanglement. Phys. Rev. Lett. 101, 200501 (2008)

    ADS  Google Scholar 

  7. Henderson, L., Vedral, V.: Classical, quantum and total correlations. J. Phys. A 34, 6899 (2001)

    ADS  MathSciNet  MATH  Google Scholar 

  8. Olliver, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)

    ADS  MATH  Google Scholar 

  9. Datta, A., Shaji, A., Caves, C.M.: Quantum discord and the power of one qubit. Phys. Rev. Lett. 100, 050502 (2008)

    ADS  Google Scholar 

  10. Devetak, I.: Distillation of local purity from quantum states. Phys. Rev. A 71, 062303 (2005)

    ADS  Google Scholar 

  11. Oppenheim, J., Horodecki, M., Horodecki, P., Horodecki, R.: Thermodynamical approach to quantifying quantum correlations. Phys. Rev. Lett. 89, 180402 (2002)

    ADS  MATH  Google Scholar 

  12. Luo, S.: Using measurement-induced disturbance to characterize correlations as classical or quantum. Phys. Rev. A 77, 022301 (2008)

    ADS  Google Scholar 

  13. Luo, S.: Wigner–Yanase skew information versus quantum Fisher information. Proc. Am. Math. Soc. 132, 885–890 (2004)

    MATH  Google Scholar 

  14. Modi, K., Paterek, T., Son, W., Vedral, V., Williamson, M.: Unified view of quantum and classical correlations. Phys. Rev. Lett. 104, 080501 (2010)

    ADS  MathSciNet  Google Scholar 

  15. Girolami, D., Tufarelli, T., Adesso, G.: Characterizing nonclassical correlations via local quantum uncertainty. Phys. Rev. Lett. 110, 240402 (2013)

    ADS  Google Scholar 

  16. Wigner, E.P., Yanase, M.M.: Information contents of distributions. Proc. Natl. Acad. Sci. USA 49, 910 (1963)

    ADS  MathSciNet  MATH  Google Scholar 

  17. Luo, S.: Wigner–Yanase Skew information and uncertainty relations. Phys. Rev. Lett. 91, 180403 (2003)

    ADS  Google Scholar 

  18. Slaoui, A., Daoud, M., Ahl Laamara, R.: The dynamics of local quantum uncertainty and trace distance discord for two-qubit X states under decoherence: a comparative study. Quantum Inf. Process. 17, 178 (2018)

    ADS  MathSciNet  MATH  Google Scholar 

  19. Slaoui, A., Shaukat, M.I., Daoud, M., Ahl Laamara, R.: Universal evolution of non-classical correlations due to collective spontaneous emission. Eur. Phys. J. Plus. 133, 413 (2018)

    Google Scholar 

  20. Khedif, Y., Daoud, M.: Local quantum uncertainty and trace distance discord dynamics for two-qubit X states embedded in non-Markovian environment. Int. J. Mod. Phys. B 32, 1850218 (2018)

    ADS  MathSciNet  MATH  Google Scholar 

  21. Jebli, L., Benzimoune, B., Daoud, M.: Local quantum uncertainty for a class of two-qubit X states and quantum correlations dynamics under decoherence. Int. J. Quant. Inf. 15, 1750001 (2017)

    MATH  Google Scholar 

  22. Sales, J., Cardoso, W., Avelar, A., Almeida, N.: Dynamics of nonclassical correlations via local quantum uncertainty for atom and field interacting into a lossy cavity QED. Phys. A 443, 399 (2016)

    MathSciNet  MATH  Google Scholar 

  23. Slaoui, A., Bakmou, L., Daoud, M., Ahl Laamara, R.: A comparative study of local quantum Fisher information and local quantum uncertainty in Heisenberg XY model. Phys. Lett. A 383, 2241 (2019)

    ADS  MathSciNet  Google Scholar 

  24. Guo, J.L., Wei, J.L., Qin, W.: Enhancement of quantum correlations in qubit-qutrit system under decoherence of finite temperature. Quantum Inf. Process. 14, 1429 (2015)

    ADS  MATH  Google Scholar 

  25. Habiballah, N., Khedif, Y., Daoud, M.: Local quantum uncertainty in XYZ Heisenberg spin models with Dzyaloshinski–Moriya interaction. Eur. Phys. J. D 72, 154 (2018)

    ADS  Google Scholar 

  26. He, Z., Yao, C., Wang, Q., Zou, J.: Measuring non-Markovianity based on local quantum uncertainty. Phys. Rev. A 90, 042101 (2014)

    ADS  Google Scholar 

  27. Bera, M.N.: Role of quantum correlation in metrology beyond standard quantum limit. arXiv:1405.5357 (2014)

  28. Lang, M.D., Caves, C.M.: Quantum discord and the geometry of Bell-diagonal states. Phys. Rev. Lett. 105, 150501 (2010)

    ADS  Google Scholar 

  29. Mazzola, L., Piilo, J., Maniscalco, S.: Sudden transition between classical and quantum decoherence. Phys. Rev. Lett. 104, 200401 (2010)

    ADS  MathSciNet  Google Scholar 

  30. Yao, Y., Li, H.M., Yin, Z.Q., Han, Z.F.: Geometric interpretation of the geometric discord. Phys. Lett. A 376, 358 (2012)

    ADS  MATH  Google Scholar 

  31. Li, B., Wang, Z.X., Fei, S.M.: Quantum discord and geometry for a class of two-qubit states. Phys. Rev. A 83, 022321 (2011)

    ADS  Google Scholar 

  32. Wang, Y.K., Ma, T., Fan, H., Fei, S.M., Wang, Z.X.: Super-quantum correlation and geometry for Bell-diagonal states with weak measurements. Quantum Inf. Process. 13, 283 (2014)

    ADS  MATH  Google Scholar 

  33. Cianciaruso, M., Bromley, T., Roga, W., Lo Franco, R., Adesso, G.: Universal freezing of quantum correlations within the geometric approach. Sci. Rep. 5, 10177 (2015)

    ADS  Google Scholar 

  34. Zhao, Z.K., Pisarczyk, R., Thompson, J., Gu, M., Vedral, V., Fitzsimons, J.: Geometry of quantum correlations in space-time. Phys. Rev. A 98, 052312 (2018)

    ADS  Google Scholar 

  35. Wang, Y.K., Shao, L.H., Ge, L.Z., Fei, S.M., Wang, Z.X.: Geometry of quantum coherence for two qubit X states. Int. J. Theor. Phys. 58, 2372 (2019)

    MathSciNet  MATH  Google Scholar 

  36. Maziero, J., Celeri, L.C., Serra, R.M., Vedral, V.: Classical and quantum correlations under decoherence. Phys. Rev. A 80, 044102 (2009)

    ADS  MathSciNet  Google Scholar 

  37. Pinto, J.P.G., Karpat, G., Fanchini, F.F.: Sudden change of quantum discord for a system of two qubits. Phys. Rev. A 88, 034304 (2013)

    ADS  Google Scholar 

  38. Yu, T., Eberly, J.H.: Quantum open system theory: bipartite aspects. Phys. Rev. Lett. 97, 140403 (2006)

    ADS  Google Scholar 

  39. Maziero, J., Werlang, T., Fanchini, F.F., Cleri, L.C., Serra, R.M.: System-reservoir dynamics of quantum and classical correlations. Phys. Rev. A 81, 022116 (2010)

    ADS  Google Scholar 

  40. Wang, B., Xu, Z.Y., Chen, Z.Q., Feng, M.: Non-Markovian effect on the quantum discord. Phys. Rev. A 81, 014101 (2010)

    ADS  Google Scholar 

  41. Bromley, T.R., Cianciaruso, M., Adesso, G.: Frozen quantum coherence. Phys. Rev. Lett. 114, 210401 (2015)

    ADS  Google Scholar 

  42. You, B., Cen, L.: Necessary and sufficient conditions for the freezing phenomena of quantum discord under phase damping. Phys. Rev. A 86, 012102 (2012)

    ADS  Google Scholar 

  43. Mazzola, L., Piilo, J., Maniscalco, S.: Frozen discord in non-Markovian dephasing channels. Int. J. Quantum Inf. 9, 981 (2011)

    MathSciNet  MATH  Google Scholar 

  44. Chanda, T., Pal, A.K., Biswas, A., Sen, A., Sen, U.: Freezing of quantum correlations under local decoherence. Phys. Rev. A 91, 062119 (2015)

    ADS  Google Scholar 

  45. Hu, Z.D., Wang, J.C., Zhang, Y.X., Zhang, Y.Q.: Sudden transitions of trace distance discord of dipoleCdipole coupled two qubits. Int. J. Mod. Phys. B 29, 1550138 (2015)

    ADS  MATH  Google Scholar 

  46. Hou, J.X., Liu, S.Y., Wang, X.H., Yang, W.L.: Role of coherence during classical and quantum decoherence. Phys. Rev. A 96, 042324 (2011)

    ADS  Google Scholar 

  47. Jia, L.X., Li, B., Yue, R.H., Fan, H.: Sudden change of quantum discord under single qubit noise. Int. J. Quantum Inf. 11, 1350048 (2013)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work is supported by the Scientific Research Project of Hunan Province Department of Education (Grant Nos. 19B060, 18A373 and 19C0539), the Project of Science and Technology Plan of Changsha (kc1809023) and the Start-up Funds for Talent Introduction and Scientific Research of Changsha University 2015 (Grant No. SF1504). Y N Guo is supported by Training Program for Excellent Young Innovators of Changsha (kq1905005).

Author information

Authors and Affiliations

  1. School of Electronic Information and Electrical Engineering, Changsha University, Changsha, 410022, Hunan, People’s Republic of China

    You-neng Guo, Hu-ping Peng & Ke Zeng

  2. College of Science, Hunan University of Technology, Zhuzhou, 412007, Hunan, China

    Guo-you Wang

Authors
  1. You-neng Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hu-ping Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ke Zeng
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Guo-you Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Ke Zeng or Guo-you Wang.

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

Guo, Yn., Peng, Hp., Zeng, K. et al. Sudden change of local quantum uncertainty and geometry for arbitrary two-qubit X-states . Quantum Inf Process 19, 304 (2020). https://doi.org/10.1007/s11128-020-02792-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-020-02792-5

Keywords

Search

Navigation