Skip to main content
SpringerLink
Log in

Thermal entanglement and lower bound of the geometric discord for a two-qutrit system with linear coupling and nonuniform external magnetic field

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

The effects of temperature and linear coupling constant on the lower bound of the geometric discord and negativity of a qutrit–qutrit system in Heisenberg model with (and without) parallel and antiparallel external magnetic fields have been investigated. We show that the lower bound of the geometric discord and negativity are about zero for negative linear coupling constant in parallel magnetic fields, while they are nonzero in the finite antiparallel magnetic fields. For negative linear coupling constant, as temperature increases, both measures become zero faster than in the case of positive linear coupling constant in antiparallel magnetic fields.

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

References

  1. 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 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Modi, K., Cable, H., Williamson, M., Vedral, V.: Quantum correlations in mixed-state metrology. Phys. Rev. X 1, 021022 (2011)

    Google Scholar 

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

    Article  ADS  Google Scholar 

  5. Luo, S.: Using measurement-induced disturbance to characterize correlations as classical or quantum. Phys. Rev. A 77, 022301 (2008)

    Article  ADS  Google Scholar 

  6. Luo, S., Fu, S.: Geometric measure of quantum discord. Phys. Rev. A 82, 034302 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Batle, J., Plastino, A., Plastino, A.R., Casas, M.: Discord-entanglement in interplay in thermodynamic limit: the XY-model. J. Quantum Inform. 11, 1350003 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  8. Divyamani, B.G.: Thermal entanglement in a two-qubit ising chain subjected to Dzyaloshinsky–Moriya interaction. Chin. Phys. Lett 30, 120301 (2013)

    Article  Google Scholar 

  9. Batle, J., Abdel-Aty, M.: Role of quantum discord and entanglement in an infinite spin chain. Quantum Inf. Rev. 2, 9 (2014)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  11. Hassan, A.S.M., Lari, B., Joag, P.S.: Thermal quantum and classical correlations in a two-qubit XX model in a nonuniform external magnetic field. J. Phys. A Math. Theor. 43, 485302 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. Soltani, M.R., Mahdavifar, S., Mahmoudi, M.: Entanglement in a two-spin system with long-range interactions. Chin. Phys. B 25, 087501 (2016)

    Article  ADS  Google Scholar 

  13. Zhang, G.F., Li, S.S., Liang, J.Q.: Thermal entanglement in Spin-1 biparticle system. Opt. Commun. 245, 457 (2005)

    Article  ADS  Google Scholar 

  14. Qin, M., Tao, Y., Hu, M., Tian, D.: Entanglement in spin-1 Heisenberg XY chain. Sci. China Ser. G-Phys. Mech. Astron. 51, 817 (2008)

    Article  ADS  Google Scholar 

  15. Zhang, G.F., Li, S.S.: The effects of nonlinear couplings and external magnetic field on the thermal entanglement in a two-spin-qutrit system. Opt. Commun. 260, 347 (2006)

    Article  ADS  Google Scholar 

  16. San Ma, X.: Thermal entanglement of a two-qutrit XX spin chain with Dzialoshinski–Moriya interaction. Opt. Commun. 281, 484 (2008)

    Article  ADS  Google Scholar 

  17. Akyz, C., Aydner, E., Mstecaplolu, E.: Thermal entanglement of a two-qutrit Ising system with Dzialoshinski–Moriya interaction. Opt. Commun. 281, 5271 (2008)

    Article  ADS  Google Scholar 

  18. Sargolzahi, I., Mirafzali, S.Y., Sarbishaei, M.: Thermal entanglement in a two-qutrit system with nonlinear coupling under nonuniform external magnetic field. Int. J. Quantum Inf. 6, 867 (2008)

    Article  MATH  Google Scholar 

  19. Jaghouri, H., Sarbishaei, M., Javidan, K.: Evolution of entropy in different types of non-Markovian three-level systems: single reservoir vs. two independent reservoirs. Pramana 86, 997 (2016)

    Article  ADS  Google Scholar 

  20. Li, G., Liu, Y., Tang, H., Yin, X., Zhang, Z.: Analytic expression of quantum correlations in qutrit Werner states undergoing local and nonlocal unitary operations. Quantum Inf. Process. 14, 559 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. Hou, X.W., Lei, X.F., Chen, B.: Thermal quantum and classical correlations in a two-qutrit system. Eur. Phys. J. D 67, 1 (2013)

    Article  Google Scholar 

  22. Li, X.J., Ji, H.H., Hou, X.W.: Thermal discord and negativity in a two-spin-qutrit system under different magnetic fields. Int. J. Quantum Inf. 11, 1350070 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. Yuan, Y.L., Hou, X.W.: Thermal geometric discords in a two-qutrit system. Int. J. Quantum Inf. 14, 1650016 (2016)

    Article  MATH  Google Scholar 

  24. Yan, X.Q., Liu, G.H., Chee, J.: Sudden change in quantum discord accompanying the transition from bound to free entanglement. Phys. Rev. A 87, 022340 (2013)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  26. Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. Daki, B., Vedral, V., Brukner, Č.: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105, 190502 (2010)

    Article  ADS  MATH  Google Scholar 

  28. Luo, S., Fu, S.: Geometric measure of quantum discord. Phys. Rev. A 82, 034302 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  29. Jaksch, D., Bruder, C., Cirac, J.I., Gardiner, C.W., Zoller, P.: Cold bosonic atoms in optical lattices. Phys. Rev. Lett. 81, 3108 (1998)

    Article  ADS  Google Scholar 

  30. Yip, S.K.: Dimer state of spin-1 bosons in an optical lattice. Phys. Rev. Lett. 90, 250402 (2003)

    Article  ADS  Google Scholar 

  31. Scarola, V.W., Sarma, S.D.: Quantum phases of the extended Bose–Hubbard Hamiltonian: possibility of a supersolid state of cold atoms in optical lattices. Phys. Rev. Lett. 95, 033003 (2005)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Ferdowsi University of Mashhad, Mashhad, 91775-1436, Iran

    Hakimeh Jaghouri, Mohsen Sarbishaei & Kurosh Javidan

Authors
  1. Hakimeh Jaghouri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohsen Sarbishaei
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kurosh Javidan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hakimeh Jaghouri.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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, 124 (2017). https://doi.org/10.1007/s11128-017-1551-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-017-1551-9

Keywords

Search

Navigation