Skip to main content
SpringerLink
Log in

Study on the correlation properties in the three-qubit spin chain of Heisenberg XYZ model

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

We study effects of magnetic field in z direction, spin–orbit interaction, coupling constant and temperature on correlations of a three-qubit Heisenberg XYZ system. We show that the magnetic field can reduce quantum correlations while spin–orbit interaction can increase them. Our findings show that quantum correlations can increase when the magnetic field and spin–orbit interaction are in the same direction. As the temperature increases, the death of bipartite negativity (N) and tripartite negativity (\(N^3\)) can occur. In some points, as temperature increases the local quantum uncertainty (LQ), the tripartite correlations (\(\tau \)) and \(N^3\) increase more than initial their values, which is interesting.

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

Similar content being viewed by others

Data availability

My manuscript has no associated data.

References

  1. Ollivier, H., Zurek, W.H.: Quantum discord, a measure of the quantumness of correlations. Phys. Rev. Lett. 88(1), 017901 (2001)

    Article  ADS  Google Scholar 

  2. Henderson, L., Vedral, V.: Classical, quantum and total correlations. J. Phys. A Math. Gen. 34(35), 6899 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  3. Ali, M., Rau, A.R.P., Alber, G.: Quantum discord for two-qubit X states. Phys. Rev. A 81(4), 042105 (2010)

    Article  ADS  Google Scholar 

  4. Modi, K., et al.: The classical-quantum boundary for correlations, discord and related measures. Rev. Mod. Phys. 84(4), 1655 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  5. Peres, A.: Separability criterion for density matrices. Phys. Rev. Lett. 77(8), 1413 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  6. Horodecki, R., et al.: Quantum entanglement. Rev. Mod. Phys. 81(2), 865 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  7. Vidal, G., Werner, R.F.: Computable measure of entanglement. Phys. Rev. A 65(3), 032314 (2002)

    Article  ADS  Google Scholar 

  8. Jaghouri, H., Sarbishaei, M., Javidan, K.: Thermal entanglement and lower bound of the geometric discord for a two-qutrit system with linear coupling and nonuniform external magnetic field. Quantum Inf. Process. 16, 1–12 (2017)

    Article  MathSciNet  Google Scholar 

  9. Jaghouri, H., et al.: Thermal quantum correlation and entanglement in the Bose-Hubbard Hamiltonian. Quantum Inf. Process. 17, 1–18 (2018)

    Article  MathSciNet  Google Scholar 

  10. Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80(10), 2245 (1998)

    Article  ADS  Google Scholar 

  11. Luo, S., Shuangshuang, F.: Measurement-induced nonlocality. Phys. Rev. Lett. 106(12), 120401 (2011)

    Article  ADS  Google Scholar 

  12. Lang, M.D., Caves, C.M.: Quantum discord and the geometry of Bell-diagonal states. Phys. Rev. Lett. 105(15), 150501 (2010)

    Article  ADS  Google Scholar 

  13. Chen, Q., et al.: Quantum discord of two-qubit X states. Phys. Rev. A 84(4), 042313 (2011)

    Article  ADS  Google Scholar 

  14. Girolami, D., Tufarelli, T., Adesso, G.: Characterizing nonclassical correlations via local quantum uncertainty. Phys. Rev. Lett. 110(24), 240402 (2013)

    Article  ADS  Google Scholar 

  15. Slaoui, A., et al.: A comparative study of local quantum Fisher information and local quantum uncertainty in Heisenberg XY model. Phys. Lett. A 383(19), 2241–2247 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  16. Ali, M.: Local quantum uncertainty for multipartite quantum systems. Eur. Phys. J. D 74(9), 1–6 (2020)

    Article  ADS  Google Scholar 

  17. Slaoui, A., Daoud, M., Laamara, R.A.: The dynamic behaviors of local quantum uncertainty for three-qubit X states under decoherence channels. Quantum Inf. Process. 18(8), 1–29 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  18. Beggi, A., Buscemi, F., Bordone, P.: Analytical expression of genuine tripartite quantum discord for symmetrical X-states. Quantum Inf. Process. 14(2), 573–592 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  19. Giorgi, G.L., et al.: Genuine quantum and classical correlations in multipartite systems. Phys. Rev. Lett. 107(19), 190501 (2011)

    Article  ADS  Google Scholar 

  20. Maziero, J., Zimmer, F.M.: Genuine multipartite system-environment correlations in decoherent dynamics. Phys. Rev. A 86(4), 042121 (2012)

    Article  ADS  Google Scholar 

  21. Bennett, C.H., et al.: Postulates for measures of genuine multipartite correlations. Phys. Rev. A 83(1), 012312 (2011)

    Article  ADS  Google Scholar 

  22. Kane, B.E.: A silicon-based nuclear spin quantum computer. Nature 393(6681), 133–137 (1998)

    Article  ADS  Google Scholar 

  23. Burkard, G., Loss, D., DiVincenzo, D.P.: Coupled quantum dots as quantum gates. Phys. Rev. B 59(3), 2070 (1999)

    Article  ADS  Google Scholar 

  24. Trauzettel, B., et al.: Spin qubits in graphene quantum dots. Nat. Phys. 33, 192–196 (2007)

    Article  Google Scholar 

  25. Khedr, A.N., et al.: Robust thermal quantum correlations induced by spin-orbit interactions. Results Phys. 66, 105–619 (2022)

    Google Scholar 

  26. Ju, F.-H., Zhang, Z.-Y., Liu, J.-M.: Entropic uncertainty relation of a qubit-qutrit Heisenberg spin model and its steering. Commun. Theor. Phys. 72(12), 125102 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  27. Ait Chlih, A., Habiballah, N., Nassik, M.: Dynamics of quantum correlations under intrinsic decoherence in a Heisenberg spin chain model with Dzyaloshinskii-Moriya interaction. Quantum Inf. Process. 20(3), 1–14 (2021)

    Article  MathSciNet  Google Scholar 

  28. Benabdallah, F., et al.: Thermal non-classical correlation via skew information, quantum Fisher information, and quantum teleportation of a spin-\(\frac{1}{2}\) Heisenberg trimer system. Eur. Phys. J. Plus 137(9), 1–18 (2022)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Physics Department, Faculty of Science, Shahid Chamran University of Ahvaz, Ahvaz, Iran

    Hakimeh Jaghouri

Authors
  1. Hakimeh Jaghouri
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hakimeh Jaghouri.

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

Jaghouri, H. Study on the correlation properties in the three-qubit spin chain of Heisenberg XYZ model. Quantum Inf Process 23, 22 (2024). https://doi.org/10.1007/s11128-023-04224-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-023-04224-6

Keywords

Search

Navigation