Skip to main content
Log in

Quantum discord in the three-spin XXZ chain with Dzyaloshinskii-Moriya interaction

  • Article
  • Published:
Science China Physics, Mechanics and Astronomy Aims and scope Submit manuscript

Abstract

The quantum discord (QD) of a three-qubit Heisenberg XXZ system with the Dzyaloshinskii-Moriya (DM) interaction parameter is investigated, and the three-qubit QD under Ornstein-Uhlenbeck noise is calculated. We find that both DM interaction parameter D z and anisotropic parameter J z can increase QD and entanglement but D z is a more efficient parameter in the antiferromagnetic case. We observe a complex range of QD with the change of D z and a sudden change of QD with the variation of J z in the ferromagnetic case. We show that the decrease durations of both QD and entanglement can be prolonged by increasing DM interaction and reducing noise bandwidth γ in the evolutionary process.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

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

    Google Scholar 

  2. Bouwmeester D, Pan J W, Mattle K, et al. Experimental quantum teleportation. Nature, 1997, 390: 575–579

    Article  ADS  Google Scholar 

  3. Mattle K, Weinfurter H, Kwiat P G, et al. Dense coding in experimental quantum communication. Phys Rev Lett, 1996, 76: 4656–4659

    Article  ADS  Google Scholar 

  4. Gisin N, Ribordy G, Tittel W, et al. Quantum cryptography. Rev Mod Phys, 2002, 74: 145–195

    Article  ADS  Google Scholar 

  5. Lanyon B P, Barbieri M, Almeida M P, et al. Experimental quantum computing without entanglement. Phys Rev Lett, 2008, 101: 200501

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  7. Werlang T, Souza S, Fanchini F F, et al. Robustness of quantum discord to sudden death. Phys Rev A, 2009, 80: 024103

    Article  ADS  Google Scholar 

  8. Zhou T, Cui J X, Long G L. Measure of nonclassical correlation in coherence-vector representation. Phys Rev A, 2011, 84: 062105

    Article  ADS  Google Scholar 

  9. Sarandy M S. Classical correlation and quantum discord in critical systems. Phys Rev A, 2009, 80: 022108

    Article  ADS  Google Scholar 

  10. Maziero J, Guzman H C, Sarandy M S, et al. Quantum and classical thermal correlations in the XY spin-1/2 chain. Phys Rev A, 2010, 82: 012106

    Article  ADS  Google Scholar 

  11. Fanchini F F, Werlang T, Brasil C A, et al. Non-Markovian dynamics of quantum discord. Phys Rev A, 2010, 81: 052107

    Article  ADS  Google Scholar 

  12. Fanchini F F, Castelano L K, Caldeira A O. Entanglement versus quantum discord in two coupled double quantum dots. New J Phys, 2010, 12: 073009

    Article  Google Scholar 

  13. Brádler K, Wilde M M, Uskov D B, et al. Identifying the quantum correlations in light-harvesting complexes. Phys Rev A, 2010, 82: 062310

    Article  ADS  Google Scholar 

  14. Liu B Q, Shao B, Li J G, et al. Quantum and classical correlations in the one-dimensional XY model with Dzyaloshinskii-Moriya interaction. Phys Rev A, 2011, 83: 052112

    Article  ADS  Google Scholar 

  15. Liu B Q, Shao B, Zou J. Quantum discord for a central two-qubit system coupled to an XY-spin-chain environment. Phys Rev A, 2010, 82: 062119

    Article  ADS  Google Scholar 

  16. Li Y C, Lin H Q. Thermal quantum and classical correlations and entanglement in the XY spin model with three-spin interaction. Phys Rev A, 2011, 83: 052323

    Article  ADS  Google Scholar 

  17. Dzyaloshinsky I. A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics. J Phys Chem Solids, 1958, 4: 241–255

    Article  ADS  Google Scholar 

  18. Moriya T. Anisotropic superexchange interaction and weak ferromagnetism. Phys Rev, 1960, 120: 91–98

    Article  ADS  Google Scholar 

  19. Kheirandish F, Akhtarshenas S J, Mohammadi H. Effect of spin-orbit interaction on entanglement of two-qubit Heisenberg XYZ systems in an inhomogeneous magnetic field. Phys Rev A, 2008, 77: 042309

    Article  ADS  Google Scholar 

  20. Ma X S, Wang A M. Bell violation for the thermal states of an XXZ spin chain with Dzyaloshinskii-Moriya interaction. Sci China-Phys Mech Astron, 2010, 53: 2074–2079

    Article  ADS  Google Scholar 

  21. Yu T, Eberly J H. Entanglement evolution in a non-Markovian environment. Opt Commun, 2010, 283: 676–680

    Article  ADS  Google Scholar 

  22. Luo S L. Quantum discord for two-qubit systems. Phys Rev A, 2008, 77: 042303

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  24. Wootters W K. Entanglement of formation of an arbitrary state of two qubits. Phys Rev Lett, 1998, 80: 2245–2248

    Article  ADS  Google Scholar 

  25. Guo K T, Liang M C, Xu H Y, et al. Entanglement in a two-spin (1/2, 3/2) mixed-spin Heisenberg XX chain with an inhomogeneous external magnetic field. Sci China-Phys Mech Astron, 2011, 54: 491–495

    Article  ADS  Google Scholar 

  26. Li J T, Yi Y Y, Li G Q. Quantum correlation in three-qubit Heisenberg model with Dzyaloshinskii-Moriya interaction. arXiv:quant-ph1104.1525v2

  27. Werlang T, Rigolin G. Thermal and magnetic quantum discord in Heisenberg models. Phys Rev A, 2010, 81: 044101

    Article  ADS  Google Scholar 

  28. Dakić B, Vedral V, Brukner Č. Necessary and sufficient condition for nonzero quantum discord. Phys Rev Lett, 2010, 105: 190502

    Article  ADS  Google Scholar 

  29. Henderson L, Vedral V. Classical, quantum and total correlations. J Phys A-Math Gen, 2001, 34: 6899–6906

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. Altintas F, Eryigit R. Quantum correlations in non-Markovian environments. Phys Lett A, 2010, 374: 4283–4296

    Article  MathSciNet  ADS  MATH  Google Scholar 

  31. Xiao X, Fang M F, Li Y L, et al. Quantum discord in non-Markovian environments. Opt Commun, 2010, 283: 3001–3005

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yong Zhang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhu, Y., Zhang, Y. Quantum discord in the three-spin XXZ chain with Dzyaloshinskii-Moriya interaction. Sci. China Phys. Mech. Astron. 55, 2081–2087 (2012). https://doi.org/10.1007/s11433-012-4871-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11433-012-4871-x

Keywords

Navigation