Skip to main content

Advertisement

Springer Nature Link
Log in

Dynamics of quantum correlations under intrinsic decoherence in a Heisenberg spin chain model with Dzyaloshinskii–Moriya interaction

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

By taking into account the effect of intrinsic decoherence and by using Milburn’s dynamical master equation, we study the temporal evolution of quantum correlations in a two-qubit XXZ Heisenberg spin chain model with Dzyaloshinskii–Moriya (DM) interaction and an external nonuniform magnetic field both directed along the z-axis. We use the concurrence (C) to detect entanglement and the local quantum uncertainty (LQU) to measure discord-like correlations. We consider three cases of initial quantum states: the mixed state, the Werner state and the pure state. For the mixed initial state and the Werner initial state, our results show that the external magnetic field strongly stimulates the effect of intrinsic decoherence which can highlight the entanglement sudden death phenomenon, while the LQU is resistant to sudden death. In addition, the DM interaction makes the effect of intrinsic decoherence more pronounced. However, a weak DM interaction can markedly improve quantum correlations and thus cause the phenomenon of entanglement sudden revival. On the other hand, and especially for the initial “uncorrelated” state (in terms of entanglement and LQU) with a zero nonuniform magnetic field and no DM interaction, it is easier to generate a strong entanglement, but it is difficult to generate LQU. Finally, we have found that when the system is initially “uncorrelated,” the nonuniform magnetic field can make the system strongly correlated for very remarkable steady-state values (in particular entanglement). Other results will also be discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47(10), 777 (1935)

    Article  ADS  MATH  Google Scholar 

  2. Bohr, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 48(8), 696 (1935)

    Article  ADS  MATH  Google Scholar 

  3. Bennett, C.H., DiVincenzo, D.P.: Quantum information and computation. Nature 404(6775), 247–255 (2000)

    Article  ADS  MATH  Google Scholar 

  4. Nielsen, M.A., Chuang, I.: Quantum computation and quantum information (2002)

  5. Wilde, M.M.: Quantum Information Theory. Cambridge University Press, Cambridge (2013)

    Book  MATH  Google Scholar 

  6. Lanyon, B., Barbieri, M., Almeida, M., White, A.: Experimental quantum computing without entanglement. Phys. Rev. Lett. 101(20), 200501 (2008)

    Article  ADS  Google Scholar 

  7. Datta, A., Vidal, G.: Role of entanglement and correlations in mixed-state quantum computation. Phys. Rev. A 75(4), 042310 (2007)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. Huang, Y.: Computing quantum discord is np-complete. New J. Phys. 16(3), 033027 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. Dakić, B., Vedral, V., Brukner, C.: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105(19), 190502 (2010)

    Article  ADS  MATH  Google Scholar 

  12. Piani, M.: Problem with geometric discord. Phys. Rev. A 86(3), 034101 (2012)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  14. Wigner, E.P., Yanase, M.M.: Information contents of distributions. In: Part I: Particles and Fields. Part II: Foundations of Quantum Mechanics, pp. 452–460. Springer (1997)

  15. Paris, M.G.: Quantum estimation for quantum technology. Int. J. Quant. Inf. 7(supp01), 125–137 (2009)

    Article  MATH  Google Scholar 

  16. Jebli, L., Benzimoun, B., Daoud, M.: Quantum correlations for two-qubit x states through the local quantum uncertainty. Int. J. Quant. Inf. 15(03), 1750020 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  17. 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(01), 1750001 (2017)

    Article  MATH  Google Scholar 

  18. 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(20), 1850218 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. Zurek, W.H.: Decoherence, einselection, and the quantum origins of the classical. Rev. Mod. Phys. 75(3), 715 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. Schlosshauer, M.A.: Decoherence and the Quantum-to-Classical Transition. Springer, New York (2007)

    Google Scholar 

  21. Zurek, W.H.: From quantum to classical. Phys. Today 37 (1991)

  22. Davies, E.B.: Quantum Theory of Open Systems. Academic Press, Cambridge (1976)

    MATH  Google Scholar 

  23. Breuer, H.-P., Petruccione, F., et al.: The Theory of Open Quantum Systems. Oxford University Press, Oxford (2002)

    MATH  Google Scholar 

  24. Moya-Cessa, H., Bužek, V., Kim, M., Knight, P.: Intrinsic decoherence in the atom-field interaction. Phys. Rev. A 48(5), 3900 (1993)

    Article  ADS  Google Scholar 

  25. Milburn, G.: Intrinsic decoherence in quantum mechanics. Phys. Rev. A 44(9), 5401 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  26. Zhang, G.-F.: Thermal entanglement and teleportation in a two-qubit heisenberg chain with Dzyaloshinski–Moriya anisotropic antisymmetric interaction. Phys. Rev. A 75(3), 034304 (2007)

    Article  ADS  Google Scholar 

  27. Habiballah, N., Khedif, Y., Daoud, M.: Local quantum uncertainty in xyz heisenberg spin models with Dzyaloshinski–Moriya interaction. Eur. Phys. J. D 72(9), 154 (2018)

    Article  ADS  Google Scholar 

  28. Zhang, Y., Zhou, Q., Xu, H., Fang, M.: Quantum-memory-assisted entropic uncertainty in two-qubit heisenberg xx spin chain model. Int. J. Theor. Phys. 58(12), 4194–4207 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  29. Dzyaloshinsky, I.: A thermodynamic theory of weak ferromagnetism of antiferromagnetics. J. Phys. Chem. Solids 4(4), 241–255 (1958)

    Article  ADS  Google Scholar 

  30. Moriya, T.: Anisotropic superexchange interaction and weak ferromagnetism. Phys. Rev. 120(1), 91 (1960)

    Article  ADS  Google Scholar 

  31. Li, D.-C., Wang, X.-P., Cao, Z.-L.: Thermal entanglement in the anisotropic Heisenberg xxz model with the Dzyaloshinskii–Moriya interaction. J. Phys. Condens. Matter 20(32), 325229 (2008)

    Article  Google Scholar 

  32. Yi-Xin, C., Zhi, Y.: Thermal quantum discord in anisotropic Heisenberg xxz model with Dzyaloshinskii–Moriya interaction. Commun. Theor. Phys. 54(1), 60 (2010)

    Article  ADS  MATH  Google Scholar 

  33. Lin-Cheng, W., Jun-Yan, Y., Xue-Xi, Y.: Thermal quantum discord in Heisenberg models with Dzyaloshinskii–Moriya interaction. Chin. Phys. B 20(4), 040305 (2011)

    Article  Google Scholar 

  34. Gong, J.-M., Tang, Q., Sun, Y.-H., Qiao, L.: Enhancing the geometric quantum discord in the Heisenberg xx chain by Dzyaloshinsky–Moriya interaction. Physica B 461, 70–74 (2015)

    Article  ADS  Google Scholar 

  35. Soltani, M., Vahedi, J., Mahdavifar, S.: Quantum correlations in the 1d spin-1/2 ising model with added Dzyaloshinskii–Moriya interaction. Physica A 416, 321–330 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  36. Mohammadi, H., Akhtarshenas, S.J., Kheirandish, F.: Influence of dephasing on the entanglement teleportation via a two-qubit Heisenberg xyz system. Eur. Phys. J. D 62(3), 439–447 (2011)

    Article  ADS  Google Scholar 

  37. Mamtimin, T., Ahmad, A., Rabigul, M., Ablimit, A., Pan-Pan, Q.: Various correlations in the anisotropic Heisenberg xyz model with Dzyaloshinskii–Moriya interaction. Chin. Phys. Lett. 30(3), 030303 (2013)

    Article  Google Scholar 

  38. Cheng-Gao, S., Guo-Feng, Z., Kai-Ming, F., Han-Jie, Z.: Measurement-induced disturbance in Heisenberg xy spin model with Dzialoshinskii–Moriya interaction under intrinsic decoherence. Chin. Phys. B 23(5), 050310 (2014)

    Article  Google Scholar 

  39. Zhang, Y., Zhou, Q., Fang, M., Kang, G., Li, X.: Quantum-memory-assisted entropic uncertainty in two-qubit Heisenberg xyz chain with Dzyaloshinskii–Moriya interactions and effects of intrinsic decoherence. Quantum Inf. Process. 17(12), 326 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  40. Guo, J.-L., Song, H.-S.: Effects of inhomogeneous magnetic field on entanglement and teleportation in a two-qubit Heisenberg xxz chain with intrinsic decoherence. Phys. Scr. 78(4), 045002 (2008)

    Article  ADS  MATH  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  42. Luo, S.: Wigner–Yanase skew information and uncertainty relations. Phys. Rev. Lett. 91(18), 180403 (2003)

    Article  ADS  Google Scholar 

  43. Werner, R.F.: Quantum states with Einstein–Podolsky–Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40(8), 4277 (1989)

    Article  ADS  MATH  Google Scholar 

  44. Mani, A., Karimipour, V., Memarzadeh, L.: Comparison of parallel and antiparallel two-qubit mixed states. Phys. Rev. A 91, 012304 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  45. Bin, S., Tian-Hai, Z., Jian, Z.: Influence of intrinsic decoherence on entanglement in two-qubit quantum Heisenberg xyz chain. Commun. Theor. Phys. 44(2), 255 (2005)

    Article  Google Scholar 

  46. Chuan-Jia, S., Wei-Wen, C., Tang-Kun, L., Ji-Bing, L., Hua, W.: Sudden death, birth and stable entanglement in a two-qubit Heisenberg xy spin chain. Chin. Phys. Lett. 25(9), 3115 (2008)

    Article  ADS  Google Scholar 

  47. Chuan-Jia, S., Tao, C., Ji-Bing, L., Wei-Wen, C., Tang-Kun, L., Yan-Xia, H., Hong, L.: Sudden birth versus sudden death of entanglement for the extended Werner-like state in a dissipative environment. Chin. Phys. B 19(6), 060303 (2010)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. EPTHE, Department of Physics, Faculty of Sciences, Ibn Zohr University, Agadir, Morocco

    Anas Ait Chlih, Nabil Habiballah & Mostafa Nassik

  2. Faculty of Applied Sciences, Ibn Zohr University, Ait-Melloul, Morocco

    Nabil Habiballah

  3. Abdus Salam International Centre for Theoretical Physics, Strada Costiera, 11, 34151, Trieste, Italy

    Nabil Habiballah

Authors
  1. Anas Ait Chlih
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nabil Habiballah
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mostafa Nassik
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anas Ait Chlih.

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

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, 92 (2021). https://doi.org/10.1007/s11128-021-03030-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-021-03030-2

Keywords

Search

Navigation