Quantum Information Processing

, Volume 13, Issue 8, pp 1789–1811 | Cite as

Quantum teleportation through noisy channels with multi-qubit GHZ states

  • Pakhshan Espoukeh
  • Pouria PedramEmail author


We investigate two-party quantum teleportation through noisy channels for multi-qubit Greenberger–Horne–Zeilinger (GHZ) states and find which state loses less quantum information in the process. The dynamics of states is described by the master equation with the noisy channels that lead to the quantum channels to be mixed states. We analytically solve the Lindblad equation for \(n\)-qubit GHZ states \(n\in \{4,5,6\}\) where Lindblad operators correspond to the Pauli matrices and describe the decoherence of states. Using the average fidelity, we show that 3GHZ state is more robust than \(n\)GHZ state under most noisy channels. However, \(n\)GHZ state preserves same quantum information with respect to Einstein–Podolsky–Rosen and 3GHZ states where the noise is in \(x\) direction in which the fidelity remains unchanged. We explicitly show that Jung et al.’s conjecture (Phys Rev A 78:012312, 2008), namely “average fidelity with same-axis noisy channels is in general larger than average fidelity with different-axes noisy channels,” is not valid for 3GHZ and 4GHZ states.


Quantum teleportation Greenberger–Horne–Zeilinger states  Noisy channels Lindblad equation 



We would like to thank Robabeh Rahimi for fruitful discussions and suggestions and for a critical reading of the paper.


  1. 1.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  2. 2.
    Bennett, C.H., Brassard, G., Crepeau, 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)MathSciNetCrossRefADSzbMATHGoogle Scholar
  3. 3.
    Chakrabarty, I.: Teleportation via a mixture of a two qubit subsystem of a N-qubit W and GHZ state. Eur. Phys. J. D 57, 265 (2010)CrossRefADSGoogle Scholar
  4. 4.
    Liang, H.-Q., Liu, J.-M., Feng, S.-S., Chen, J.-G.: Quantum teleportation with partially entangled states via noisy channels. Quantum Inf. Process. 12, 2671 (2013)MathSciNetCrossRefADSzbMATHGoogle Scholar
  5. 5.
    Wang, X.-W., Shan, Y.-G., Xia, L.-X., Lu, M.-W.: Dense coding and teleportation with one-dimensional cluster states. Phys. Lett. A 364, 7 (2007)CrossRefADSzbMATHGoogle Scholar
  6. 6.
    Paul, N., Menon, J.V., Karumanchi, S., Muralidharan, S., Panigrahi, P.K.: Quantum tasks using six qubit cluster states. Quantum Inf. Process. 10, 619 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Karlsson, A., Bourennane, M.: Quantum teleportation using three-particle entanglement. Phys. Rev. A 58, 4394 (1998)MathSciNetCrossRefADSGoogle Scholar
  8. 8.
    Wang, L.-Q., Zha, X.-W.: Two schemes of teleportation one-particle state by a three-particle GHZ state. Opt. Commun. 283, 4118 (2010)CrossRefADSGoogle Scholar
  9. 9.
    Gorbachev, V.N., Rodichkina, A.A., Truilko, A.I.: On preparation of the entangled W-states from atomic ensembles. Phys. Lett. A 310, 339 (2003)MathSciNetCrossRefADSzbMATHGoogle Scholar
  10. 10.
    Joo, J., Park, Y.-J., Oh, S., Kim, J.: Quantum teleportation via a W state. New J. Phys. 5, 136 (2003)CrossRefADSGoogle Scholar
  11. 11.
    Agrawal, P., Pati, A.: Perfect teleportation and superdense coding with W states. Phys. Rev. A 74, 062320 (2006)CrossRefADSGoogle Scholar
  12. 12.
    Hu, M.-L.: Robustness of Greenberger–Horne–Zeilinger and W states for teleportation in external environments. Phys. Lett. A 375, 922 (2011)CrossRefADSGoogle Scholar
  13. 13.
    Pati, A.K.: Assisted cloning and orthogonal complementing of an unknown state. Phys. Rev. A 61, 022308 (2000)MathSciNetCrossRefADSGoogle Scholar
  14. 14.
    Jung, E., Hwang, M.R., Park, D.K., Son, J.W., Tamaryan, S.: Perfect quantum teleportation and superdense coding with \(P_{max} = 1/2\) states. arXiv:0711.3520
  15. 15.
    Ma, Z.H., Zhang, F.L., Deng, D.L., Chen, J.L.: Bounds of concurrence and their relation with fidelity and frontier states. Phys. Lett. A 373, 1616 (2009)CrossRefADSzbMATHGoogle Scholar
  16. 16.
    Wang, X., Sun, Z., Wang, Z.D.: Operator fidelity susceptibility: an indicator of quantum criticality. Phys. Rev. A 79, 012105 (2010)CrossRefADSGoogle Scholar
  17. 17.
    Ma, J., Xu, L., Xiong, H., Wang, X.: Reduced fidelity susceptibility and its finite-size scaling behaviors in the Lipkin–Meshkov–Glick model. Phys. Rev. E 78, 051126 (2008)CrossRefADSGoogle Scholar
  18. 18.
    Lu, X.-M., Sun, Z., Wang, X., Zanardi, P.: Operator fidelity susceptibility, decoherence, and quantum criticality. Phys. Rev. A 78, 032309 (2008)CrossRefADSGoogle Scholar
  19. 19.
    Giorda, P., Zanardi, P.: Quantum chaos and operator fidelity metric. Phys. Rev. E 81, 017203 (2010)MathSciNetCrossRefADSGoogle Scholar
  20. 20.
    Horodecki, M., Horodocki, P., Horodocki, R.: General teleportation channel, singlet fraction, and quasidistillation. Phys. Rev. A 60, 1888 (1999)MathSciNetCrossRefADSzbMATHGoogle Scholar
  21. 21.
    Banaszek, K.: Fidelity balance in quantum operations. Phys. Rev. Lett. 86, 1366 (2001)CrossRefADSGoogle Scholar
  22. 22.
    Jung, E., Hwang, M.R., Park, D.K., Son, J.W., Tamaryan, S.: Mixed-state entanglement and quantum teleportation through noisy channels. J. Phys. A 41, 385302 (2008)MathSciNetCrossRefADSzbMATHGoogle Scholar
  23. 23.
    Oh, S., Lee, S., Lee, H.W.: Fidelity of quantum teleportation through noisy channels. Phys. Rev. A 66, 022316 (2002)MathSciNetCrossRefADSGoogle Scholar
  24. 24.
    Han, X.P., Liu, J.M.: Amplitude damping effects on controlled teleportation of a qubit by a tripartite W state. Phys. Scr. 78, 015001 (2008)MathSciNetCrossRefADSzbMATHGoogle Scholar
  25. 25.
    Rao, D.D.B., Panigrahi, P.K., Mitra, C.: Teleportation in the presence of common bath decoherence at the transmitting station. Phys. Rev. A 78, 022336 (2008)CrossRefADSGoogle Scholar
  26. 26.
    Jung, E., Hwang, M.R., Ju, Y.H., Kim, M.S., Yoo, S.K., Kim, H., Park, D.K., Son, J.W., Tamaryan, S., Cha, S.-K.: Greenberger–Horne–Zeilinger versus W states: quantum teleportation through noisy channels. Phys. Rev. A 78, 012312 (2008)CrossRefADSGoogle Scholar
  27. 27.
    Lindblad, G.: On the generators of quantum dynamical semigroups. Commun. Math. Phys. 48, 119 (1976)MathSciNetCrossRefADSzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Physics, Science and Research BranchIslamic Azad UniversityTehranIran

Personalised recommendations