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Quantum correlation dynamics of a three-qubit XXZ spin chain with spin–orbit coupling in the presence of intrinsic decoherence

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Abstract

We study on the quantum correlation dynamics of a three-qubit Heisenberg XXZ spin chain with spin–orbit coupling under the intrinsic decoherence. Mixed Werner state is assumed to be an initial state and the system evolves according to the exact Milburn’s equation, not to the approximate one. The time evolution of the density matrix is calculated accurately, based on a new method other than the ones used in previous studies which studied intrinsic decoherence in two-qubit systems. We use the concurrence and quantum discord as computational measures to investigate the effects of various parameters on quantum correlations. It is shown that quantum correlation characteristics are irrespective of whether the system is ferromagnetic or antiferromagnetic. In contrast to Dzyaloshinskii–Moriya interaction, Kaplan–Shekhtman–Entin-Wohlman–Aharony interaction can be used to modify the frequency of quantum correlations. In general, under the intrinsic decoherence, quantum discord is more robust than entanglement, but it is possible to manipulate the anisotropic parameter to overcome decoherence and maintain the entanglement stably.

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References

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

    MATH  Google Scholar 

  2. 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 

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

    Article  ADS  MathSciNet  Google Scholar 

  4. 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 

  5. 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 

  6. 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 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  9. Paula, F.M., de Oliveira, T.R., Sarandy, M.S.: Geometric quantum discord through the Schatten 1-norm. Phys. Rev. A 87, 064101 (2013)

    Article  ADS  Google Scholar 

  10. Bakry, H., Mohamed, A.S.A., Zidan, N.: Properties of two two-level atoms interacting with intensity-dependent coupling. Int. J. Theor. Phys. 57, 539–548 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  11. Zidan, N.: Entanglement and quantum discord of two moving atoms. Appl. Math. 05, 16 (2014)

    Article  Google Scholar 

  12. Jiang, T.Y., Fang, Y.Y., Li, Y.H., Xu, X.Y., Liu, J.M.: Dynamics of quantum correlation and entropic uncertainty in spin- $\frac{1}{2}$ alternating transverse Ising model. Ann. Phys. 534, 2100352 (2022)

    Article  MathSciNet  Google Scholar 

  13. 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 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  17. Kaplan, T.A.: Single-band Habbard model with spin-orbit coupling. Z. Phys. B Condens. Matter 49, 313 (1983)

    Article  ADS  Google Scholar 

  18. Shekhtman, L., Entin-Wohlman, O., Aharony, A.: Moriya’s anisotropic superexchange interaction, frustration, and Dzyaloshinsky’s weak ferromagnetism. Phys. Rev. Lett. 69, 836 (1992)

    Article  ADS  Google Scholar 

  19. Shekhtman, L., Entin-Wohlman, O., Aharony, A.: Bond-dependent symmetric and antisymmetric superexchange interactions in La2CuO4. Phys. Rev. B 47, 174 (1993)

    Article  ADS  Google Scholar 

  20. Zheludev, A., Maslov, S., Tsukada, I., Zaliznyak, I., Regnault, L.P., Masuda, T., Uchinokura, K., Erwin, R., Shirane, G.: Experimental evidence for Kaplan-Shekhtman–Entin-Wohlman–Aharony interactions in Ba2CuGe2O7. Phys. Rev. Lett. 81, 5410 (1998)

    Article  ADS  Google Scholar 

  21. Zidan, N.: Quantum discord of a two-qubit anisotropy XXZ Heisenberg chain with Dzyaloshinskii-Moriya interaction. J. Quantum Inf. Sci. 04, 02 (2014)

    Google Scholar 

  22. Xiong, S., Sun, Z., Liu, J.M.: Entropic uncertainty relation and quantum phase transition in spin-1/2 Heisenberg chain. Laser Phys. Lett. 17, 095203 (2020)

    Article  ADS  Google Scholar 

  23. 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, 125102 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  24. Yurischev, M.A.: On the quantum correlations in two-qubit XYZ spin chains with Dzyaloshinsky-Moriya and Kaplan–Shekhtman–Entin-Wohlman–Aharony interactions. Quantum Inf. Process. 19, 336 (2020)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. Khedif, Y., Haddadi, S., Pourkarimi, M.R., Daoud, M.: Thermal correlations and entropic uncertainty in a two-spin system under DM and KSEA interactions. Mod. Phys. Lett. A 36, 2150209 (2021)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  26. El Aroui, A., Khedif, Y., Habiballah, N., Nassik, M.: Characterizing the thermal quantum correlations in a two-qubit Heisenberg XXZ spin-1/2 chain under Dzyaloshinskii-Moriya and Kaplan–Shekhtman–Entin–Wohlman–Aharony interactions. Opt. Quant. Electron. 54, 694 (2022)

    Article  Google Scholar 

  27. Mohamed, A.B.A., Khedr, A.N., Haddadi, S., Ur Rahman, A., Tammam, M., Pourkarimi, M.R.: Intrinsic decoherence effects on nonclassical correlations in a symmetric spin–orbit model. Results Phys. 39, 105693 (2022)

    Article  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  29. He, Z., Xiong, Z., Zhang, Y.: Influence of intrinsic decoherence on quantum teleportation via two-qubit Heisenberg XYZ chain. Phys. Lett. A 354, 79 (2006)

    Article  ADS  Google Scholar 

  30. Yu, P.F., Cai, J.G., Liu, J.M., Shen, G.T.: Effects of phase decoherence on the entanglement of a two-qubit anisotropic Heisenberg XYZ chain with an in-plane magnetic field. Eur. Phys. J. D 44, 151 (2007)

    Article  ADS  Google Scholar 

  31. Zidan, N.: Dynamics of correlations in the presences of intrinsic decoherence. Int. J. Theor. Phys. 55, 1274 (2016)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  33. Bužek, V., Konopka, M.: Dynamics of open systems governed by the Milburn equation. Physical Review A 58(3), 1735 (1998)

    Article  ADS  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  36. Yu, T., Eberly, J.H.: Evolution from entanglement to decoherence of bipartite mixed “X” states. Quantum Inf. Comput. 7, 459 (2007)

    MathSciNet  MATH  Google Scholar 

  37. 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 

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Acknowledgements

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

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Authors and Affiliations

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

    Tae-Hung Ryang, Yong-Hyon Choe, Se-Jong Ryo & Jong-Yon Kim

  2. Science Library, University of Science, Pyongyang, Democratic People’s Republic of Korea

    Yong-Gil Kim

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  1. Tae-Hung Ryang
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  2. Yong-Hyon Choe
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  3. Yong-Gil Kim
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  4. Se-Jong Ryo
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  5. Jong-Yon Kim
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Contributions

J-YK and S-JR proposed the idea in this paper and made the plan. T-HR wrote this manuscript. Y-HC calculated the state evolution of the system under the intrinsic decoherence. Y-GK investigated the effects of several parameters on quantum correlations. All authors have been tested and approved the final manuscript.

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Correspondence to Tae-Hung Ryang.

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Ryang, TH., Choe, YH., Kim, YG. et al. Quantum correlation dynamics of a three-qubit XXZ spin chain with spin–orbit coupling in the presence of intrinsic decoherence. Quantum Inf Process 22, 319 (2023). https://doi.org/10.1007/s11128-023-04055-5

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