Skip to main content
SpringerLink
Log in

Dzyaloshinskii–Moriya interaction as an agent to free the bound entangled states

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

In the present paper, we investigate the efficacy of Dzyaloshinskii–Moriya (DM) interaction to convert the bound entangled states into free entangled states. We consider the tripartite hybrid system as a pair of non interacting two qutrits initially prepared in bound entangled states and one auxiliary qubit. Here, we consider two types of bound entangled states investigated by Horodecki. The auxiliary qubit interacts with any one of the qutrit of the pair through DM interaction. We show that by tuning the probability amplitude of auxiliary qubit and DM interaction strength, one can free the bound entangled states, which can be further distilled. We use the reduction criterion to find the range of the parameters of probability amplitude of auxiliary qubit and DM interaction strength, for which the states are distillable. The realignment criterion and negativity have been used for detection and quantification of entanglement.

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
Fig. 7

Similar content being viewed by others

References

  1. Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777–780 (1935)

    Article  ADS  MATH  Google Scholar 

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

    MATH  Google Scholar 

  3. Bennett, C.H., Brassard, G., Crépeau, C., Jozsa, A., Peres, Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70, 1895–1899 (1993)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. Lugiato, L.: Quantum imaging. J. Opt. B Quantum Semiclass 4, 3 (2002)

    Article  Google Scholar 

  5. Meyer, D.: Quantum strategies. Phys. Rev. Lett. 82, 1052–1055 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Ekert, A.K.: Quantum cryptography based on Bells theorem. Phys. Rev. Lett. 67, 661–663 (1991)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Yu, T., Eberly, J.H.: Finite-time disentanglement via spontaneous emission. Phys. Rev. Lett. 93, 140404 (2004)

    Article  ADS  Google Scholar 

  8. Yu, T., Eberly, J.H.: Sudden death of entanglement. Science 30, 598–601 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. Affleek, I., Haldane, F.D.M.: Critical theory of quantum spin chains. Phys. Rev. 36, 5291–5300 (1987)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  11. Moriya, T.: New mechanism of anisotropic superexchange interaction. Phys. Rev. Lett. 4, 228–230 (1960)

    Article  ADS  Google Scholar 

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

    ADS  Google Scholar 

  13. Qiang, Z., Xiao-Ping, Z., Qi-Jun, Z., Zhong-Zhou, R.: Entanglement dynamics of a Heisenberg chain with Dzyaloshinskii–Moriya interaction. Chin. Phys. B 18, 3210 (2009)

    Article  ADS  Google Scholar 

  14. Qiang, Z., Ping, S., Xiao-Ping, Z., Zhong-Zhou, R.: Control of entanglement sudden death induced by Dzyaloshinskii–Moriya interaction. Chin. Phys. C 34, 1583–1586 (2010)

    Article  ADS  Google Scholar 

  15. Qiang, Z., Qi-Jun, Z., Xiao-Ping, Z., Zhong-Zhou, R.: Controllable entanglement sudden birth of Heisenberg spins. Chin. Phys. C 35, 135–138 (2011)

    Article  ADS  Google Scholar 

  16. Albanese, C.: On the spectrum of the Heisenberg Hamiltonian. J. Stat. Phys. 55, 297–309 (1989)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. Horodecki, M., Horodecki, P. Horodecki, R.: Mixed-state entanglement and quantum communication. In: G. Albert et al. (eds.) Quantum Information. Springer Tracts in Modern Physics, vol. 173, pp. 151. Springer, Berlin (2001) (also available as arXiv:quant-ph/0109124)

  18. Krammer, P.: Quantum entanglement: detection, classification and quantification. Diploma Thesis, Universitat Wien (2005)

  19. Horodecki, P.: Separability criterion and inseparable mixed states with positive partial transposition. Phys. Lett. A. 232, 333–339 (1997)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. Horodecki, M., Horodecki, P., Horodecki, R.: Mixed-state entanglement and distillation: is there a bound entanglement in nature? Phys. Rev. Lett. 80, 5239–5242 (1998)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. Horodecki, M., Horodecki, P., Horodecki, R.: Distillation and bound entanglement. Quantum Inf. Comput. 1, 45–47 (2001)

    MathSciNet  MATH  Google Scholar 

  22. Horodecki, P.: Bound entanglement can be activated. Phys. Rev. Lett. 82, 1056–1059 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. Dür, W., Cirac, J.I.: Activating bound entanglement in multiparticle systems. Phys. Rev. A. 62, 022302 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  24. Kaneda, F., Shimizu, R., Ishizaka, S., Mitsumori, Y., Kosaka, H., Edamatsu, K.: Experimental activation of bound entanglement. Phys. Rev. Lett. 109, 040501 (2012)

    Article  ADS  Google Scholar 

  25. Baghbanzadeh, S., Rezakhani, A.T.: Distillation of free entanglement from bound entangled states using weak measurements. Phys. Rev. A 88, 062320 (2013)

    Article  ADS  Google Scholar 

  26. Sharma, K.K., Awasthi, S.K., Pandey, S.N.: Entanglement sudden death and birth in qubit–qutrit systems under Dzyaloshinskii–Moriya interaction. Quantum Inf. Process. 12, 3437–3447 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. Sharma, K.K., Pandey, S.N.: Entanglement dynamics in two-parameter qubit–qutrit states under Dzyaloshinskii–Moriya interaction. Quantum Inf. Process. 13, 2017–2038 (2014)

    Article  ADS  MATH  Google Scholar 

  28. Sharma, K.K., Pandey, S.N.: Influence of Dzyaloshinshkii–Moriya interaction on quantum correlations in two qubit Werner states and MEMS. Quantum Inf. Process. 14, 1361 (2015)

  29. Sharma, K.K., Pandey, S.N.: Entanglement dynamics in qutrit–qutrit system: DM interaction as a resource to free the bound entangled states. arXiv:1412.4883v2

  30. Horodecki, M., Horodecki, P.: Reduction criterion of separability and limits for a class of distillation protocols. Phy. Rev. A 59, 4206 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  31. Plenio, M.B., Virmani, S.: An introduction to entanglement measures. Quantum Inf. Comput. 7, 1–51 (2007)

    MathSciNet  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  33. Horodecki, M., Horodecki, P., Horodecki, R.: Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A 223, 1–8 (1996)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  34. Peres, A.: Quantum Theory: Concepts and Methods. Kluwer Academic Publishers, Dordrecht (1995)

    MATH  Google Scholar 

  35. Peres, A.: Higher order Schmidt decompositions. Phys. Lett. A 202, 16–17 (1995)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  36. Schmidt, E.: Zur theorie der linearen und nichtlinearen Integralgleichungen. I. Teil: Entwicklung willkrlicher funktionen nach systemen vorgeschriebener. Math. Ann. 63, 433–476 (1907)

    Article  MathSciNet  Google Scholar 

  37. Ekert, A., Knight, P.L.: Entangled quantum systems and the Schmidt decomposition. Am. J. Phys. 63, 415 (1995)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  38. Derkacz, L., Jakobczyk, L.: Delayed birth of distillable entanglement in the evolution of bound entangled states. Phys. Rev. A 82, 022312 (2010)

    Article  ADS  Google Scholar 

  39. Qian, G., Guan, X.: Quantum dynamics of bound entangled states. Commun. Theor. Phys. 49, 343–346 (2008)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

We would like to thank the anonymous reviewers for going through the manuscript very carefully and suggesting many changes which have greatly enhanced the clarity and presentation of the results.

Author information

Authors and Affiliations

  1. Department of Physics, Motilal Nehru National Institute of Technology, Allahabad, 211004, India

    Kapil K. Sharma & S. N. Pandey

Authors
  1. Kapil K. Sharma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. N. Pandey
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. N. Pandey.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sharma, K.K., Pandey, S.N. Dzyaloshinskii–Moriya interaction as an agent to free the bound entangled states. Quantum Inf Process 15, 1539–1551 (2016). https://doi.org/10.1007/s11128-015-1234-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-015-1234-3

Keywords

Search

Navigation