Skip to main content
SpringerLink
Log in

Local Quantum Uncertainty for the Thermal State of a Four-Qubit Spin Chain under Decoherence Channels

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

Abstract

We consider a four-qubit Heisenberg XY spin chain with Dzyaloshinskii-Moriya interaction. We use the local quantum uncertainty as a measure of nonclassical correlations to evaluate the thermal quantum correlations between two spins which are located at both ends of the chain. Also we study the behavior of local quantum uncertainty under dephasing, depolarizing and phase flip channels. Here, we demonstrate the effects of temperature, Heisenberg exchange interaction, Dzyaloshinskii-Moriya interaction, and decoherence parameters on local quantum uncertainty, and provide a way to increase or maximize the quantum correlations. The exchange interaction and the Dzyaloshinskii-Moriya interaction have the same effect on local quantum uncertainty. The results are irrespective of whether the considered system is ferromagnetic or antiferromagnetic.

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
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Data Availability

All data generated or analyzed during this study are included in this paper.

References

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

    MATH  Google Scholar 

  2. Le Bellac, M.: A Short Introduction to Quantum Information and Quantum Computation. Cambridge University Press, Cambridge (2006)

    Book  MATH  Google Scholar 

  3. Bouwmeester, D., Pan, J.W., Mattle, K., Eibl, M., Weinfurter, H., Zeilinger, A.: Experimental quantum teleportation. Nature. 390, 6660 (1997)

    Article  MATH  Google Scholar 

  4. Braunstein, S.L., Kimble, H.J.: Teleportation of continuous quantum variables. Phys. Rev. Lett. 80, 869 (1998)

    Article  ADS  Google Scholar 

  5. Mattle, K., Weinfurter, H., Kwiat, P.G., Zeilinger, A.: Dense coding in experimental quantum communication. Phys. Rev. Lett. 76, 4656 (1996)

    Article  ADS  Google Scholar 

  6. Li, X., Pan, Q., Jing, J., Zhang, J., Xie, C., Peng, K.: Quantum dense coding exploiting a bright Einstein–Podolsky–Rosen beam. Phys. Rev. Lett. 88, 047904 (2002)

    Article  ADS  Google Scholar 

  7. Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661 (1991)

    Article  ADS  MATH  Google Scholar 

  8. Bennett, C.H.: Quantum cryptography using any two nonorthogonal states. Phys. Rev. Lett. 68, 557 (1992)

    Article  ADS  MATH  Google Scholar 

  9. Daoud, M., Ez-Zahraouy, H.: Three-dimensional quantum key distribution in the presence of several eavesdroppers. Phys. Scr. 84, 045018 (2011)

    Article  ADS  MATH  Google Scholar 

  10. 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 

  11. Datta, A., Vidal, G.: Role of entanglement and correlations in mixed-state quantum computation. Phys.Rev. A. 75, 042310 (2007)

    Article  ADS  Google Scholar 

  12. Ferraro, A., Aolita, L., Cavalcanti, D., Cucchietti, F.M., Acin, A.: Almost all quantum states have nonclassical correlations. Phys. Rev. A. 81, 052318 (2010)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  16. Datta, A.: Quantum discord between relatively accelerated observers. Phys. Rev. A. 80, 052304 (2009)

    Article  ADS  Google Scholar 

  17. Pirandola, S.: Quantum discord as a resource for quantum cryptography. Sci. Rep. 4, 6956 (2014)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  19. 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 

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

    Article  ADS  MATH  Google Scholar 

  21. Huang, Y.H.: Quantum discord for two-qubit X states: analytical formula with very small worst-case error. Phys. Rev. A. 88, 014302 (2013)

    Article  ADS  Google Scholar 

  22. Dakic, B., Vedral, V., Brukner, C.: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105, 190502 (2010)

    Article  ADS  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  24. Wigner, E.P., Yanase, M.M.: Information contents of distributions. Proc. Natl. Acad. Sci. U. S. A. 49, 910 (1963)

    Article  ADS  MATH  Google Scholar 

  25. 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  MATH  Google Scholar 

  26. Cordero, O., Villegas, A., Alvarez, J.R., Leon-Montiel, R.D., Passos, M.H., Torres, J.P.: Equivalence regimes for geometric quantum discord and local quantum uncertainty. Phys. Rev. A. 104, 042401 (2021)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  28. El Bakraoui, M., Slaoui, A., El Hadfi, H., Daoud, M.: Enhancing the estimation precision of an unknown phase shift in multipartite Glauber coherent states via skew information correlations and local quantum fisher information. J. Opt. Soc. Am. B. 39, 1297 (2022)

    Article  ADS  Google Scholar 

  29. Loss, D., Burkard, G., DiVincenzo, D.P.: Electron spins in quantum dots as quantum bits. J. Nanopart. Res. 2, 401 (2000)

    Article  ADS  Google Scholar 

  30. Divincenzo, D.P., Bacon, D., Kempe, J., Burkard, G., Whaley, K.B.: Universal quantum computation with the exchange interaction. Nature. 408, 339 (2000)

    Article  ADS  Google Scholar 

  31. Hu, X., de Sousa, R., Das Sarma, S.: Interplay between Zeeman coupling and swap action in spin-based quantum computer models: error correction in inhomogeneous magnetic fields. Phys. Rev. Lett. 86, 918 (2001)

    Article  ADS  Google Scholar 

  32. Bose, S.: Quantum communication through an unmodulated spin chain. Phys. Rev. Lett. 91, 207901 (2003)

    Article  ADS  Google Scholar 

  33. Tian, L.J., Yan, Y.Y., Qin, L.G.: Quantum correlation in three-qubit Heisenberg model with Dzyaloshinskii-Moriya interaction. Commun. Theor. Phys. 58, 39 (2012)

    Article  ADS  MATH  Google Scholar 

  34. Haseli, S.: Local quantum Fisher information and local quantum uncertainty in two-qubit Heisenberg XYZ chain with Dzyaloshinskii–Moriya interactions. arXiv:2005.00425v1 [quant-ph] (2020)

  35. Wen, S.J., Li, W.D., Hu, J.J., Ji, Y.H.: Influence of Dzyaloshinskii–Moriya interaction in the sinusoid magnetic field on the thermal quantum correlation of inhomogeneous Heisenberg spin chain. Optik. 125, 5785 (2014)

    Article  ADS  Google Scholar 

  36. Zhu, Y., Zhang, Y.: Quantum discord in the three-spin XXZ chain with Dzyaloshinskii-Moriya interaction. Sci. China-Phys. Mech. Astron. 55, 2081 (2012)

    Article  ADS  Google Scholar 

  37. Zhou, C.B., Xiao, S.Y., Zhang, X., Ran, Y.Q.: Effect of Dzyaloshinskii-Moriya interaction on thermal quantum correlation in a two-qubit Heisenberg XXZ model with an inhomogeneous external magnetic field. J. Supercond. Nov. Magn. 29, 367 (2016)

    Article  Google Scholar 

  38. Pourkarimi, M.R., Rahnama, M., Rooholamini, H.: Decoherence effect on quantum correlation and entanglement in a two-qubit spin chain. Int. J. Theor. Phys. 54, 1085 (2015)

    Article  MATH  Google Scholar 

  39. Pourkarimi, M.R.: The dynamics of quantum correlations in multi-qubit spin chains under the effect of Dzyaloshinskii-Moriya interaction. Int. J. Theor. Phys. 57, 1158 (2018)

    Article  MATH  Google Scholar 

  40. Dzyaloshinsky, I.: A thermodynamic theory of weak ferromagnetism of antiferromagnetics. J. Phys.Chem. Solids. 4, 241 (1958)

    Article  ADS  Google Scholar 

  41. Moriya, T.: New mechanism of anisotropic superexchange interaction. Phys. Rev. Lett. 4, 228 (1960)

    Article  ADS  Google Scholar 

  42. Luo, S.L.: Quantum versus classical uncertainty. Theor. Math. Phys. 143, 681 (2005)

    Article  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by the Department of Physics, University of Science, Pyongyang, DPR Korea.

Author information

Authors and Affiliations

  1. Department of Physics, University of Science, Pyongyang, Democratic People’s Republic of Korea

    Ryang Tae-Hung, Ri Nam-Ung, Ri Pyong, Sin Chang-Rim & Kim Jong-Yon

Authors
  1. Ryang Tae-Hung
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ri Nam-Ung
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ri Pyong
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Sin Chang-Rim
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Kim Jong-Yon
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to this paper.

- Kim Jong-Yon and Sin Chang-Rim proposed the idea in this paper and made the plan.

- Ryang Tae-Hung wrote this manuscript.

- Ri Nam-Ung calculated the local quantum uncertainty for the thermal state.

- Ri Pyong investigated the effects of different decoherence channels on quantum correlations.

All authors have been tested and approved the final manuscript.

Corresponding author

Correspondence to Ryang Tae-Hung.

Ethics declarations

Conflicts of Interest/Competing Interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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

Tae-Hung, R., Nam-Ung, R., Pyong, R. et al. Local Quantum Uncertainty for the Thermal State of a Four-Qubit Spin Chain under Decoherence Channels. Int J Theor Phys 62, 1 (2023). https://doi.org/10.1007/s10773-022-05233-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10773-022-05233-4

Keywords

Search

Navigation