Advertisement

International Journal of Theoretical Physics

, Volume 50, Issue 8, pp 2410–2425 | Cite as

Controlled Remote Preparation of a Two-Qubit State via Positive Operator-Valued Measure and Two Three-Qubit Entanglements

  • Jin-Fan SongEmail author
  • Zhang-Yin WangEmail author
Article

Abstract

Utilizing a proper positive operator-valued measure (POVM) instead of usual projective measurement, we present a new scheme for remote preparation of a general two-qubit state in either distant ministrant’s place. In the scheme, we exploit a GHZ-type state and a W-type state as the shared quantum channel, and the remote two-qubit preparation can be realized in a probabilistic manner via two ministrants’ collaboration. Furthermore, we also explore the scheme’s applications to some special ensembles of states in detail. The success probabilities in different cases are calculated, respectively, which show that the remote preparation can be achieved with higher probability provided that the prepared state belongs to the special ensembles.

Keywords

Remote state preparation GHZ-type state W-type state Positive operator-valued measure Unitary operation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bennett, C.H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Phys. Rev. Lett. 70, 1895 (1993) ADSzbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Lo, H.K.: Phys. Rev. A 62, 012313 (2000) ADSCrossRefGoogle Scholar
  3. 3.
    Pati, A.K.: Phys. Rev. A 63, 014302 (2001) ADSCrossRefGoogle Scholar
  4. 4.
    Bennett, C.H., et al.: Phys. Rev. Lett. 87, 077902 (2001) ADSCrossRefGoogle Scholar
  5. 5.
    Devetak, I., Berger, T.: Phys. Rev. Lett. 87, 177901 (2001) ADSCrossRefGoogle Scholar
  6. 6.
    Zeng, B., Zhang, P.: Phys. Rev. A 65, 022316 (2002) ADSCrossRefGoogle Scholar
  7. 7.
    Berry, D.W., Sanders, B.C.: Phys. Rev. Lett. 90, 027901 (2003) ADSCrossRefGoogle Scholar
  8. 8.
    Kurucz, Z., Adam, P., Janszky, J.: Phys. Rev. A 73, 062301 (2006) ADSCrossRefGoogle Scholar
  9. 9.
    Hayashi, A., Hashimoto, T., Horibe, M.: Phys. Rev. A 67, 052302 (2003) ADSCrossRefGoogle Scholar
  10. 10.
    Abeyesinghe, A., Hayden, P.: Phys. Rev. A 68, 062319 (2003) ADSCrossRefGoogle Scholar
  11. 11.
    Ye, M.Y., Zhang, Y.S., Guo, G.C.: Phys. Rev. A 69, 022310 (2004) ADSCrossRefGoogle Scholar
  12. 12.
    Yu, Y.F., Feng, J., Zhan, M.S.: Phys. Lett. A 310, 329 (2003) ADSzbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Huang, Y.X., Zhan, M.S.: Phys. Lett. A 327, 404 (2004) ADSCrossRefMathSciNetzbMATHGoogle Scholar
  14. 14.
    Paris, M.G.A., Cola, M., Bonifacio, R.: J. Opt. B 5, S360 (2003) ADSCrossRefGoogle Scholar
  15. 15.
    Kurucz, Z., Adam, P., Kis, Z., Janszky, J.: Phys. Rev. A 72, 052315 (2005) ADSCrossRefGoogle Scholar
  16. 16.
    Babichev, S.A., Brezger, B., Lvovsky, A.I.: Phys. Rev. Lett. 92, 047903 (2004) ADSCrossRefGoogle Scholar
  17. 17.
    Gour, G., Sanders, B.C.: Phys. Rev. Lett. 93, 260501 (2004) ADSCrossRefGoogle Scholar
  18. 18.
    Berry, D.W.: Phys. Rev. A 70, 062306 (2004) ADSCrossRefGoogle Scholar
  19. 19.
    Bennett, C.H., Hayden, P., Leung, D.W., Shor, P.W., Winter, A.: IEEE Trans. Inf. Theory 51, 56 (2005) CrossRefMathSciNetGoogle Scholar
  20. 20.
    Peng, X.H., Zhu, X., Fang, X., Feng, M., Liu, M., Gao, K.: Phys. Lett. A 306, 271 (2003) ADSCrossRefGoogle Scholar
  21. 21.
    Xiang, G.Y., Li, J., Bo, Y., Guo, G.C.: Phys. Rev. A 72, 012315 (2005) ADSCrossRefGoogle Scholar
  22. 22.
    Peters, N.A., Barreiro, J.T., Goggin, M.E., Wei, T.C., Kwiat, P.G.: Phys. Rev. Lett. 94, 150502 (2005) ADSCrossRefGoogle Scholar
  23. 23.
    Shi, B.S., Tomita, A.: J. Opt. B 4, 380 (2002) ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    Liu, J.M., Wang, Y.Z.: Phys. Lett. A 316, 159 (2003) ADSCrossRefMathSciNetzbMATHGoogle Scholar
  25. 25.
    Liu, J.M., et al.: Europhys. Lett. 87, 30006 (2009) ADSCrossRefGoogle Scholar
  26. 26.
    Liu, J.M., et al.: J. Phys. B 42, 055508 (2009) ADSCrossRefGoogle Scholar
  27. 27.
    Xiao, X.Q., et al.: Int. J. Theor. Phys. 46, 2378 (2007) zbMATHCrossRefGoogle Scholar
  28. 28.
    Yu, C.S., Song, H.S., Wang, Y.H.: Phys. Rev. A 73, 022340 (2006) ADSCrossRefGoogle Scholar
  29. 29.
    Dai, H.Y., Chen, P.X., Liang, L.M., Li, C.Z.: Phys. Lett. A 355, 285 (2006) ADSCrossRefGoogle Scholar
  30. 30.
    Dai, H.Y., et al.: Commun. Theor. Phys. 50, 73 (2008) ADSCrossRefGoogle Scholar
  31. 31.
    Dai, H.Y., et al.: Chin. Phys. B 17, 28 (2008) ADSGoogle Scholar
  32. 32.
    Zhan, Y.B.: Commun. Theor. Phys. 43, 637 (2005) CrossRefGoogle Scholar
  33. 33.
    Ma, P.C., Zhan, Y.B.: Chin. Phys. 17, 445 (2008) CrossRefGoogle Scholar
  34. 34.
    Ma, P.C., Zhan, Y.B.: Opt. Commun. 283, 2640 (2010) ADSCrossRefGoogle Scholar
  35. 35.
    Zhang, Y.Q., Jin, X.R., Zhang, S.: Chin. Phys. B 14, 1732 (2005) ADSCrossRefGoogle Scholar
  36. 36.
    Xia, Y., et al.: J. Phys. B, At. Mol. Opt. Phys. 40, 3719 (2007) ADSCrossRefGoogle Scholar
  37. 37.
    Xia, Y., et al.: Opt. Commun. 277, 219 (2007) ADSCrossRefGoogle Scholar
  38. 38.
    Wang, Y.H., Song, H.S.: Opt. Commun. 281, 489 (2008) ADSCrossRefGoogle Scholar
  39. 39.
    Wang, Z.Y.: Int. J. Quant. Inform. Accepted, in press Google Scholar
  40. 40.
    Wang, Z.Y.: Int. J. Theor. Phys. 49, 1357 (2010) zbMATHCrossRefGoogle Scholar
  41. 41.
    Wang, Z.Y., et al.: Commun. Theor. Phys. 52, 235 (2009) ADSzbMATHCrossRefGoogle Scholar
  42. 42.
    Liu, Y.M., Wang, Z.Y., Liu, X.S., Zhang, Z.J.: Int. J. Quantum Inf. 7, 991 (2009) zbMATHCrossRefGoogle Scholar
  43. 43.
    Wang, D., et al.: Opt. Commun. 281, 871 (2008) ADSCrossRefGoogle Scholar
  44. 44.
    Shi, G.F.: Mod. Phys. Lett. B 24, 995 (2010) ADSzbMATHCrossRefGoogle Scholar
  45. 45.
    Yan, F.L., Zhang, G.H.: Int. J. Quantum Inf. 6, 485 (2008) zbMATHCrossRefMathSciNetGoogle Scholar
  46. 46.
    Wang, M.Y., Yan, F.L.: Commun. Theor. Phys. 54, 792 (2010) ADSCrossRefMathSciNetzbMATHGoogle Scholar
  47. 47.
    Hou, K., et al.: Int. J. Quantum Inf. 6, 1183 (2008) zbMATHCrossRefGoogle Scholar
  48. 48.
    Deng, L., Chen, A.X., Xu, Y.Q.: Chin. Phys. B 17, 3725 (2008) ADSCrossRefGoogle Scholar
  49. 49.
    Ba An, N., Kim, J.: J. Phys. B 41, 095501 (2008) ADSCrossRefGoogle Scholar
  50. 50.
    Ba An, N.: J. Phys. B 42, 125501 (2009) ADSCrossRefGoogle Scholar
  51. 51.
    Ba An, N.: Opt. Commun. 2(83), 4113 (2010) ADSCrossRefGoogle Scholar
  52. 52.
    An, N.Ba., Kim, J.: Int. J. Quantum Inf. 6, 1051 (2008) zbMATHCrossRefGoogle Scholar
  53. 53.
    Luo, M.X., Chen, X.B., Ma, S.Y., Yang, Y.X., Hu, Z.M.: J. Phys. B 43, 065501 (2010) ADSCrossRefGoogle Scholar
  54. 54.
    Luo, M.X., et al.: Int. J. Theor. Phys. 49, 1262 (2010) zbMATHCrossRefGoogle Scholar
  55. 55.
    Mei, Y.X., Chen, L., Chen, Y.X.: Chin. Phys. Lett. 23, 548 (2006) ADSCrossRefGoogle Scholar
  56. 56.
    Tan, J., Fang, M.F.: Chin. Phys. B 15, 2514 (2006) CrossRefGoogle Scholar
  57. 57.
    Li, W.L., Li, C.F., Guo, G.C.: Phys. Rev. A 61, 034301 (2000) ADSCrossRefMathSciNetGoogle Scholar
  58. 58.
    Helstrom, C.W.: Quantum Dectection and Estimation Theory. Academic Press, New York (1976) Google Scholar
  59. 59.
    Mar, T., Horodecki, P.: quant-ph/9906039
  60. 60.
    Yan, F.L., Ding, H.W.: Chin. Phys. Lett. 23, 17 (2006) ADSCrossRefGoogle Scholar
  61. 61.
    Wang, Z.Y., et al.: Commun. Theor. Phys. 46, 859 (2006) CrossRefGoogle Scholar
  62. 62.
    Bouwmeester, D., Pan, J.W., Daniell, M., Weinfurter, H., Zeilinger, A.: Phys. Rev. Lett. 82, 1345 (1999) ADSzbMATHCrossRefMathSciNetGoogle Scholar
  63. 63.
    Solano, E., Agarwal, D.S., Walther, H.: Phys. Rev. Lett. 90, 027903 (2003) ADSCrossRefGoogle Scholar
  64. 64.
    Sackett, C.A., Kielpinski, D., King, B.E., et al.: Nature 404, 256 (2000) ADSCrossRefGoogle Scholar
  65. 65.
    Guo, G.P., Li, C.F., Li, J., Guo, G.C.: Phys. Rev. A 65, 042102 (2002) ADSCrossRefGoogle Scholar
  66. 66.
    Zou, X.B., Pahlke, K., Mathis, W.: Phys. Rev. A 66, 044302 (2001) ADSCrossRefGoogle Scholar
  67. 67.
    Zheng, S.B.: Phys. Rev. A 70, 045804 (2004) ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.College of Physics & Electronic EngineeringNanyang Normal UniversityNanyang HenanChina
  2. 2.Key Laboratory of Optoelectronic Information Acquisition & Manipulation of Ministry of Education of China, School of Physics & Material ScienceAnhui UniversityHefeiChina

Personalised recommendations