Skip to main content
SpringerLink
Log in

Information-theoretical Discord for a Class of Three-qubit X States

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

Abstract

Based on the definition of multipartite quantum discord proposed in [Phys. Rev. Lett. 124, 110401 (2020)], we give the analytic expression for the information-theoretical multipartite quantum discord of one type of three-qubit X states which depend on four real parameters. In addition, we present the level surfaces of multipartite quantum discord of X states. As an application, we investigate the dynamic behavior of multipartite quantum discord for the three-qubit X states under the phase flip channel, which presents the sudden change of multipartite quantum discord.

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

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Huang, Y.: Computing quantum discord is NP-complete. New J. Phys. 16, 033027 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. Ali M.: Quantum discord for a two-parameter class of states in \(2 \otimes d\) quantum systems. J. Phys. A Math. Theor. 43, 495303 (2010)

  3. Lanyon, B.P., Barbieri, M., Almeida, M.P., et al.: Experimental quantum computing without entanglement. Phys. Rev. Lett. 101, 200501 (2008)

    Article  ADS  Google Scholar 

  4. Xie, C., Zhang, Z., Chen, J., et al.: Analytic Expression of Quantum Discords in Werner States under LQCC. Entropy. 22, 147 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  5. Ali, M., Rau, A.R.P., Alber G.: Quantum discord for two-qubit X states. Phys. Rev. A. 81, 042105, 069902 (2010)

  6. Madhok, V., Datta, A.: Quantum discord as a resource in quantum communication. Int. J. Mod. Phys. B. 27, 1345041 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Datta, A., Shaji, A.: Quantum discord and quantum computingan appraisal. Int. J. Quantum Inf. 9, 1787 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  8. Merali Z.: The power of discord: physicists have always thought quantum computing is hard because quantum states are incredibly fragile. But could noise and messiness actually help things along?. Nature. 474, 24 (2011)

  9. Yao, Y., Li, D., Sun, C.P.: Quantum coherence fraction. Phys. Rev. A. 100, 032324 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  10. Yu, D., Zhang, L., Yu, C.: Quantifying coherence in terms of the pure-state coherence. Phys. Rev. A. 101, 062114 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  11. Li, N., Luo, S.: Total versus quantum correlations in quantum states. Phys. Rev. A. 76, 032327 (2007)

    Article  ADS  Google Scholar 

  12. Mazzola, L., Piilo, J., Maniscalco, S.: Sudden Transition between Classical and Quantum Decoherence. Phys. Rev. Lett. 104, 200401 (2010)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  14. Theurer, T., Satyajit, S., Plenio, M.B.: Quantifying Dynamical Coherence with Dynamical Entanglement. Phys. Rev. Lett. 125, 130401 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  15. Xi, Y., Zhang, T., Zheng, Z.J., et al.: Converting quantum coherence to genuine multipartite entanglement and nonlocality. Phys. Rev. A. 100, 022310 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  16. Werlang, T., Souza, S., Fanchini, F.F., et al.: Robustness of quantum discord to sudden death. Phys. Rev. A. 80, 024103 (2009)

    Article  ADS  Google Scholar 

  17. Sarandy, M.S.: Classical correlation and quantum discord in critical systems. Phys. Rev. A. 80, 022108 (2009)

    Article  ADS  Google Scholar 

  18. Daki\(\acute{c}\), B., Vedral, V., Brukner, \(\check{C}\).: Necessary and Sufficient Condition for Nonzero Quantum Discord. Phys. Rev. Lett. 105, 190502 (2010)

  19. Daki\(\acute{c}\), B., Lipp, Y.O., Ma, X., et al.: Quantum discord as resource for remote state preparation. Nature Phys. 8, 666 (2012)

  20. Dillenschneider, R.: Quantum discord and quantum phase transition in spin chains. Phys. Rev. B. 78, 224413 (2008)

    Article  ADS  Google Scholar 

  21. Pirandola, S.: Quantum discord as a resource for quantum cryptography. Sci. Rep. 4, 1 (2014)

    Google Scholar 

  22. Ollivier, H., Zurek, W.H.: Quantum Discord: A Measure of the Quantumness of Correlations. Phys. Rev. Lett. 88, 017901 (2001)

    Article  ADS  MATH  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. Rulli, C. C., Sarandy, M. S.: Global quantum discord in multipartite systems. Phys. Rev. A. 84, 042109 (2011)

    Article  ADS  Google Scholar 

  25. Luo, S., Fu, S.: Geometric measure of quantum discord. Phys. Rev. A. 82, 034302 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  26. Radhakrishnan, C., Lauriére, M., Byrnes, T.: Multipartite generalization of quantum discord. Phys. Rev. Lett. 124, 110401 (2020)

  27. Luo, S.: Quantum discord for two-qubit systems. Phys. Rev. A. 77, 042303 (2008)

    Article  ADS  Google Scholar 

  28. 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)

    Article  ADS  Google Scholar 

  29. Lang, M.D., Caves, C.M.: Quantum Discord and the Geometry of Bell-Diagonal States. Phys. Rev. Lett. 105, 150501 (2010)

    Article  ADS  Google Scholar 

  30. Chen, Q., Zhang, C., Yu, S., et al.: Quantum discord of two-qubit \(X\) states. Phys. Rev. A. 84, 042313 (2011)

  31. Vinjanampathy, S., Rau, A.R.P.: Quantum discord for qubitCqudit systems. J. Phys. A: Math. Theor. 45, 095303 (2012)

    Article  ADS  MATH  Google Scholar 

  32. Bylicka, B., Chruściński, D.: Witnessing quantum discord in \(2 \times N\) systems. Phys. Rev. A 81, 062102 (2010)

  33. Karpat, G., Gedik, Z.: Invariant quantum discord in qubitCqutrit systems under local dephasing. Physica Scripta. T153, 014036 (2013)

    Article  ADS  Google Scholar 

  34. Ma, Z., Chen, Z., Fanchini, F.F., et al.: Quantum Discord for \(d\otimes 2\) Systems. Sci. Rep. 5, 10262 (2015)

  35. Shi, M., Yang, W., Jiang, F., et al.: Quantum discord of two-qubit rank-2 states. J Phys. A: Math. Theor. 44, 415304 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  36. Zenchuk, A.I.: Unitary invariant discord as a measures of bipartite quantum correlations in an N-qubit quantum system. Quantum Inf. Process. 11, 1551 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  37. Fanchini, F.F., Werlang, T., Brasil, C.A., et al.: Non-Markovian dynamics of quantum discord. Phys. Rev. A. 81, 052107 (2010)

    Article  ADS  Google Scholar 

  38. Jafarizadeh, M.A., Karimi, N., Zahir, H.: Quantum discord for generalized bloch sphere states. Eur. Phys. J. D. 68, 136 (2014)

    Article  ADS  Google Scholar 

  39. Jafarizadeh, M.A., Karimi, N., Amidi, D., et al.: Quantum Discord of 2-Dimensional Bell-Diagonal States. Int. J. Theor. Phys. 55, 1543 (2016)

    Article  MATH  Google Scholar 

  40. Slaoui, A., Daoud, M., Ahl, Laamara R.: The dynamic behaviors of local quantum uncertainty for three-qubit X states under decoherence channels. Quantum Inf. Process. 18, 250 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  41. Li, B., Zhu, C.L., Liang, X.B., et al.: Quantum discord for multiqubit systems. Phys. Rev. A. 104, 012428 (2021)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  43. Yu, T., Eberly, J.H.: Quantum Open System Theory: Bipartite Aspects. Phys. Rev. Lett. 97, 140403 (2006)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos.11771011,11775040,12011530014) and the Natural Science Foundation of Shanxi Province, China (Grant Nos.201801D221032, 201801D121016) and Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (Grant No. 2019L0178).

Author information

Authors and Affiliations

  1. College of Mathematics, Institute of Mathematics, Taiyuan University of Technology, 030024, Taiyuan, China

    Jia-Ning Wei, Zhou-Bo Duan & Jun Zhang

  2. College of Data Science, Taiyuan University of Technology, 030024, Taiyuan, China

    Jun Zhang

Authors
  1. Jia-Ning Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhou-Bo Duan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jun Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhou-Bo Duan.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wei, JN., Duan, ZB. & Zhang, J. Information-theoretical Discord for a Class of Three-qubit X States. Int J Theor Phys 61, 257 (2022). https://doi.org/10.1007/s10773-022-05240-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10773-022-05240-5

Keywords

Search

Navigation