Quantum Information Processing

, Volume 13, Issue 8, pp 1659–1676 | Cite as

Tripartite quantum operation sharing with two asymmetric three-qubit W states in five entanglement structures

  • Qibin Ji
  • Yimin Liu
  • Chuanmei Xie
  • Xiaofeng Yin
  • Zhanjun Zhang
Article

Abstract

Tripartite remote sharing of any single-qubit operation with two asymmetric three-qubit W states is amply treated. Five schemes are put forward with the W states in five different entanglement structures corresponding to five different distributions of two identical qubit trios in three locations. For all schemes, two features about the security and the agent symmetry are analyzed and confirmed. Moreover, resource consumption, necessary-operation complexity, success probability and efficiency are also worked out and compared mutually. For all schemes, quantum resource consumption and necessary-operation complexity are same. The last scheme needs to cost two additional classical bits than the former four schemes. Nonetheless, the last scheme is deterministic and has the highest efficiency in contrast to the other four probabilistic schemes with lower efficiencies. Through some analyses, it is found that both success probability and intrinsic efficiency of each scheme are completely determined by the corresponding entanglement structure of the two W states. The underlying physics of this feature is revealed. In addition, the implementation feasibility of all the schemes is analyzed and thus confirmed according to the current experimental techniques.

Keywords

Single-qubit operation sharing Asymmetric W state Entanglement structure Success probability Efficiency 

Notes

Acknowledgments

This work is supported by the National Natural Science Foundation of China under Grant Nos. 11375011 and 11372122, the Natural Science Foundation of Anhui province under Grant No. 1408085MA12 and the 211 Project of Anhui University.

References

  1. 1.
    Bennett, C.H., Brassard, G., Crépeau, C.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70, 1895 (1993)MathSciNetCrossRefADSMATHGoogle Scholar
  2. 2.
    Gottesman, D., Chuang, I.: Demonstrating the viability of universal quantum computation using tele-portation and single-qubit operations. Nature 402, 390 (1999)CrossRefADSGoogle Scholar
  3. 3.
    Zhang, Z.J., Liu, Y.M., Wang, D.: Perfect teleportation of arbitrary n-qudit states using different quantum channels. Phys. Lett. A 372, 28 (2007)CrossRefADSMATHGoogle Scholar
  4. 4.
    Cheung, C.Y., Zhang, Z.J.: Criterion for faithful teleportation with an arbitrary multiparticle channel. Phys. Rev. A 80, 022327 (2009)CrossRefADSGoogle Scholar
  5. 5.
    Muralidharan, S., Panigrahi, P.K.: Perfect teleportation, quantum-state sharing, and superdense coding through a genuinely entangled five-qubit state. Phys. Rev. A 77, 032321 (2008)CrossRefADSGoogle Scholar
  6. 6.
    Wang, M.Y., Yan, F.L.: Chain teleportation via partially entangled states. Eur. Phys. J. D 54, 111 (2009)MathSciNetCrossRefADSGoogle Scholar
  7. 7.
    Bouwmeester, D., et al.: Experimental quantum teleportation. Nature 390, 575 (1997)CrossRefADSGoogle Scholar
  8. 8.
    Furusawa, A., et al.: Unconditional quantum teleportation. Science 282, 706 (1998)CrossRefADSGoogle Scholar
  9. 9.
    Hillery, M., Bǔzk, V.: Quantum secret sharing. Phys. Rev. A 59, 1829 (1999)MathSciNetCrossRefADSGoogle Scholar
  10. 10.
    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)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Choudhury, S., Muralidharan, S., Panigrahi, P.K.: Quantum teleportation and state sharing using a genuinely entangled six-qubit state. J. Phys. A Math. Theor. 42, 115303 (2009)MathSciNetCrossRefADSMATHGoogle Scholar
  12. 12.
    Deng, F.G., et al.: Improving the security of multiparty quantum secret sharing against Trojan horse attack. Phys. Rev. A 72, 044302 (2005)CrossRefADSGoogle Scholar
  13. 13.
    Yan, F.L., Wang, D.: Probabilistic and controlled teleportation of unknown quantum states. Phys. Lett. A 316, 297 (2003)MathSciNetCrossRefADSMATHGoogle Scholar
  14. 14.
    Muralidharan, S., Panigrahi, P.K.: Quantum-information splitting using multipartite cluster states. Phys. Rev. A 78, 062333 (2008)CrossRefADSGoogle Scholar
  15. 15.
    Muralidharan, S., Jain, S., Panigrahi, P.K.: Splitting of quantum information using N-qubit linear cluster states. Opt. Commun. 284, 1082 (2011)CrossRefADSGoogle Scholar
  16. 16.
    Prasath, E.S., et al.: Multipartite entangled magnon states as quantum communication channels. Quantum Inf. Process. 11, 397 (2012)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Shamir, A.: How to share a secret. Commun. ACM 22, 612 (1979)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Huelga, S.F., et al.: Quantum remote control: teleportation of unitary operations. Phys. Rev. A 63, 042303 (2001)MathSciNetCrossRefADSMATHGoogle Scholar
  19. 19.
    Huelga, S.F., et al.: Remote control of restricted sets of operations: teleportation of angles. Phys. Rev. A 65, 042316 (2002)CrossRefADSGoogle Scholar
  20. 20.
    Wang, A.M., Zhao, N.B.: Hybrid protocol of remote implementations of quantum operations. Phys. Rev. A 76, 062317 (2007)CrossRefADSGoogle Scholar
  21. 21.
    Wang, A.M., Zhao, B.: Local implementation of nonlocal operations with block forms. Phys. Rev. A 79, 014305 (2008)MathSciNetMATHGoogle Scholar
  22. 22.
    Zhang, Z.J., Cheung, C.Y.: Shared quantum remote control: quantum operation sharing. J. Phys. B 44, 165508 (2011)CrossRefADSGoogle Scholar
  23. 23.
    Liu, D.C., et al.: Generalized three-party qubit operation sharing. Int. J. Quantum Inf. 11, 1350011 (2013)MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Ye, B.L., et al.: Remotely sharing single-qubit operation with five-qubit genuine state. Chin. Phys. Lett. 30, 020301 (2013)CrossRefADSGoogle Scholar
  25. 25.
    Ji, Q.B., et al.: Quantum operation sharing with symmetric and asymmetric W states. Quantum Inf. Process. 12, 2453 (2013)MathSciNetCrossRefADSMATHGoogle Scholar
  26. 26.
    Ji, Q.B., et al.: Single-qubit operation sharing with Bell and W product states. Commun. Theor. Phys. 60, 165 (2013)CrossRefADSGoogle Scholar
  27. 27.
    Wang, S.F., et al.: Deterministic single-qubit operation sharing with five-qubit cluster state. Quantum Inf. Process. 12, 2497 (2013)MathSciNetCrossRefADSMATHGoogle Scholar
  28. 28.
    Liu, D.C., et al.: Shared quantum control via sharing operation on remote single qutrit. Quantum Inf. Process. 12, 3527 (2013)MathSciNetCrossRefADSMATHGoogle Scholar
  29. 29.
    Xing H., et al.: Four-party deterministic operation sharing with six-qubit cluster state. Quantum Inf. Process. doi: 10.1007/s11128-014-0750-x (2014)
  30. 30.
    Dür, W., et al.: Three qubits can be entangled in two inequivalent ways. Phys. Rev. A 62, 062314 (2000)MathSciNetCrossRefADSGoogle Scholar
  31. 31.
    Shi, B.S., Tomita, A.: Teleportation of an unknown state by W state. Phys. Lett. A 296, 161 (2002)MathSciNetCrossRefADSMATHGoogle Scholar
  32. 32.
    Agrawal, P., Pati, A.: Perfect teleportation and superdense coding with W states. Phys. Rev. A 74, 062320 (2006)CrossRefADSGoogle Scholar
  33. 33.
    Li, L.Z., Qiu, D.W.: The states of W-class as shared resources for perfect teleportation and super- dense coding. J. Phys. A Math. Theor. 40, 10871 (2007)MathSciNetCrossRefADSMATHGoogle Scholar
  34. 34.
    Liu, Y.M., et al.: Tripartition of arbitrary single-qubit quantum information by using asymmetric four-qubit W state. Int. J. Quantum Inf. 7, 349 (2009)CrossRefMATHGoogle Scholar
  35. 35.
    Joo, J., et al.: Quantum teleportation via a W state. New J. Phys. 5, 136 (2003)MathSciNetCrossRefADSGoogle Scholar
  36. 36.
    Zhan, Y.B.: Teleportation of N-particle entangled W state via entanglement swapping. Chin. Phys. 13, 1801 (2004)CrossRefADSGoogle Scholar
  37. 37.
    Zuo, X.Q., et al.: Minimal classical communication cost and measurement complexity in splitting two-qubit quantum information via asymmetric W states. Int. J. Quantum Inf. 6, 1245 (2008)CrossRefMATHGoogle Scholar
  38. 38.
    Zuo, X.Q., et al.: Bisplitting an arbitrary N-qubit state with a class of asymmetric three-qubit W states. Int. J. Theor. Phys. 48, 1950 (2009)CrossRefMathSciNetMATHGoogle Scholar
  39. 39.
    Zhang, Z.J., et al.: Multiparty quantum secret sharing of secure direct communication. Phys. Lett. A 342, 60 (2005)CrossRefADSMATHGoogle Scholar
  40. 40.
    Zhang, Z.J., Man, Z.X.: Multiparty quantum secret sharing of classical messages based on entanglement swapping. Phys. Rev. A 72, 022303 (2005)Google Scholar
  41. 41.
    Deng, F.G., et al.: Bidirectional quantum secret sharing and secret splitting with polarized single photons. Phys. Lett. A 337, 329 (2005)CrossRefADSMATHGoogle Scholar
  42. 42.
    Han, L.F., Liu, Y.M., Zhang, Z.J.: Improving the security of a quantum secret sharing protocol between multiparty and multiparty without entanglement. Phys. Lett. A 361, 24 (2007)MathSciNetCrossRefADSMATHGoogle Scholar
  43. 43.
    Han, L.F., et al.: Efficient multiparty-to-multiparty quantum secret sharing via continuous variable operations. Chin. Phys. Lett. 24, 3312 (2007)CrossRefADSGoogle Scholar
  44. 44.
    Han, L.F., et al.: Remote preparation of a class of three-qubit states. Opt. Commun. 281, 2690 (2008)CrossRefADSGoogle Scholar
  45. 45.
    Long, G.L., Liu, X.S.: Theoretical efficient high capacity quantum key distribution scheme. Phys. Rev. A 65, 032302 (2002)CrossRefADSGoogle Scholar
  46. 46.
    Xiao, L., Long, G.L., et al.: Efficient multiparty quantum-secret-sharing schemes. Phys. Rev. A 69, 052307 (2004)MathSciNetCrossRefADSGoogle Scholar
  47. 47.
    Chen, X., et al.: Quantum state sharing of an arbitrary three-qubit state by using three sets of W-class states. Quantum Inf. Process. 12, 2405 (2013)MathSciNetCrossRefADSMATHGoogle Scholar
  48. 48.
    Gao, Y.X., et al.: Preparation of Greenberger–Horne–Zeilinger and W states on a one-dimensional Ising chain by global control. Phys. Rev. A 87, 032335 (2013)CrossRefADSGoogle Scholar
  49. 49.
    Sweke, R., Sinayskiy, I., Petruccione, F.: Dissipative preparation of large W states in optical cavities. Phys. Rev. A 87, 042323 (2013)CrossRefADSGoogle Scholar
  50. 50.
    Solano, E., et al.: Reliable teleportation in trapped ions. Eur. Phys. J. D 13, 121 (2001)CrossRefADSGoogle Scholar
  51. 51.
    Riebe, M., et al.: Deterministic quantum teleportation with atoms. Nature 429, 734 (2004)CrossRefADSGoogle Scholar
  52. 52.
    Barrett, M.D., et al.: Deterministic quantum teleportation of atomic qubits. Nature 429, 737 (2004)CrossRefADSGoogle Scholar
  53. 53.
    Zheng, S.B.: Scheme for approximate conditional teleportation of an unknown atomic state without the Bell-state measurement. Phys. Rev. A 69, 064302 (2004)CrossRefADSGoogle Scholar
  54. 54.
    Ikram, M., Zhu, S.Y., Zubairy, M.S.: Quantum teleportation of an entangled state. Phys. Rev. A 62, 022307 (2000)MathSciNetCrossRefADSGoogle Scholar
  55. 55.
    Boschi, D., et al.: Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 80, 1121 (1998)MathSciNetCrossRefADSMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Qibin Ji
    • 1
  • Yimin Liu
    • 2
  • Chuanmei Xie
    • 1
  • Xiaofeng Yin
    • 1
  • Zhanjun Zhang
    • 1
  1. 1.School of Physics and Materials ScienceAnhui UniversityHefei China
  2. 2.Department of PhysicsShaoguan UniversityShaoguan China

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