Skip to main content
SpringerLink
Log in

Pairwise Quantum Discord for a Symmetric Multi-Qubit System in Different Types of Noisy Channels

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

Abstract

We study the pairwise quantum discord (QD) for a symmetric multi-qubit system in different types of noisy channels, such as phase-flip, amplitude damping, phase-damping, and depolarizing channels. Using the QD and geometric quantum discord (GMQD) to quantify quantum correlations, some analytical and numerical results are presented. The results show that, the QD dynamics is strongly related to the number of spin particles N as well as the initial parameter 𝜃 of the one-axis twisting collective state. With the number of spin particles N increasing, the amount of the QD increases. However, when the amount of the QD arrives at a stable maximal value, the QD is independence of the number of spin particles N increasing. The behavior of the QD is symmetrical during a period 0 ≤ 𝜃 ≤ 2π. Moreover, we compare the QD dynamics with the GMQD for a symmetric multi-qubit system in different types of noisy channels.

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
Fig. 3

Similar content being viewed by others

References

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

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

    Article  MathSciNet  MATH  ADS  Google Scholar 

  3. Ollivier, H., Zurek, W.H.: Quantum discord: A measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)

    Article  MATH  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  5. Werlang, T., Souza, S., Fanchini, F.F., Villas Boas, C.J.: Robustness of quantum discord to sudden death. Phys. Rev. A 80, 024103 (2009)

    Article  ADS  Google Scholar 

  6. Xi, Z.J., Lu, X.M., Wang, X.G., Li, Y.M.: Necessary and sufficient condition for saturating the upper bound of quantum discord. Phys. Rev. A 85, 032109 (2012)

    Article  ADS  Google Scholar 

  7. Brodutch, A.: Discord and quantum computational resources. Phys. Rev. A 88, 022307 (2013)

    Article  ADS  Google Scholar 

  8. Yao, J.Y., Dong, Y.L., Zhu, S.Q.: Quantum discord of non-X State. Commun. Theor. Phys. 59, 693–699 (2013)

    Article  MathSciNet  ADS  Google Scholar 

  9. Daoud, M., Ahl Laamara, R.: Quantum discord of Bell cat states under amplitude damping. J. Phys. A: Math. Theor. 45, 325302 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  10. Wu, X.H., Zhou, T.: Quantum discord for the general two-qubit case. Quantum Inf. Pro. doi:10.1007/s11128-015-0962-8 (2015)

  11. Modi, K., Brodutch, A., Cable, H., Paterek, T., Vedral, V.: The classical-quantum boundary for correlations: Discord and related measures. Rev. Mod. Phys. 84, 1655 (2012)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  13. Céleri, L.C., Maziero, J., Serra, R.M.: Theoretical and experimental aspects of quantum discord and related measure. Int. J. Quantum Inform. 9, 1837 (2011)

    Article  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  15. Tanaś: Quantum discord: Evolution of quantum correlations in a two-atom system. Phys. Scr. T. 153, 014059 (2013)

    ADS  Google Scholar 

  16. Luo, S.L.: Quantum discord for two-qubit systemst. Phys. Rev. A 77, 042303 (2008)

    Article  ADS  Google Scholar 

  17. Fanchini, F.F., Werlang, T., Brasil, C.A., Arruda, L.G.E., Caldeira, A.O.: Non-Markovian dynamics of quantum discord. Phys. Rev. A 81, 052107 (2010)

    Article  ADS  Google Scholar 

  18. Galve, F., Giorgi, G.L., Zambrini, R.: Maximally discordant mixed states of two qubits. Phys. Rev. A 83, 012102 (2011)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  20. Chen, Q., Zhang, C.J., Yu, S.X., Yi, X.X., Oh, C.H.: Quantum discord of two-qubit X states. Phys. Rev. A 84, 042313 (2011)

    Article  ADS  Google Scholar 

  21. 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 

  22. Wang, C.Z., Li, C.X., Nie, L.Y, Li, J.F.: Classical correlation and quantum discord mediated by cavity in two coupled qubits. J.Phys. B: At. Mol. Opt. Phys. 44, 015503 (2011)

    Article  ADS  Google Scholar 

  23. DakiĆ, B., Vedral, V., Brukner, C̆̆.: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105 (2010)

  24. Amesen, M.C., Bose, S., Vedral, V.: Natural thermal and magnetic entanglement in the 1D Heisenberg model. Phys. Rev. Lett. 87, 017901 (2001)

    Article  ADS  Google Scholar 

  25. Wang, X.G.: Entanglement in the quantum Heisenberg XY model. Phys. Rev. A 64, 012313 (2001)

    Article  ADS  Google Scholar 

  26. Diósi, L.: Three-party pure quantum states are determined by two two-party reduced states. Phys. Rev. A 70, 010302 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  27. Jones, N.S., Linden, N.: Parts of quantum states. Phys. Rev. A 71, 012324 (2005)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  28. Zhou, D.L.: Irreducible multiparty correlations in quantum states without maximal rank. Phys. Rev. Lett. 101, 180505 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  29. Wang, X.G., Sander, B.C.: Spin squeezing and pairwise entanglement for symmetric multiqubit states. Phys. Rev. A 68, 012101 (2003)

    Article  ADS  Google Scholar 

  30. Wang, X.G., Mølmer, K.: Pairwise entanglement in symmetric multi-qubit systems. Eur. Phys. J. D 18, 385–391 (2002)

    ADS  Google Scholar 

  31. Yin, X.L., Xi, Z.J., Lu, X.M., Sun, Z., Wang, X.G.: Geometric measure of quantum discord for superpositions of Dicke states. J. Phys. B: Mol. Opt. Phys. 44, 245502 (2011)

    Article  ADS  Google Scholar 

  32. Xi, Z.J., Xiong, H.N., Li, Y.M., Wang, X.G.: Pairwise quantum correlations for superpositions of dicke states. Commun. Theor. Phys. 57, 771–779 (2012)

    Article  MATH  ADS  Google Scholar 

  33. Ramzan, M.: Decoherence dynamics of discord for multipartite quantum systems. Eur. Phys. J. D 67, 170 (2013)

    Article  ADS  Google Scholar 

  34. Kitagawa, M., Ueda, M.: Sgueezed spin states. Phys. Rev. A 47, 5138 (1993)

    Article  ADS  Google Scholar 

  35. Vidal, J.: Concurrence in collective models. Phys. Rev. A 73, 062318 (2006)

    Article  ADS  Google Scholar 

  36. Yin, X.L., Wang, X.Q., Ma, J., Wang, X.G.: Spin squeezing and concurrence. J. Phys. B: Mol. Opt. Phys. 44, 015501 (2011)

    Article  ADS  Google Scholar 

  37. Yin, X.L., Ma, J., Wang, X.G., Nori, F.: Spin squeezing under non-Markovian channels by Hierarchy equation method. Phys. Rev. A 86, 012308 (2012)

    Article  ADS  Google Scholar 

  38. Wang, X.Q., Ma, J., Song, L.J., Zhang, X.H., Wang, X.G.: Spin squeezing, negative correlations, and concurrence in the quantum kicked top model. Phys. Rev. E 82, 056205 (2010)

    Article  ADS  Google Scholar 

  39. Zhong, W., Liu, J., Ma, J., Wang, X.G.: Quantum Fisher information and spin squeezing in one-axis twisting model. Chin. Phys. B 23, 060302 (2014)

    Article  ADS  Google Scholar 

  40. Wang, X.G., Miranowicz, A., Liu, Y.X., Sun, C.P., Nori, F.: Sudden vanishing of spin squeezing under decoherence. Phys. Rev. A 81, 022106 (2010)

    Article  ADS  Google Scholar 

  41. Piani, M.: Problem with geometric discord. Phys. Rev. A 86, 034101 (2012)

    Article  ADS  Google Scholar 

  42. Xu, Z.Y., Yang, W.L., Xiao, X., Feng, M.: Comparison of different measures for quantum discord under non-Markovian noise. J. Phys. A: Math. Theor. 44, 395304 (2011)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

This work is supported by Hunan Provincial Innovation Foundation for Postgraduate (No. CX2014B194) and Scientific Research Foundation of Hunan Provincial Education Department No. 13C039).

Author information

Authors and Affiliations

  1. Department of Electronic and Communication Engineering, Changsha University, Changsha, Hunan, 410022, People’s Republic of China

    You-Neng Guo & Ke Zeng

  2. College of Science, Hunan University of Technology, Zhuzhou, 412008, People’s Republic of China

    Guo-You Wang

Authors
  1. You-Neng Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ke Zeng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Guo-You Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ke Zeng.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Guo, YN., Zeng, K. & Wang, GY. Pairwise Quantum Discord for a Symmetric Multi-Qubit System in Different Types of Noisy Channels. Int J Theor Phys 55, 2894–2903 (2016). https://doi.org/10.1007/s10773-016-2920-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-016-2920-3

Keywords

Search

Navigation