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

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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.

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References

  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)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. Lo, H.K.: Classical-communication cost in distributed quantum-information processing: a generalization of quantum-communication complexity. Phys. Rev. A 62, 012313 (2000)

    Article  ADS  Google Scholar 

  3. Pati, A.K.: Minimum classical bit for remote preparation and measurement of a qubit. Phys. Rev. A 63, 014302 (2001)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  5. Devetak, I., Berger, T.: Low-entanglement remote state preparation. Phys. Rev. Lett. 87, 197901 (2001)

    Article  ADS  Google Scholar 

  6. Leung, D.W., Shor, P.W.: Oblivious remote state preparation. Phys. Rev. Lett. 90, 127905 (2003)

    Article  ADS  Google Scholar 

  7. Berry, D.W., Sanders, B.C.: Optimal remote state preparation. Phys. Rev. Lett. 90, 057901 (2003)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  9. Kurucz, Z., Adam, P., Kis, Z., Janszky, J.: Continuous variable remote state preparation. Phys. Rev. A 72, 052315 (2005)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  11. Wang, Y.H., Song, H.S.: Preparation of partially entangled W state and deterministic multi-controlled teleportation. Opt. Commun. 281, 489–493 (2008)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  14. Ma, P.C., Zhan, Y.B.: Scheme for remotely preparing a four-particle entangled cluster-type state. Opt. Commun. 283, 2640–2643 (2010)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. Zhan, Y.B.: Deterministic remote preparation of arbitrary two- and three-qubit states. EPL 98, 40005 (2012)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  MATH  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  24. Rosenfeld, W., Berner, S., Volz, J., Weber, M., Weinfurter, H.: Remote preparation of an atomic quantum memory. Phys. Rev. Lett. 98, 050504 (2007)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  29. Yeo, Y., Chua, W.K.: Teleportation and dense coding with genuine multipartite entanglement. Phys. Rev. Lett. 96, 060502 (2006)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  31. Wang, X.W., Xia, L.X., Wang, Z.Y., Zhang, D.Y.: Hierarchical quantum-information splitting. Opt. Commun. 283, 1196–1199 (2010)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  33. Wang, X.W., Yang, G.J.: Generation and discrimination of a type of four-partite entangled state. Phys. Rev. A 78, 024301 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  34. Wang, X.W.: Method for generating a new class of multipartite entangled state in cavity quantum electrodynamics. Opt. Commun. 282, 1052–1055 (2009)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  36. Wang, H.F., Zhang, S.: Linear optical generation of multipartite entanglement with conventional photon detectors. Phys. Rev. A 79, 042336 (2009)

    Article  ADS  Google Scholar 

  37. Luo, M.X., Deng, Y.: Joint remote preparation of an arbitrary 4-qubit \(\chi \)-state. Int. J. Theor. Phys. 51, 3027–3036 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  38. Cameron, P.J.: Permutation Groups. LMS Student Text, 45. Cambridge University Press, Cambridge (1999)

    Book  Google Scholar 

  39. Bennett, C.H., Bernstein, H.J., Popescu, S., Schumacher, B.: Concentrating partial entanglement by local operations. Phys. Rev. A 53, 2046–2052 (1996)

    Article  ADS  Google Scholar 

Download references

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).

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Authors and Affiliations

  1. School of Mathematics and Information Sciences, Henan University, Kaifeng, 475004, China

    Song-Ya Ma

  2. Information Security and National Computing Grid Laboratory, School of Information Science and Technology, Southwest Jiaotong University, Chengdu, 610031, China

    Ming-Xing Luo

  3. Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Xiu-Bo Chen & Yi-Xian Yang

  4. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China

    Xiu-Bo Chen & Yi-Xian Yang

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  1. Song-Ya Ma
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  2. Ming-Xing Luo
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Correspondence to Song-Ya Ma.

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Ma, SY., Luo, MX., Chen, XB. et al. Schemes for remotely preparing an arbitrary four-qubit \(\chi \)-state. Quantum Inf Process 13, 1951–1965 (2014). https://doi.org/10.1007/s11128-014-0788-9

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  • DOI: https://doi.org/10.1007/s11128-014-0788-9

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