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Linear-Optical Proposal for Implementation of the Two-Logic-Qubit Controlled Phase Gate in Decoherence-Free Subspace with Conventional Photon Detectors

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Abstract

A linear-optical scheme is proposed to implement the nondeterministic two-qubit controlled phase gate in decoherence-free subspace (DFS) with a certain success probability. The proposed setup requires simple linear-optical elements, two pairs of the two-photon polarization entangled states as auxiliary resource, and the conventional photon detectors that only distinguish the vacuum and nonvacuum Fock number states. A sophisticated single-photon detector distinguishing one or two photon states is unnecessary. This makes the protocol more realizable in experiments.

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References

  1. Steane, A.: Proc. R. Soc. A 452, 2551 (1996)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. Calderbank, A.R., Shor, P.W.: Phys. Rev. A 54, 1098 (1996)

    Article  ADS  Google Scholar 

  3. Chiaverini, J., Leibfried, D., Schaetz, T., Barrett, M.D., Blakestad, R.B., Britton, J., Itano, W.M., Jost, J.D., Knill, E., Langer, C., Ozeri, R., Wineland, D.J.: Nat. (London) 432, 602 (2004)

    Article  ADS  Google Scholar 

  4. Duan, L.M., Cirac, J.I., Zoller, P.: Science 292, 1695 (2001)

    Article  ADS  Google Scholar 

  5. Jones, J.A., Vedral, V., Ekert, A., Castagnoli, G.: Nat. (London) 403, 869 (2000)

    Article  ADS  Google Scholar 

  6. Zhu, S.L., Wang, Z.D.: Phys. Rev. Lett. 91, 187902 (2003)

    Article  ADS  Google Scholar 

  7. Feng, X.L., Wang, Z., Wu, C., Kwek, L.C., Lai, C.H., Oh, C.H.: vol. 75, p 052312 (2007)

  8. Kastoryano, M.J., Reiter, F., Sørensen, A.S.: Phys. Rev. Lett. 106, 090502 (2011)

    Article  ADS  Google Scholar 

  9. Bhaktavatsala Rao, D.D., Mølmer, K.: Phys. Rev. Lett. 111, 033606 (2013)

    Article  Google Scholar 

  10. Carr, A.W., Saffman, M. Phys. Rev. Lett. 111, 033607 (2013)

    Article  ADS  Google Scholar 

  11. Shen, L.T., Chen, X.Y., Yang, Z.B., Wu, H. Z., Zheng, S.B.: Europhys. Lett. 99, 20003 (2012)

    Article  ADS  Google Scholar 

  12. Song, J., Xia, Y., Sun, X.D., Song, H.S.: Phys. Rev. A 86, 034303 (2012)

    Article  ADS  Google Scholar 

  13. Shao, X.Q., You, J.B., Zheng, T.Y., Oh, C.H., Zhang, S.: Phys. Rev. A 89, 052313 (2014)

    Article  ADS  Google Scholar 

  14. Su, S.L., Shao, X.Q., Wang, H.F., Zhang, S.: Phys. Rev. A 90, 054302 (2014)

    Article  ADS  Google Scholar 

  15. Su, S.L., Shao, X.Q., Wang, H.F., Zhang, S.: ibid. Sci. Rep. 4, 7566 (2014)

    Article  Google Scholar 

  16. Bennett, C.H., Brassard, G., Popescu, S., Schumacher, B., Smolin, J.A., Wootters, W.K.: Phys. Rev. Lett. 76, 722 (1996)

    Article  ADS  Google Scholar 

  17. Pan J.W., Gasparoni, S., Ursin, R., Weihs, G., Zeilinger, A.: Nature (London) 423, 417 (2003)

    Article  ADS  Google Scholar 

  18. Sheng, Y.B., Deng, F.G., Zhou, H.Y.: Phys. Rev. A 77, 042308 (2008)

    Article  ADS  Google Scholar 

  19. Pan, J.W., Simon, C., Zellinger, A.: Nature 410, 1067 (2001)

    Article  ADS  Google Scholar 

  20. Simon, C., Pan, J.W.: Phys. Rev. Lett. 89, 257901 (2002)

    Article  ADS  Google Scholar 

  21. Wang, C., Zhang, Y., Jin, G.S.: Quant. Inf. Comput. 11, 0988 (2011)

    MathSciNet  Google Scholar 

  22. Wang, C., Zhang, Y., Jin, G.S.: Phys. Rev. A 84, 032307 (2011)

    Article  ADS  Google Scholar 

  23. Sheng, Y.B., Zhou, L., Long, G.L.: Phys. Rev. A 88, 022302 (2013)

    Article  ADS  Google Scholar 

  24. Ren, B.C., Deng, F.G.: Laser Phys. Lett. 10, 115201 (2013)

    Article  ADS  Google Scholar 

  25. Ren, B.C., Du, F.F., Deng, F.G.: Phys. Rev. A 90, 052309 (2014)

    Article  ADS  Google Scholar 

  26. Sheng, Y.B., Deng, F.G.: Phys. Rev. A 81, 032307 (2010)

    Article  ADS  Google Scholar 

  27. Li, X.H.: Phys. Rev. A 82, 044304 (2010)

    Article  ADS  Google Scholar 

  28. Sheng, Y.B., Deng, F.G.: Phys. Rev. A 82, 044305 (2010)

    Article  ADS  Google Scholar 

  29. Deng, F.G.: Phys. Rev. A 83, 062316 (2011)

    Article  ADS  Google Scholar 

  30. Sheng, Y.B., Zhou, L.: Laser Phys. Lett. 11, 085203 (2014)

    Article  ADS  Google Scholar 

  31. Sheng, Y.B., Zhou, L.: Sci. Rep. 5, 7815 (2015)

    Article  ADS  Google Scholar 

  32. Bennett, C.H., Bernstein, H. J., Popescu, S., Schumacher, B.: Phys. Rev. A 53, 2046 (1996)

    Article  ADS  Google Scholar 

  33. Yamamoto, T., Koashi, M., Imoto, N.: Phys. Rev. A 64, 012304 (2001)

    Article  ADS  Google Scholar 

  34. Zhao, Z., Pan, J.W., Zhan, M.S.: Phys. Rev. A 64, 014301 (2001)

    Article  ADS  Google Scholar 

  35. Sheng, Y.B., Deng, F.G., Zhou, H.Y.: Phys. Rev. A 77, 062325 (2008)

    Article  ADS  Google Scholar 

  36. Sheng, Y.B., Zhou, L., Zhao, S.M., Zheng, B.Y.: Phys. Rev. A 85, 012307 (2012)

    Article  ADS  Google Scholar 

  37. Deng, F.G.: Phys. Rev. A 85, 022311 (2012)

    Article  ADS  Google Scholar 

  38. Wang, C.: Phys. Rev. A 86, 012323 (2012)

    Article  ADS  Google Scholar 

  39. Ren, B.C., Du, F.F., Deng, F.G.: Phys. Rev. A 88, 012302 (2013)

    Article  ADS  Google Scholar 

  40. Ren, B.C., Long, G.L.: Opt. Express 22, 6547 (2014)

    Article  ADS  Google Scholar 

  41. Li, X.H., Ghose, S.: Laser phys. Lett. 11, 125201 (2014)

    Article  ADS  Google Scholar 

  42. Li, X.H., Ghose, S.: Opt. Express 23, 3550 (2015)

    Article  ADS  Google Scholar 

  43. Li, X.H., Deng, F.G., Zhou, H.Y.: Appl. Phys. Lett. 91, 144101 (2007)

    Article  ADS  Google Scholar 

  44. Deng, F.G., Li, X.H., Zhou, H.Y.: Quant. Inform. Comput. 11, 913 (2011)

    MathSciNet  MATH  Google Scholar 

  45. Duan, L.M., Guo, G.-C.: Phys. Rev. Lett. 79, 1953 (1997)

    Article  ADS  Google Scholar 

  46. Zanardi, P., Rasetti, M.: Phys. Rev. Lett. 79, 3306 (1997)

    Article  ADS  Google Scholar 

  47. Lidar, D.A., Chuang, I.L., Whaley, K.B.: Phys. Rev. Lett. 81, 2594 (1998)

    Article  ADS  Google Scholar 

  48. Feng, M.: Phys. Rev. A 63, 052308 (2001)

    Article  ADS  Google Scholar 

  49. Kielpinski, D., Monroe, C., Wineland, D.J.: Nat. (London) 417, 709 (2002)

    Article  ADS  Google Scholar 

  50. Li, X.H., Deng, F.G., Zhou, H.Y.: Phys. Rev. A 78, 022321 (2008)

    Article  ADS  Google Scholar 

  51. Boileau, J.C., Gottesman, D., Laflamme, R., Poulin, D., Spekkens, R.W.: Phys. Rev. Lett. 92, 017901 (2004)

    Article  ADS  Google Scholar 

  52. Li, C.Y., Zhang, Z.R., Sun, S.H., Jiang, M.S., Liang, L.M.: J. Opt. Soc. Am. B 30, 1872 (2013)

    Article  ADS  Google Scholar 

  53. Zhang, Z.R., Li, C.Y., Wu, C.W., Dai, H.Y., Li, C.Z.: Phys. Rev. A 86, 042320 (2012)

    Article  ADS  Google Scholar 

  54. Zhang, Z.R., Wu, C.W., Li, C.Y., Dai, H.Y., Li, C.Z.: Phys. Rev. A 87, 062325 (2013)

    Article  ADS  Google Scholar 

  55. Kwiat, P., Berglund, A.J., Altepeter, J.B., White, A.G.: Science 290, 498 (2000)

    Article  ADS  Google Scholar 

  56. Bourennane, M., Eibl, M., Gaertner, S., Kurtsiefer, C., Cabello, A., Weinfurter, H.: Phys. Rev. Lett. 92, 107901 (2004)

    Article  ADS  Google Scholar 

  57. Viola, L., Fortunato, E.M., Pravia, M.A., Knill, E., Laflamme, R., Cory, D.G.: Science 293, 2059 (2001)

    Article  ADS  Google Scholar 

  58. Roos, C.F., Lancaster, G.P.T., Riebe, M., Häffner, H., Hänsel, W., Gulde, S., Becher, C., Eschner, J., Schmidt-Kaler, F., Blatt, R.: Phys. Rev. Lett. 92, 220402 (2004)

    Article  ADS  Google Scholar 

  59. Häffner, H., Schmidt-Kaler, F., Hänsel, W., Roos, C.F., Körber, T., Chwalla, M., Riebe, M., Benhelm, J., Rapol, U.D., Becher, C., Blatt, R.: Appl. Phys. B 81, 151 (2005)

    Article  ADS  Google Scholar 

  60. Kielpinski, D., Meyer, V., Rowe, M.A., Sackett, C.A., Itano, W.M., Monroe, C., Wineland, D.J.: Science 291, 1013 (2001)

    Article  ADS  Google Scholar 

  61. Brooke, P.G.: Phys. Rev. A 75, 022320 (2007)

    Article  ADS  Google Scholar 

  62. Taylor, J.M., Engel, H.A., Dür, W., Yacoby, A., Marcus, C.M., Zoller, P., Lukin, M.D.: Nat. Phys. 1, 177 (2005)

    Article  Google Scholar 

  63. Feng, Z.B, Zhang, X.D.: Phys. Lett. A 372, 16 (2007)

    Article  ADS  Google Scholar 

  64. Browne, D.E., Rudolph, T.: Phys. Rev. Lett. 95, 010501 (2005)

    Article  ADS  Google Scholar 

  65. Franson, J.D., Donegan, M.M., Fitch, M.J., Jacobs, B.C., Pittman, T.B.: ibid 89, 137901 (2002)

    Article  ADS  Google Scholar 

  66. Okamoto, R., Hofmann, H.F., Takeuchi, S., Sasaki, K.: ibid 95, 210506 (2005)

    Article  ADS  Google Scholar 

  67. Thiel, C., Von Zanthier, J., Bastin, T., Solano, E., Agarwal, G.S.: ibid 99, 193602 (2007)

    Article  ADS  Google Scholar 

  68. Zeilinger, A., Horne, M.A., Weinfurter, H., żukowski1, M.: ibid 78 (1997). 3031

  69. Xia, Y., Song, J., Song, H.S.: Appl. Phys. Lett. 92, 021127 (2008)

    Article  ADS  Google Scholar 

  70. Xia, Y., Lu, P.-M., Zeng, Y.-Z.: Quant. Inf. Process. 11, 605 (2012)

    Article  Google Scholar 

  71. Wang, H.F., Zhang, S.: Phys. Rev. A 79, 042336 (2009)

    Article  ADS  Google Scholar 

  72. Zou, X.B., Li, K., Guo, G.C.: Phys. Rev. A 74, 044305 (2006)

    Article  ADS  Google Scholar 

  73. Wang, T.J., Deng, F.G.: Commun. Theor. Phys. 55, 795 (2011)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  74. Li, X.H., Zhao, B.K., Sheng, Y.B., Deng, F.G., Zhou, H.Y.: Int. J. Quantum Inform. 7, 1479 (2009)

    Article  MATH  Google Scholar 

  75. Li, T., Deng, F.-G.: Int. J. Theor. Phys. 53, 3026 (2014)

    Article  MATH  Google Scholar 

  76. Wang, H.F.: Int. J. Theor. Phys. 52, 15 (2013)

    Article  MATH  Google Scholar 

  77. Pittman, T.B., Jacobs, B.C., Franson, J.D.: Phys. Rev. A 64, 062311 (2001)

    Article  ADS  Google Scholar 

  78. Pittman, T.B., Jacobs, B.C., Franson, J.D.: ibid Phys. Rev. A 69, 042306 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  79. Zou, X.B., Zhang, S.L., Li, K., Guo, G.C.: Phys. Rev. A 75, 034302 (2007)

    Article  ADS  Google Scholar 

  80. Barnett, S.M., Phillips, L.S., Pegg, D.T.: Opt. Commu 158, 45 (1998)

    Article  ADS  Google Scholar 

  81. Akopian, N., Lindner, N.H., Poem, E., Berlatzky, Y., Avron, J., Gershoni, D., Gerardot, B.D., Petroff, P. M.: Phys. Rev. Lett. 96, 130501 (2006)

    Article  ADS  Google Scholar 

  82. Benson, O., Santori, C., Pelton, M., Yamamoto, Y.: Phys. Rev. Lett. 84, 2513 (2000)

    Article  ADS  Google Scholar 

  83. Yamamoto, T., Hayashi, K., Özdemir, S.K., Koashi, M., Imoto, N.: Nat. Photon 2, 488 (2008)

    Article  Google Scholar 

  84. Walther, P., Resch, K.J., Zeilinger, A.: Phys. Rev. Lett. 94, 240501 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  85. Tashima, T., Wakatsuki, T., Özdemir, S.K., Yamamoto, T., Koashi, M., Imoto, N.: Phys. Rev. Lett. 102, 130502 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  86. Glancy, S., LoSecco, J.M., Vasconcelos, H.M., Tanner, C.E.: Phys. Rev. A 65, 062317 (2002)

    Article  ADS  Google Scholar 

  87. Knill, E., Laflamme, R., Milburn, G.J.: Nat. (London) 409, 46 (2001)

    Article  ADS  Google Scholar 

  88. Ralph, T.C., Langford, N.K., Bell, T.B., White, A.G.: Phys. Rev. A 65, 062324 (2002)

    Article  ADS  Google Scholar 

  89. Gasparoni, S., Pan, J.W., Walther, P., Rudolph, T., Zeilinger, A.: Phys. Rev. Lett. 93, 020504 (2004)

    Article  ADS  Google Scholar 

  90. O’Brien, J.L., Pryde, G.J., White, A.G., Ralph, T.C., Branning, D.: Nat. (London) 426, 264 (2003)

    Article  ADS  Google Scholar 

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Correspondence to Shou Zhang.

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This work is supported by the National Natural Science Foundation of China under Grant Nos. 61465013, 11465020, and 11264042; the Program for Chun Miao Excellent Talents of Jilin Provincial Department of Education under Grant No. 201316; and the Talent Program of Yanbian University of China under Grant No. 950010001.

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Su, SL., Guo, Q., Wang, HF. et al. Linear-Optical Proposal for Implementation of the Two-Logic-Qubit Controlled Phase Gate in Decoherence-Free Subspace with Conventional Photon Detectors. Int J Theor Phys 55, 447–456 (2016). https://doi.org/10.1007/s10773-015-2679-y

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