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Quantum Information Processing

, Volume 13, Issue 9, pp 1951–1965 | Cite as

Schemes for remotely preparing an arbitrary four-qubit \(\chi \)-state

  • Song-Ya Ma
  • Ming-Xing Luo
  • Xiu-Bo Chen
  • Yi-Xian Yang
Article

Abstract

Two schemes via different entangled resources as the quantum channel are proposed to realize remote preparation of an arbitrary four-particle \(\chi \)-state with high success probabilities. To design these protocols, some useful and general measurement bases are constructed, which have no restrictions on the coefficients of the prepared states. It is shown that through a four-particle projective measurement and two-step three-particle projective measurement under the novel sets of mutually orthogonal basis vectors, the original state can be prepared with the probability 50 and 100 %, respectively. And for the first scheme, the special cases of the prepared state that the success probability reaches up to 100 % are discussed by the permutation group. Furthermore, the present schemes are extended to the non-maximally entangled quantum channel, and the classical communication costs are calculated.

Keywords

Remote state preparation Four-qubit \(\chi \)-state  Complete orthogonal basis Projective measurement Permutation group 

Notes

Acknowledgments

This work is supported by the National Natural Science Foundation of China (Nos. 61201253, 61303039, 61272514, 61003287, 61170272, 61121061, 61161140320), Fundamental Research Funds for the Central Universities (No. 2682014CX095), Program for New Century Excellent Talents in University (No. NCET-13-0681), the National Development Foundation for Cryptological Research (Grant No. MMJJ201401012), the Fok Ying Tong Education Foundation (No. 131067).

References

  1. 1.
    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, 1895–1899 (1993)MathSciNetCrossRefADSMATHGoogle Scholar
  2. 2.
    Lo, H.K.: Classical-communication cost in distributed quantum-information processing: a generalization of quantum-communication complexity. Phys. Rev. A 62, 012313 (2000)CrossRefADSGoogle Scholar
  3. 3.
    Pati, A.K.: Minimum classical bit for remote preparation and measurement of a qubit. Phys. Rev. A 63, 014302 (2001)CrossRefADSGoogle Scholar
  4. 4.
    Bennett, C.H., DiVincenzo, D.P., Shor, P.W., Smolin, J.A., Terhal, B.M., Wootters, W.K.: Remote state preparation. Phys. Rev. Lett. 87, 077902 (2001)CrossRefADSGoogle Scholar
  5. 5.
    Devetak, I., Berger, T.: Low-entanglement remote state preparation. Phys. Rev. Lett. 87, 197901 (2001)CrossRefADSGoogle Scholar
  6. 6.
    Leung, D.W., Shor, P.W.: Oblivious remote state preparation. Phys. Rev. Lett. 90, 127905 (2003)CrossRefADSGoogle Scholar
  7. 7.
    Berry, D.W., Sanders, B.C.: Optimal remote state preparation. Phys. Rev. Lett. 90, 057901 (2003)CrossRefADSGoogle Scholar
  8. 8.
    Ye, M.Y., Zhang, Y.S., Guo, G.C.: Faithful remote state preparation using finite classical bits and a nonmaximally entangled state. Phys. Rev. A 69, 022310 (2004)CrossRefADSGoogle Scholar
  9. 9.
    Kurucz, Z., Adam, P., Kis, Z., Janszky, J.: Continuous variable remote state preparation. Phys. Rev. A 72, 052315 (2005)CrossRefADSGoogle Scholar
  10. 10.
    Dai, H.Y., Chen, P.X., Liang, L.M., Li, C.Z.: Classical communication cost and remote preparation of the four-particle GHZ class state. Phys. Lett. A 355, 285–288 (2006)CrossRefADSGoogle Scholar
  11. 11.
    Wang, Y.H., Song, H.S.: Preparation of partially entangled W state and deterministic multi-controlled teleportation. Opt. Commun. 281, 489–493 (2008)CrossRefADSGoogle Scholar
  12. 12.
    Luo, M.X., Chen, X.B., Ma, S.Y., Yang, Y.X., Niu, X.X.: Joint remote preparation of an arbitrary three-qubit state. Opt. Commun. 283, 4796–4801 (2010)CrossRefADSGoogle Scholar
  13. 13.
    Luo, M.X., Chen, X.B., Ma, S.Y., Yang, Y.X., Hu, Z.M.: Deterministic remote preparation of an arbitrary W-class state with multiparty. J. Phys. B: At. Mol. Opt. Phys. 43, 065501 (2010)CrossRefADSGoogle Scholar
  14. 14.
    Ma, P.C., Zhan, Y.B.: Scheme for remotely preparing a four-particle entangled cluster-type state. Opt. Commun. 283, 2640–2643 (2010)CrossRefADSGoogle Scholar
  15. 15.
    Ma, S.Y., Chen, X.B., Luo, M.X., Zhang, R., Yang, Y.X.: Remote preparation of a four-particle entangled cluster-type state. Opt. Commun. 284, 4088–4093 (2011)CrossRefADSGoogle Scholar
  16. 16.
    An, N.B., Bich, C.T., Don, N.V.: Joint remote preparation of four-qubit cluster-type states revisited. J. Phys. B: At. Mol. Opt. Phys. 44, 135506 (2011)CrossRefADSGoogle Scholar
  17. 17.
    Zha, X.W., Song, H.Y.: Remote preparation of a two-particle state using a four-qubit cluster state. Opt. Commun. 284, 1472–1474 (2011)CrossRefADSGoogle Scholar
  18. 18.
    Xiao, X.Q., Liu, J.M., Zeng, G.H.: Joint remote state preparation of arbitrary two- and three-qubit states. J. Phys. B: At. Mol. Opt. Phys. 44, 075501 (2011)CrossRefADSGoogle Scholar
  19. 19.
    Chen, X.B., Ma, S.Y., Su, Y., Zhang, R., Yang, Y.X.: Controlled remote state preparation of arbitrary two and three qubit states via the Brown state. Quantum Inf. Process. 11, 1653–1667 (2012)MathSciNetCrossRefADSMATHGoogle Scholar
  20. 20.
    Zhan, Y.B.: Deterministic remote preparation of arbitrary two- and three-qubit states. EPL 98, 40005 (2012)CrossRefADSGoogle Scholar
  21. 21.
    Wang, Z.Y.: Highly efficient remote preparation of an arbitrary three-qubit state via a four-qubit cluster state and an EPR state. Quantum Inf. Process. 12, 1321–1334 (2013)CrossRefADSMATHGoogle Scholar
  22. 22.
    Peng, X., Zhu, X., Fang, X., Feng, M., Liu, M., Gao, K.: Experimental implementation of remote state preparation by nuclear magnetic resonance. Phys. Lett. A 306, 271–276 (2003)CrossRefADSGoogle Scholar
  23. 23.
    Peters, N.A., Barreiro, J.T., Goggin, M.E., Wei, T.C., Kwiat, P.G.: Remote state preparation: arbitrary remote control of photon polarization. Phys. Rev. Lett. 94, 150502 (2005)CrossRefADSGoogle Scholar
  24. 24.
    Rosenfeld, W., Berner, S., Volz, J., Weber, M., Weinfurter, H.: Remote preparation of an atomic quantum memory. Phys. Rev. Lett. 98, 050504 (2007)CrossRefADSGoogle Scholar
  25. 25.
    Xu, X.B., Liu, J.M.: Probabilistic remote preparation of a three-atom GHZ class state via cavity QED. Can. J. Phys. 84, 1089–1095 (2006)CrossRefADSGoogle Scholar
  26. 26.
    Barreiro, J.T., Wei, T.C., Kwiat, P.G.: Remote preparation of single-photon “hybrid” entangled and vector-polarization states. Phys. Rev. Lett. 105, 030407 (2010)CrossRefADSGoogle Scholar
  27. 27.
    Killoran, N., Biggerstaff, D.N., Kaltenbaek, R., Resch, K.J., Lutkenhaus, N.: Derivation and experimental test of fidelity benchmarks for remote preparation of arbitrary qubit states. Phys. Rev. A 81, 012334 (2010)CrossRefADSGoogle Scholar
  28. 28.
    Luo, M.X., Chen, X.B., Yang, Y.X., Niu, X.X.: Experimental architecture of joint remote state preparation. Quantum Inf. Process. 11, 751–767 (2012)MathSciNetCrossRefMATHGoogle Scholar
  29. 29.
    Yeo, Y., Chua, W.K.: Teleportation and dense coding with genuine multipartite entanglement. Phys. Rev. Lett. 96, 060502 (2006)CrossRefADSGoogle Scholar
  30. 30.
    Lin, S., Wen, Q.Y., Gao, F., Zhu, F.C.: Quantum secure direct communication with \(\chi \)-type entangled states. Phys. Rev. A 78, 064304 (2008)CrossRefADSGoogle Scholar
  31. 31.
    Wang, X.W., Xia, L.X., Wang, Z.Y., Zhang, D.Y.: Hierarchical quantum-information splitting. Opt. Commun. 283, 1196–1199 (2010)CrossRefADSGoogle Scholar
  32. 32.
    Qu, Z.G., Chen, X.B., Luo, M.X., Niu, X.X., Yang, Y.X.: Quantum steganography with large payload based on entanglement swapping of \(\chi \)-type entangled states. Opt. Commun. 284, 2075–2082 (2011)CrossRefADSGoogle Scholar
  33. 33.
    Wang, X.W., Yang, G.J.: Generation and discrimination of a type of four-partite entangled state. Phys. Rev. A 78, 024301 (2008)MathSciNetCrossRefADSGoogle Scholar
  34. 34.
    Wang, X.W.: Method for generating a new class of multipartite entangled state in cavity quantum electrodynamics. Opt. Commun. 282, 1052–1055 (2009)CrossRefADSGoogle Scholar
  35. 35.
    Liu, G.Y., Kuang, L.M.: Production of genuine entangled states of four atomic qubits. J. Phys. B: At. Mol. Opt. Phys. 42, 165505 (2009)CrossRefADSGoogle Scholar
  36. 36.
    Wang, H.F., Zhang, S.: Linear optical generation of multipartite entanglement with conventional photon detectors. Phys. Rev. A 79, 042336 (2009)CrossRefADSGoogle Scholar
  37. 37.
    Luo, M.X., Deng, Y.: Joint remote preparation of an arbitrary 4-qubit \(\chi \)-state. Int. J. Theor. Phys. 51, 3027–3036 (2012)MathSciNetCrossRefMATHGoogle Scholar
  38. 38.
    Cameron, P.J.: Permutation Groups. LMS Student Text, 45. Cambridge University Press, Cambridge (1999)CrossRefGoogle Scholar
  39. 39.
    Bennett, C.H., Bernstein, H.J., Popescu, S., Schumacher, B.: Concentrating partial entanglement by local operations. Phys. Rev. A 53, 2046–2052 (1996)CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Song-Ya Ma
    • 1
  • Ming-Xing Luo
    • 2
  • Xiu-Bo Chen
    • 3
    • 4
  • Yi-Xian Yang
    • 3
    • 4
  1. 1.School of Mathematics and Information SciencesHenan UniversityKaifengChina
  2. 2.Information Security and National Computing Grid Laboratory, School of Information Science and TechnologySouthwest Jiaotong UniversityChengduChina
  3. 3.Information Security Center, State Key Laboratory of Networking and Switching TechnologyBeijing University of Posts and TelecommunicationsBeijingChina
  4. 4.State Key Laboratory of Information Security, Institute of Information EngineeringChinese Academy of SciencesBeijingChina

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