Quantum Information Processing

, Volume 14, Issue 6, pp 2067–2076 | Cite as

Sudden death of distillability in a two-qutrit anisotropic Heisenberg spin model

  • You-neng Guo
  • Mao-fa FangEmail author
  • Hong-mei Zou
  • Shi-yang Zhang
  • Xiang Liu


Sudden death of distillability for a two-qutrit anisotropic Heisenberg XX chain with Dzyaloshinskii–Moriya (DM) interaction in an inhomogeneous magnetic field is studied in detail. By using the negativity and realignment criterion, we show that certain initial prepared free entangled states may become bound entangled or separable states in a finite time. Moreover, the influences of the isotropic bilinear interaction parameter, the external magnetic field strength, the DM interaction parameter, as well as the intrinsic decoherence parameter on the possibility of distillability sudden death (DSD) have been studied. The results show, controlling the isotropic bilinear interaction parameter, the external magnetic field strength, the DM interaction parameter, as well as the intrinsic decoherence parameter, can accelerate the possibility of DSD in the present model.


Dzyaloshinskii–Moriya interaction Realignment criterion  Distillability sudden death 



This work is supported by the National Natural Science Foundation of China (Grant Nos. 11374096 and 11074072) and Hunan Provincial Innovation Foundation for Postgraduate (CX2014B194).


  1. 1.
    Yu, T., Eberly, J.H.: Finite-time disentanglement via spontaneous emission. Phys. Rev. Lett. 93, 140404 (2004)CrossRefADSGoogle Scholar
  2. 2.
    Yu, T., Eberly, J.H.: Phonon decoherence of quantum entanglement: robust and fragile states. Phys. Rev. B 66, 193306 (2002)CrossRefADSGoogle Scholar
  3. 3.
    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)CrossRefADSzbMATHMathSciNetGoogle Scholar
  4. 4.
    Jaeger, G.S., Sergienko, A.V.: Entanglement sudden death: a threat to advanced quantum key distribution. Nat. Comput. 13, 459–467 (2014)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Al-Qasimi, A., James, D.F.V.: Sudden death of entanglement at finite temperature. Phys. Rev. A 77, 012117 (2008)CrossRefADSGoogle Scholar
  6. 6.
    Jared, H.: Cole: understanding entanglement sudden death through multipartite entanglement and quantum correlations. J. Phys. A Math. Theory 43, 135301 (2010)CrossRefADSGoogle Scholar
  7. 7.
    Song, W., Chen, L., Zhu, S.L.: Sudden death of distillability in qutrit–qutrit systems. Phys. Rev. A 80, 012331 (2009)CrossRefADSGoogle Scholar
  8. 8.
    Baghbanzadeh, S., Alipour, S., Rezakhani, A.T.: Bound entanglement in quantum phase transitions. Phys. Rev. A 81, 042302 (2010)CrossRefADSGoogle Scholar
  9. 9.
    Baghbanzadeh, S., Rezakhani, A.T.: Distillation of free entanglement from bound entangled states using weak measurements. Phys. Rev. A 88, 062320 (2013)CrossRefADSGoogle Scholar
  10. 10.
    Shor, P.W., Smolin, J.A., Thapliyal, A.V.: Superactivation of bound entanglement. Phys. Rev. Lett. 90, 107901 (2003)CrossRefADSMathSciNetGoogle Scholar
  11. 11.
    Ali, M.: Distillability sudden death in qutrit–qutrit systems under amplitude damping. J. Phys. B At. Mol. Opt. Phys. 43, 045504 (2010)CrossRefADSGoogle Scholar
  12. 12.
    Ali, M.: Distillability sudden death in qutrit–qutrit systems under global and multilocal dephasing. Phys. Rev. A 81, 042303 (2010)CrossRefADSGoogle Scholar
  13. 13.
    Ali, M., Huang, J.: Distillability sudden birth of entanglement for qutrit–qutrit systems. Chin. Phys. Lett. 31, 110301 (2014)CrossRefGoogle Scholar
  14. 14.
    Ali, M.: Comments on “Distillability sudden death in qutritqutrit systems under thermal reservoirs”. Chin. Phys. B 23, 090306 (2014)CrossRefGoogle Scholar
  15. 15.
    Guo, Y.N., Fang, M.F., Zhang, S.Y., Liu, X.: Distillability sudden death in two-qutrit systems with external magnetic field and Dzyaloshinskii–Moriya interaction due to decoherence. Eur. Phys. Lett. 108, 47002 (2014)CrossRefADSGoogle Scholar
  16. 16.
    Sun, Z., Wang, X.G., Gao, Y.B., Sun, C.P.: Decoherence in time evolution of bound entanglement. Eur. Phys. J. D. 46, 521–530 (2008)CrossRefADSGoogle Scholar
  17. 17.
    Cheng, W., Xu, F., Li, H., Wang, G.: Entanglement and distillability in qutrit–qutrit systems by convex linear combination. Int. J. Theor. Phys. 52, 1061–1074 (2013)CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    Albayrak, E.: Thermal entanglement in the anisotropic Heisenberg model with Dzyaloshinskii–Moriya interaction in an inhomogeneous magnetic field. Eur. Phys. J. B 72, 491–496 (2009)CrossRefADSGoogle Scholar
  19. 19.
    Milburn, G.J.: Intrinsic decoherence in quantum mechanics. Phys. Rev. A 44, 5401 (1991)Google Scholar
  20. 20.
    Xu, J.B., Zou, X.B.: Dynamic algebraic approach to the system of a three-level atom in the configuration. Phys. Rev. A 60, 4743 (1999)CrossRefADSGoogle Scholar
  21. 21.
    Liu, B.Q., Shao, B., Zou, J.: Tripartite states Bell-nonlocality sudden death with intrinsic decoherence. Phys. Lett. A 374, 1970–1974 (2010)CrossRefADSzbMATHMathSciNetGoogle Scholar
  22. 22.
    Horodecki, P., Horodecki, M., Horodecki, R.: Bound entanglement can be activated. Phys. Rev. Lett. 82, 1056 (1999)CrossRefADSzbMATHMathSciNetGoogle Scholar
  23. 23.
    Sharma, K.K., Pandey, S.N.: Dzyaloshinskii–Moriya interaction as an agent to free the bound entangled states. arXiv: 1501.00942
  24. 24.
    Guo, J.L., Song, H.S.: Effects of inhomogeneous magnetic field on entanglement and teleportation in a two-qubit Heisenberg XXZ chain with intrinsic decoherence. Phys. Scr. 78, 045002 (2008)CrossRefADSGoogle Scholar
  25. 25.
    Chen, K., Wu, L.A.: A matrix realignment method for recognizing entanglement. Quantum Inf. Comput. 3, 193–202 (2003)zbMATHMathSciNetGoogle Scholar
  26. 26.
    Vidal, G., Werner, R.F.: Computable measure of entanglement. Phys. Rev. A 65, 032314 (2002)CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • You-neng Guo
    • 1
  • Mao-fa Fang
    • 1
    Email author
  • Hong-mei Zou
    • 1
  • Shi-yang Zhang
    • 1
  • Xiang Liu
    • 1
  1. 1.Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Department of PhysicsHunan Normal UniversityChangshaPeople’s Republic of China

Personalised recommendations