Quantum Information Processing

, Volume 13, Issue 6, pp 1413–1424 | Cite as

Deterministic transmission of an arbitrary single-photon polarization state through bit-flip error channel

  • Li Dong
  • Jun-Xi Wang
  • Hong-Zhi Shen
  • Dan Li
  • Xiao-Ming Xiu
  • Ya-Jun Gao
  • X. X. Yi


We present two error-tolerance transmission protocols of a single-photon polarization state when bit-flip error is taken into account. For achieving the transmission target of the single-photon state, the first protocol needs to encode it to a nonmaximally entangled Bell state. Exploiting the interaction of the polarization entanglement with spatial entanglement between two photons, its success probability is 100 %. Different from the first protocol, the second one utilizes the idea of teleportation with an auxiliary Bell state. By performing quantum nondemolition measurement to analyze the parity, conventional measurement, and unitary transformation operations, the success probability of the second protocol is approximately unity. Furthermore, the second protocol can be generalized to the error-tolerance transmission of an arbitrary mixed state or the distribution of an arbitrary multi-photon entangled state.


Error-tolerance transmission Bit-flip error channel  Parity analysis 



This study was supported by the National Natural Science Foundation of China (Grant Nos. 11305016, 61301133, 11271055) and the Research Programs of the Educational Office of Liaoning Province of China (Grant No. L2013425). We acknowledge anonymous reviewers for enlightening instructions.


  1. 1.
    Shor, P.W.: Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52(4), R2493–R2496 (1995)ADSCrossRefGoogle Scholar
  2. 2.
    Steane, A.M.: Error correcting codes in quantum theory. Phys. Rev. Lett. 77(5), 793–797 (1996)MathSciNetADSCrossRefMATHGoogle Scholar
  3. 3.
    Bennett, C.H., DiVincenzo, D.P., Smolin, J.A., Wootters, W.K.: Mixed-state entanglement and quantum error correction. Phys. Rev. A 54(5), 3824–3851 (1996)MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    Laflamme, R., Miquel, C., Paz, J.P., Zurek, W.H.: Perfect quantum error correcting code. Phys. Rev. Lett. 77(1), 198–201 (1996)ADSCrossRefGoogle Scholar
  5. 5.
    Bouwmeester, D.: Bit-flip-error rejection in optical quantum communication. Phys. Rev. A 63(3), 040301 (2001)ADSCrossRefGoogle Scholar
  6. 6.
    Kalamidas, D.: Feasible quantum error detection with linear optics. Phys. Lett. A 321(2), 87–93 (2004)MathSciNetADSCrossRefMATHGoogle Scholar
  7. 7.
    Wang, X.-B.: Quantum error-rejection code with spontaneous parametric down-conversion. Phys. Rev. A 69(2), 022320 (2004)ADSCrossRefGoogle Scholar
  8. 8.
    Yamamoto, T., Shimamura, J., Özdemir, S.K., Koashi, M., Imoto, N.: Faithful qubit distribution assisted by one additional qubit against collective noise. Phys. Rev. Lett. 95(4), 040503 (2005)ADSCrossRefGoogle Scholar
  9. 9.
    Kalamidas, D.: Single-photon quantum error rejection and correction with linear optics. Phys. Lett. A 343(5), 331–335 (2005)ADSCrossRefMATHGoogle Scholar
  10. 10.
    Li, X.-H., Deng, F.-G., Zhou, H.-Y.: Faithful qubit transmission against collective noise without ancillary qubits. Appl. Phys. Lett. 91(14), 144101 (2007)ADSCrossRefGoogle Scholar
  11. 11.
    Li, X.-H., Zhao, B.-K., Sheng, Y.-B., Deng, F.-G., Zhou, H.-Y.: Efficient faithful qubit transmission with frequency degree of freedom. Opt. Commun. 282(19), 4025–4027 (2009)ADSCrossRefGoogle Scholar
  12. 12.
    Deng, F.-G., Li, X.-H., Zhou, H.-Y.: Passively self-error-rejecting qubit transmission over a collective-noise channel. Quantum Inf. Comput. 11, 0913–0924 (2011)MathSciNetMATHGoogle Scholar
  13. 13.
    Salemian, S., Mohammadnejad, S.: An error-free protocol for quantum entanglement distribution in long-distance quantum communication. Chin. Sci. Bull. 56(7), 618–625 (2011)CrossRefGoogle Scholar
  14. 14.
    Pan, J.-W., Chen, Z.-B., Lu, C.-Y., Weinfurter, H., Zeilinger, A., Zukowski, M.: Multiphoton entanglement and interferometry. Rev. Mod. Phys. 84(2), 777–838 (2012)ADSCrossRefGoogle Scholar
  15. 15.
    Zanardi, P., Rasetti, M.: Noiseless quantum codes. Phys. Rev. Lett. 79(17), 3306–3309 (1997)ADSCrossRefGoogle Scholar
  16. 16.
    Boileau, J.-C., Gottesman, D., Laflamme, R., Poulin, D., Spekkens, R.: Robust polarization-based quantum key distribution over a collective-noise channel. Phys. Rev. Lett. 92(1), 017901 (2004)ADSCrossRefGoogle Scholar
  17. 17.
    Wang, X.-B.: Fault tolerant quantum key distribution protocol with collective random unitary noise. Phys. Rev. A 72(5), 050304(R) (2005)ADSCrossRefGoogle Scholar
  18. 18.
    Aolita, L., Walborn, S.: Quantum communication without alignment using multiple-qubit single-photon states. Phys. Rev. Lett. 98(10), 100501 (2007)ADSCrossRefGoogle Scholar
  19. 19.
    Li, X.-H., Deng, F.-G., Zhou, H.-Y.: Efficient quantum key distribution over a collective noise channel. Phys. Rev. A 78(2), 022321 (2008)ADSCrossRefGoogle Scholar
  20. 20.
    Sheng, Y.-B., Deng, F.-G.: Efficient quantum entanglement distribution over an arbitrary collective-noise channel. Phys. Rev. A 81(4), 042332 (2010)ADSCrossRefGoogle Scholar
  21. 21.
    Li, X.-H.: Deterministic polarization-entanglement purification using spatial entanglement. Phys. Rev. A 82(4), 044304 (2010)ADSCrossRefGoogle Scholar
  22. 22.
    Deng, F.-G.: One-step error correction for multipartite polarization entanglement. Phys. Rev. A 83(6), 062316 (2011)ADSCrossRefGoogle Scholar
  23. 23.
    Dong, L., Xiu, X.-M., Gao, Y.-J., Yi, X.X.: Controlled quantum key distribution with three-photon polarization-entangled states via the collective noise channel. J. Exp. Theor. Phys. 113(4), 583–591 (2011)ADSCrossRefGoogle Scholar
  24. 24.
    Yang, Y.-G., Teng, Y.-W., Chai, H.-P., Wen, Q.-Y.: Fault-tolerant quantum secret sharing against collective noise. Phys. Scr. 83(2), 25003 (2011)CrossRefMATHGoogle Scholar
  25. 25.
    Andersson, E., Curty, M., Jex, I.: Experimentally realizable quantum comparison of coherent states and its applications. Phys. Rev. A 74(2), 022304 (2006)ADSCrossRefGoogle Scholar
  26. 26.
    He, B., Ren, Y., Bergou, J.: Creation of high-quality long-distance entanglement with flexible resources. Phys. Rev. A 79(5), 052323 (2009)ADSCrossRefGoogle Scholar
  27. 27.
    Turchette, Q.A., Hood, C.J., Lange, W., Mabuchi, H., Kimble, H.J.: Measurement of conditional phase shifts for quantum logic. Phys. Rev. Lett. 75(25), 4710–4713 (1995)MathSciNetADSCrossRefMATHGoogle Scholar
  28. 28.
    Rauschenbeutel, A., Nogues, G., Osnaghi, S., Bertet, P., Brune, M., Raimond, J., Haroche, S.: Coherent operation of a tunable quantum phase gate in cavity QED. Phys. Rev. Lett. 83(24), 5166–5169 (1999)ADSCrossRefGoogle Scholar
  29. 29.
    Koashi, M., Yamamoto, T., Imoto, N.: Probabilistic manipulation of entangled photons. Phys. Rev. A 63(1), 030301(R) (2001)ADSCrossRefGoogle Scholar
  30. 30.
    Knill, E., Laflamme, R., Milburn, G.J.: A scheme for efficient quantum computation with linear optics. Nature 409(6816), 46–52 (2001)ADSCrossRefMATHGoogle Scholar
  31. 31.
    Yi, X.X., Su, X.H., You, L.: Conditional quantum phase gate between two 3-state atoms. Phys. Rev. Lett. 90(9), 097902 (2003)ADSCrossRefGoogle Scholar
  32. 32.
    Knill, E.: Bounds on the probability of success of postselected nonlinear sign shifts implemented with linear optics. Phys. Rev. A 68(6), 064303 (2003)ADSCrossRefGoogle Scholar
  33. 33.
    Xiu, X.-M., Dong, L., Shen, H.-Z., Gao, Y.-J., Yi, X.X.: Construction scheme of a two-photon polarization controlled arbitrary phase gate mediated by weak cross-phase modulation. J. Opt. Soc. Am. B 30(3), 589–597 (2013)ADSCrossRefGoogle Scholar
  34. 34.
    Pittman, T., Jacobs, B., Franson, J.: Probabilistic quantum logic operations using polarizing beam splitters. Phys. Rev. A 64(6), 062311 (2001)ADSCrossRefGoogle Scholar
  35. 35.
    Pittman, T., Fitch, M., Jacobs, B., Franson, J.: Experimental controlled-NOT logic gate for single photons in the coincidence basis. Phys. Rev. A 68(3), 032316 (2003)ADSCrossRefGoogle Scholar
  36. 36.
    Scheel, S., Munro, W., Eisert, J., Nemoto, K., Kok, P.: Feed-forward and its role in conditional linear optical quantum dynamics. Phys. Rev. A 73(3), 034301 (2006)ADSCrossRefGoogle Scholar
  37. 37.
    Kok, P., Nemoto, K., Ralph, T.C., Dowling, J.P., Milburn, G.J.: Linear optical quantum computing with photonic qubits. Rev. Mod. Phys. 79(1), 135–174 (2007)ADSCrossRefGoogle Scholar
  38. 38.
    Nemoto, K., Munro, W.J.: Nearly deterministic linear optical controlled-NOT gate. Phys. Rev. Lett. 93(25), 250502 (2004)ADSCrossRefGoogle Scholar
  39. 39.
    Lin, Q., Li, J.: Quantum control gates with weak cross-Kerr nonlinearity. Phys. Rev. A 79(2), 022301 (2009)ADSCrossRefGoogle Scholar
  40. 40.
    Wang, M.-F., Jiang, N.-Q., Jin, Q.-L., Zheng, Y.-Z.: Continuous-variable controlled-Z gate using an atomic ensemble. Phys. Rev. A 83(6), 062339 (2011)ADSCrossRefGoogle Scholar
  41. 41.
    Xiu, X.-M., Dong, L., Gao, Y.-J., Yi, X.X.: Nearly deterministic controlled-not gate with weak cross-kerr nonlinearities. Quantum Info. Comput. 12(1–2), 0159–0170 (2012)MathSciNetMATHGoogle Scholar
  42. 42.
    Barrett, S.D., Kok, P., Nemoto, K., Beausoleil, R.G., Munro, W.J., Spiller, T.P.: Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities. Phys. Rev. A 71(6), 060302 (2005)ADSCrossRefGoogle Scholar
  43. 43.
    Munro, W.J., Nemoto, K., Spiller, T.P.: Weak nonlinearities: a new route to optical quantum computation. N. J. Phys. 7(1), 137 (2005)CrossRefGoogle Scholar
  44. 44.
    Guo, Q., Bai, J., Cheng, L.-Y., Shao, X.-Q., Wang, H.-F., Zhang, S.: Simplified optical quantum-information processing via weak cross-Kerr nonlinearities. Phys. Rev. A 83(5), 054303 (2011)ADSCrossRefGoogle Scholar
  45. 45.
    Wang, X.-W., Zhang, D.-Y., Tang, S.-Q., Xie, L.-J., Wang, Z.-Y., Kuang, L.-M.: Photonic two-qubit parity gate with tiny cross-Kerr nonlinearity. Phys. Rev. A 85(5), 052326 (2012)ADSCrossRefGoogle Scholar
  46. 46.
    Xiu, X.-M., Dong, L., Gao, Y.-J., Yi, X.X.: Quantum key distribution with Einstein–Podolsky–Rosen pairs associated with weak cross-Kerr nonlinearities. J. Opt. Soc. Am. B 29(10), 2869–2874 (2012)ADSCrossRefGoogle Scholar
  47. 47.
    Wang, X.-W., Tang, S.-Q., Xie, L.-J., Zhang, D.-Y.: Nondestructive two-photon parity detector with near unity efficiency. Opt. Commun. 296, 153–157 (2013)ADSCrossRefGoogle Scholar
  48. 48.
    Munro, W.J., Nemoto, K., Beausoleil, R.G., Spiller, T.P.: High-efficiency quantum-nondemolition single-photon-number-resolving detector. Phys. Rev. A 71(3), 033819 (2005)ADSCrossRefGoogle Scholar
  49. 49.
    Fleischhauer, M., Imamoglu, A., Marangos, J.P.: Electromagnetically induced transparency: optics in coherent media. Rev. Mod. Phys. 77(2), 633–673 (2005)ADSCrossRefGoogle Scholar
  50. 50.
    Chen, Y.-F., Wang, C.-Y., Wang, S.-H., Yu, I.: Low-light-level cross-phase-modulation based on stored light pulses. Phys. Rev. Lett. 96(4), 043603 (2006)ADSCrossRefGoogle Scholar
  51. 51.
    Wang, Z.-B., Marzlin, K.-P., Sanders, B.C.: Large cross-phase modulation between slow copropagating weak pulses in \(^{87}\)Rb. Phys. Rev. Lett. 97(6), 063901 (2006)ADSCrossRefGoogle Scholar
  52. 52.
    Sheng, Y.-B., Deng, F.-G., Zhou, H.-Y.: Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity. Phys. Rev. A 77(4), 042308 (2008)ADSCrossRefGoogle Scholar
  53. 53.
    Sheng, Y.-B., Deng, F.-G., Zhou, H.-Y.: Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics. Phys. Rev. A 77(6), 062325 (2008)ADSCrossRefGoogle Scholar
  54. 54.
    Lin, Q., He, B.: Single-photon logic gates using minimal resources. Phys. Rev. A 80(10), 042310 (2009)ADSCrossRefGoogle Scholar
  55. 55.
    Sheng, Y.-B., Deng, F.-G.: Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement. Phys. Rev. A 81(3), 032307 (2010)MathSciNetADSCrossRefGoogle Scholar
  56. 56.
    Lin, Q., He, B.: Efficient generation of universal two-dimensional cluster states with hybrid systems. Phys. Rev. A 82(8), 022331 (2010)ADSCrossRefGoogle Scholar
  57. 57.
    Bing, H., Ren, Y.-H., Bergou, J.: Universal entangler with photon pairs in arbitrary states. J. Phys. B At. Mol. Opt. Phys. 43(2), 025502 (2010)ADSCrossRefGoogle Scholar
  58. 58.
    He, B., MacRae, A., Han, Y., Lvovsky, A., Simon, C.: Transverse multimode effects on the performance of photon-photon gates. Phys. Rev. 83(2), 022312 (2011)ADSCrossRefGoogle Scholar
  59. 59.
    Lo, H.-Y., Chen, Y.-C., Chen, H.-C., Chen, J.-X., Chen, Y.-C., Yu, I.A., Chen, Y.-F.: Electromagnetically-induced-transparency-based cross-phase-modulation at attojoule levels. Phys. Rev. A 83(4), 041804(R) (2011)ADSCrossRefGoogle Scholar
  60. 60.
    He, B., Scherer, A.: Continuous-mode effects and photon-photon phase gate performance. Phys. Rev. A 85(3), 033814 (2012)ADSCrossRefGoogle Scholar
  61. 61.
    Siomau, M., Kamli, A.A., Moiseev, S.A., Sanders, B.C.: Entanglement creation with negative index metamaterials. Phys. Rev. A 85(5), 050303(R) (2012)ADSCrossRefGoogle Scholar
  62. 62.
    Sheng, Y.-B., Zhou, L., Zhao, S.-M., Zheng, B.-Y.: Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs. Phys. Rev. A 85(1), 012307 (2012)ADSCrossRefGoogle Scholar
  63. 63.
    Sheng, Y.-B., Zhou, L., Zhao, S.-M.: Efficient two-step entanglement concentration for arbitrary W states. Phys. Rev. A 85(4), 042302 (2012)ADSCrossRefGoogle Scholar
  64. 64.
    Zhou, L., Sheng, Y.-B., Cheng, W.-W., Gong, L.-Y., Zhao, S.-M.: Efficient entanglement concentration for arbitrary less-entangled NOON states. Quantum Info. Process. 12(2), 1307–1320 (2013)MathSciNetADSCrossRefMATHGoogle Scholar
  65. 65.
    Sheng, Y.-B., Zhou, L., Long, G.-L.: Hybrid entanglement purification for quantum repeaters. Phys. Rev. A 88(2), 022302 (2013)ADSCrossRefGoogle Scholar
  66. 66.
    Sheng, Y.-B., Zhou, L.: Quantum entanglement concentration based on nonlinear optics for quantum communications. Entropy 15(5), 1776–1820 (2013)MathSciNetADSCrossRefMATHGoogle Scholar
  67. 67.
    Zhou, L., Sheng, Y.-B., Cheng, W.-W., Gong, L.-Y., Zhao, S.-M.: Efficient entanglement concentration for arbitrary single-photon multimode W state. J. Opt. Soc. Am. B 30(1), 71 (2013)ADSCrossRefGoogle Scholar
  68. 68.
    Xia, Y., Lu, M., Song, J., Lu, P-m, Song, H-s: Effective protocol for preparation of four-photon polarization-entangled decoherence-free states with cross-Kerr nonlinearity. J. Opt. Soc. Am. B 30(2), 421–428 (2013)ADSCrossRefGoogle Scholar
  69. 69.
    Xiu, X.-M., Dong, L., Shen, H.-Z., Gao, Y.-J., Yi., X.X.: Preparing, linking, and unlinking cluster-type polarization-entangled states by integrating modules. Prog. Theor. Exp. Phys. 2013(9), 093A01 (2013)CrossRefGoogle Scholar
  70. 70.
    Wang, X.-W., Zhang, D.-Y., Tang, S.-Q., Xie, L.-J.: Nondestructive Greenberger–Horne–Zeilinger–state analyzer. Quantum Inf. Process. 12(2), 1065–1075 (2013)MathSciNetADSCrossRefMATHGoogle Scholar
  71. 71.
    Dong, L., Xiu, X.-M., Gao, Y.-J., Yi, X.X.: A nearly deterministic scheme for generating \(\chi \)-type entangled states with weak cross-Kerr nonlinearities. Quantum Inf. Process. 12(4), 1787–1795 (2013)MathSciNetADSCrossRefMATHGoogle Scholar
  72. 72.
    Xiu, X.-M., Dong, L., Shen, H.-Z., Gao, Y.-J., Yi, X.X.: Two-party quantum privacy comparison with polarization-entangled Bell states and the Coherent states. Quantum Inf. Comput. 14(3–4), 0236–0254 (2014)MathSciNetGoogle Scholar
  73. 73.
    Shapiro, J.: Single-photon Kerr nonlinearities do not help quantum computation. Phys. Rev. A 73(6), 062305 (2006)ADSCrossRefGoogle Scholar
  74. 74.
    Shapiro, J.H., Razavi, M.: Continuous-time cross-phase modulation and quantum computation. N. J. Phys. 9(1), 16 (2007)CrossRefGoogle Scholar
  75. 75.
    Gea-Banacloche, J.: Impossibility of large phase shifts via the giant Kerr effect with single-photon wave packets. Phys. Rev. A 81(4), 043823 (2010)ADSCrossRefGoogle Scholar
  76. 76.
    He, B., Lin, Q., Simon, C.: Cross-Kerr nonlinearity between continuous-mode coherent states and single photons. Phys. Rev. A 83(5), 053826 (2011)ADSCrossRefGoogle Scholar
  77. 77.
    Feizpour, A., Xing, X., Steinberg, A.M.: Amplifying single photon nonlinearly using weak measurement. Phys. Rev. Lett. 107(13), 133603 (2011)ADSCrossRefGoogle Scholar
  78. 78.
    Hoi, I.-C., Kockum, A.F., Palomaki, T., Stace, T.M., Fan, B., Tornberg, L., Sathyamoorthy, S.R., Johansson, G., Delsing, P., Wilson, C.M.: Giant cross-Kerr effect for propagating microwaves induced by an artificial atom. Phys. Rev. Lett. 111(5), 053601 (2013)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Li Dong
    • 1
    • 2
  • Jun-Xi Wang
    • 1
  • Hong-Zhi Shen
    • 2
  • Dan Li
    • 3
  • Xiao-Ming Xiu
    • 1
    • 2
  • Ya-Jun Gao
    • 1
  • X. X. Yi
    • 2
  1. 1.College of Mathematics and PhysicsBohai UniversityJinzhouPeople’s Republic of China
  2. 2.School of Physics and Optoelectronic TechnologyDalian University of TechnologyDalianPeople’s Republic of China
  3. 3.Department of Electrical and Electronics EngineeringChengdu Technological UniversityChengduPeople’s Republic of China

Personalised recommendations