Skip to main content
SpringerLink
Log in

Robustness of Greenberger\(\textendash \)Horne\(\textendash \)Zeilinger and W states against Dzyaloshinskii-Moriya interaction

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

In this article, the robustness of tripartite Greenberger–Horne–Zeilinger (GHZ) and W states is investigated against Dzyaloshinskii-Moriya (i.e. DM) interaction. We consider a closed system of three qubits and an environmental qubit. The environmental qubit interacts with any one of the three qubits through DM interaction. The tripartite system is initially prepared in GHZ and W states, respectively. The composite four qubits system evolve with unitary dynamics. We detach the environmental qubit by tracing out from four qubits, and profound impact of DM interaction is studied on the initial entanglement of the system. As a result, we find that the bipartite partitions of W states suffer from entanglement sudden death (i.e. ESD), while tripartite entanglement does not. On the other hand, bipartite partitions and tripartite entanglement in GHZ states do not feel any influence of DM interaction. So, we find that GHZ states have robust character than W states. In this work, we consider generalised GHZ and W states, and three \(\pi \) is used as an entanglement measure. This study can be useful in quantum information processing where unwanted DM interaction takes place.

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. Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (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. Schrödinger, E.: Discussion of probability relations between separated systems. Math. Proc. Camb. Philos. Soc. 31, 555 (1935)

    Article  ADS  MATH  Google Scholar 

  4. Schrödinger, E.: Probability relations between separated systems. Math. Proc. Camb. Philos. Soc. 32, 446 (1936)

    Article  ADS  MATH  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Bouwmeester, D., Pan, J.W., Mattle, K., Eibl, M., Weinfurter, H., Zeilinger, A.: Experimental quantum teleportation. Nature 390, 575 (1997)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. Meyer, D.: Quantum strategies. Phys. Rev. Lett. 82, 1052 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  10. Hillery, M., Buek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59, 1829 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  11. Wiebe, N., Kapoor, A., Svorey, K.M.: Quantum algorithms for nearest-neighbor methods for supervised and unsupervised learning. arXiv:1401.2142v2 (2014)

  12. Lloyd, S., Mohseni, Rebentrost, M. P.: Quantum algorithms for supervised and unsupervised machine learning. arXiv:1307.0411v2 (2014)

  13. Yoo, S., Bang, J., Lee, C., Lee, J.: A quantum speedup in machine learning: finding an N-bit Boolean function for a classification. New J. Phys. 16, 103014 (2014)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. 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 

  17. 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 (2010)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  19. 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 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  22. Sharma, K.K., Pandey, S.N.: Dzyaloshinshkii-Moriya interaction as an agent to free the bound entangled states. Quantum. Info. Process. 15, 1539 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. Sharma, K.K., Pandey, S.N.: Dynamics of entanglement in two parameter qubit-qutrit states with x-component of DM interaction. Commun. Theor. Phys. 65, 278 (2016)

    Article  ADS  Google Scholar 

  24. Dzyaloshinskii, I.: A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics. J. Phys. Chem. Solids 4, 241 (1958)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    ADS  Google Scholar 

  27. Heinze, S., Von Bergmann, K., Menzel, M., Brede, J., Kubetzka, A., Wiesendanger, R., Bihlmayer, G., Blgel, S.: Spontaneous atomic scale magnetic skyrmion lattice in two dimensions. Nat. Phys. 7, 713 (2011)

    Article  Google Scholar 

  28. Fert, A., Cros, V., Sampaio, J.: Skyrmions on the track. Nat. Nanotechnol. 8, 152 (2013)

    Article  ADS  Google Scholar 

  29. Zhou, Y., Iacocca, E., Awad, A.A., Dumas, R.K., Zhang, F.C., Braun, H.B., Akerman, J.: Dynamically stabilized magnetic skyrmions. Nat. Commun. 6, 8193 (2015)

    Article  ADS  Google Scholar 

  30. Zhang, X.C., Ezawa, M., Zhou, Y.: Magnetic skyrmion logic gates: conversion, duplication and merging of skyrmions. Sci. Rep. 5, 9400 (2014)

    Article  Google Scholar 

  31. Zang, G.F.: Thermal entanglement and teleportation in a two-qubit Heisenberg chain with Dzyaloshinski-Moriya anisotropic antisymmetric interaction. Phys. Rev. A 75, 034304 (2007)

    Article  ADS  Google Scholar 

  32. Akyüz, C., Aydner, E., Müstecaploglu, Ö.E.: Thermal entanglement of a two-qutrit Ising system with DzialoshinskiMoriya interaction. Opt. Commun. 281, 5271 (2008)

    Article  ADS  Google Scholar 

  33. Greenberger, D.M., Horne, M.A., Zeilinger, A.: Going beyond Bell’s Theorem. arXiv:0712.0921 (2007)

  34. Dür, W., Vidal, G., Cirac, J.I.: Three qubits can be entangled in two inequivalent ways. Phys. Rev. A 62, 062314 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  35. Fleischhauer, M., Lukin, M.D.: Quantum memory for photons: dark-state polaritons. Phys. Rev. A 65, 022314 (2002)

    Article  ADS  Google Scholar 

  36. Zang, X.P., Yang, M., Ozaydin, F., Song, W., Cao, Z.L.: Deterministic generation of large scale atomic W states. Opt. Express 24, 12293 (2016)

    Article  ADS  Google Scholar 

  37. Zang, X.P., Yang, M., Ozaydin, F., Song, W., Cao, Z.L.: Generating multi-atom entangled W states via light-matter interface based fusion mechanism. Sci. Rep. 5, 16245 (2015)

    Article  ADS  Google Scholar 

  38. Ozaydin, F., Altintas, A.A.: Quantum metrology: surpassing the shot-noise limit with Dzyaloshinskii-Moriya interaction. Sci. Rep. 5, 16360 (2015)

    Article  ADS  Google Scholar 

  39. Ozaydina, F., Altintas, A.A., Yesilyurt, C., Bugud, S., Erole, V.: Quantum fisher information of bipartitions of W states. Acta. Phys. Pol. A 127, 4 (2015)

    Google Scholar 

  40. Ozaydin, F., Altintas, A.A., Bugu, S., Yesilyurt, C., Arik, M.: Quantum fisher information of several qubits in the superposition of a GHZ and two W states with arbitrary relative Phase. Int. J. Theor. Phys. 53, 3219 (2014)

    Article  MATH  Google Scholar 

  41. Yi, X.J., Huang, G.Q., Wang, J.M.: Quantum fisher information of a 3-qubit state. Int. J. Theor. Phys. 51, 3458 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  42. Weinstein, Y.S.: Tripartite entanglement witnesses and entanglement sudden death. Phy. Rev. A. 79, 012318 (2009)

    Article  ADS  Google Scholar 

  43. Hu, T., Ren, H., Xue, K.: Tripartite entanglement sudden death in Yang-Baxter systems. Quantum Inf. Process 10, 705 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  44. Vedral, V., Plenio, M.B., Rippin, M.A., Knight, P.L.: Quantifying entanglement. Phys. Rev. Lett. 78, 2275 (1997)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  45. Cheng Ou, Y., Fan, H.: Monogamy inequality in terms of negativity for three-qubit states. Phy. Rev. A. 75, 062308 (2007)

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

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  51. Coffman, V., Kundu, J., Wootters, W.K.: Distributed entanglement. Phys. Rev. A 61, 052306 (2000)

    Article  ADS  Google Scholar 

  52. Li, Q., Cui, J., Wnag, S., Long, G.L.: Study of a monogamous entanglement measure for three-qubit quantum systems. Quantum Inf. Process 15, 2405 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai, 400076, India

    Kapil K. Sharma

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

    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 Kapil K. Sharma.

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. Robustness of Greenberger\(\textendash \)Horne\(\textendash \)Zeilinger and W states against Dzyaloshinskii-Moriya interaction. Quantum Inf Process 15, 4995–5009 (2016). https://doi.org/10.1007/s11128-016-1443-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-016-1443-4

Keywords

Search

Navigation