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Quantum error rejection for faithful quantum communication over noise channels

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Abstract

Quantum state transmission is a prerequisite for various quantum communication networks. The channel noise inevitably introduces distortion of quantum states passing through either a free-space channel or a fibre channel, which leads to errors or decreases the security of a practical quantum communication network. Quantum error rejection is a useful technology to faithfully transmit quantum states over large-scale quantum channels. It provides the communication parties with an uncorrupted quantum state by rejecting error states. Usually, additional photons or degrees of freedom are required to overcome the adverse effects of channel noise. As quantum error rejection method consumes less quantum resource than other anti-noise methods, it is more convenient to perform error-rejection quantum state transmission with current technology. In this review, several typical quantum error-rejection schemes for single-photon state transmission are introduced in brief and some error-rejection schemes for entanglement distribution are also briefly presented.

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References

  1. H. J. Kimble, Nature 453, 1023 (2008), arXiv: 0806.4195.

    ADS  Google Scholar 

  2. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74, 145 (2002).

    ADS  Google Scholar 

  3. I. Buluta, and F. Nori, Science 326, 108 (2009).

    ADS  Google Scholar 

  4. I. M. Georgescu, S. Ashhab, and F. Nori, Rev. Mod. Phys. 86, 153 (2014), arXiv: 1308.6253.

    ADS  Google Scholar 

  5. H. Fan, Acta. Phys. Sin. 67, 120301 (2018).

    Google Scholar 

  6. B. X. Wang, M. J. Tao, Q. Ai, T. Xin, N. Lambert, D. Ruan, Y. C. Cheng, F. Nori, F. G. Deng, and G. L. Long, npj Quantum Inf. 4, 52 (2018).

    ADS  Google Scholar 

  7. C. H. Bennett, and G. Brassard, in Proceedings of IEEE International Conference on Computers, Systems and Signal Processing Bangalore, India (IEEE, New York, 1984), pp. 175–179.

    Google Scholar 

  8. C. H. Bennett, Phys. Rev. Lett. 68, 3121 (1992).

    ADS  MathSciNet  Google Scholar 

  9. A. K. Ekert, Phys. Rev. Lett. 67, 661 (1991).

    ADS  MathSciNet  Google Scholar 

  10. C. H. Bennett, G. Brassard, and N. D. Mermin, Phys. Rev. Lett. 68, 557 (1992).

    ADS  MathSciNet  Google Scholar 

  11. Y. Fu, H. L. Yin, T. Y. Chen, and Z. B. Chen, Phys. Rev. Lett. 114, 090501 (2015), arXiv: 1412.0832.

    ADS  Google Scholar 

  12. N. Wang, S. Du, W. Liu, X. Wang, Y. Li, and K. Peng, Phys. Rev. Appl. 10, 064028 (2018).

    ADS  Google Scholar 

  13. Q. Liao, Y. Guo, D. Huang, P. Huang, and G. Zeng, New J. Phys. 20, 023015 (2018), arXiv: 1708.04074.

    ADS  Google Scholar 

  14. Z. Chen, Y. Zhang, G. Wang, Z. Li, and H. Guo, Phys. Rev. A 98, 012314 (2018), arXiv: 1802.02725.

    ADS  Google Scholar 

  15. X. Ma, P. Zeng, and H. Zhou, Phys. Rev. X 8, 031043 (2018).

    Google Scholar 

  16. H. K. Lo, M. Curty, and K. Tamaki, Nat. Photon 8, 595 (2014), arXiv: 1505.05303.

    ADS  Google Scholar 

  17. Q. Zhang, F. Xu, Y. A. Chen, C. Z. Peng, and J.W. Pan, Opt. Express 26, 24260 (2018), arXiv: 1809.02291.

    ADS  Google Scholar 

  18. M. Hillery, V. Bužek, and A. Berthiaume, Phys. Rev. A 59, 1829 (1999).

    ADS  MathSciNet  Google Scholar 

  19. A. Karlsson, M. Koashi, and N. Imoto, Phys. Rev. A 59, 162 (1999).

    ADS  Google Scholar 

  20. L. Xiao, G. Lu Long, F. G. Deng, and J. W. Pan, Phys. Rev. A 69, 052307 (2004).

    ADS  Google Scholar 

  21. B. Gu, L. Mu, L. Ding, C. Zhang, and C. Li, Opt. Commun. 283, 3099 (2010).

    ADS  Google Scholar 

  22. Z. Zhang, and Z. Man, Phys. Rev. A 72, 022303 (2005).

    ADS  MathSciNet  Google Scholar 

  23. Y. Zhou, J. Yu, Z. Yan, X. Jia, J. Zhang, C. Xie, and K. Peng, Phys. Rev. Lett. 121, 150502 (2018).

    ADS  Google Scholar 

  24. G. L. Long, and X. S. Liu, Phys. Rev. A 65, 032302 (2002).

    ADS  Google Scholar 

  25. F. G. Deng, G. L. Long, and X. S. Liu, Phys. Rev. A 68, 042317 (2003).

    ADS  Google Scholar 

  26. F. G. Deng, and G. L. Long, Phys. Rev. A 69, 052319 (2004).

    ADS  Google Scholar 

  27. Z.-R. Zhou, Y.-B. Sheng, P.-H. Niu, L.-G. Yin, and G.-L. Long, arXiv: 1805.07228.

  28. P. H. Niu, Z. R. Zhou, Z. S. Lin, Y. B. Sheng, L. G. Yin, and G. L. Long, Sci. Bull. 63, 1345 (2018).

    Google Scholar 

  29. W. Zhang, D. S. Ding, Y. B. Sheng, L. Zhou, B. S. Shi, and G. C. Guo, Phys. Rev. Lett. 118, 220501 (2017), arXiv: 1609.09184.

    ADS  Google Scholar 

  30. F. Zhu, W. Zhang, Y. Sheng, and Y. Huang, Sci. Bull. 62, 1519 (2017).

    Google Scholar 

  31. F. Z. Wu, G. J. Yang, H. B. Wang, J. Xiong, F. Alzahrani, A. Hobiny, and F. G. Deng, Sci. China-Phys. Mech. Astron. 60, 120313 (2017).

    ADS  Google Scholar 

  32. S. S. Chen, L. Zhou, W. Zhong, and Y. B. Sheng, Sci. China-Phys. Mech. Astron. 61, 090312 (2018).

    Google Scholar 

  33. R. Qi, Z. Sun, Z. Lin, P. Niu, W. Hao, L. Song, Q. Huang, J. Gao, L. Yin, and G. L. Long, Light Sci. Appl. 8, 22 (2019), arXiv: 1810.11806.

    ADS  Google Scholar 

  34. S. Rosenblum, S. Parkins, and B. Dayan, Phys. Rev. A 84, 033854 (2011), arXiv: 1109.1197.

    ADS  Google Scholar 

  35. L. Zhou, L. P. Yang, Y. Li, and C. P. Sun, Phys. Rev. Lett. 111, 103604 (2013), arXiv: 1303.3687.

    ADS  Google Scholar 

  36. J. Lu, L. Zhou, L. M. Kuang, and F. Nori, Phys. Rev. A 89, 013805 (2014), arXiv: 1310.7286.

    ADS  Google Scholar 

  37. K. Xia, G. Lu, G. Lin, Y. Cheng, Y. Niu, S. Gong, and J. Twamley, Phys. Rev. A 90, 043802 (2014), arXiv: 1407.3080.

    ADS  Google Scholar 

  38. I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, Science 345, 903 (2014), arXiv: 1405.0937.

    ADS  Google Scholar 

  39. W.-B. Yan, and H. Fan, Sci. Rep. 4, 4820 (2014).

    Google Scholar 

  40. S. Xu, H. Z. Shen, and X. X. Yi, J. Opt. Soc. Am. B 33, 1600 (2016).

    ADS  Google Scholar 

  41. C. Cao, Y. W. Duan, X. Chen, R. Zhang, T. J. Wang, and C. Wang, Opt. Express 25, 16931 (2017).

    ADS  Google Scholar 

  42. C. H. Yan, Y. Li, H. Yuan, and L. F. Wei, Phys. Rev. A 97, 023821 (2018).

    ADS  Google Scholar 

  43. W. B. Yan, W. Y. Ni, J. Zhang, F. Y. Zhang, and H. Fan, Phys. Rev. A 98, 043852 (2018), arXiv: 1803.04086.

    ADS  Google Scholar 

  44. K. Xia, F. Nori, and M. Xiao, Phys. Rev. Lett. 121, 203602 (2018).

    ADS  Google Scholar 

  45. R. H. Hadfield, Nat. Photon 3, 696 (2009).

    ADS  Google Scholar 

  46. W. B. Gao, A. Imamoglu, H. Bernien, and R. Hanson, Nat. Photon 9, 363 (2015).

    ADS  Google Scholar 

  47. D. D. Awschalom, R. Hanson, J. Wrachtrup, and B. B. Zhou, Nat. Photon 12, 516 (2018).

    ADS  Google Scholar 

  48. B. S. Shi, D. S. Ding, and W. Zhang, J. Phys. B-At. Mol. Opt. Phys. 51, 032004 (2018).

    ADS  Google Scholar 

  49. S. Pirandola, J. Eisert, C. Weedbrook, A. Furusawa, and S. L. Braunstein, Nat. Photon 9, 641 (2015), arXiv: 1505.07831.

    ADS  Google Scholar 

  50. V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, Rev. Mod. Phys. 81, 1301 (2009), arXiv: 0802.4155.

    ADS  Google Scholar 

  51. X. K. Song, Q. Ai, J. Qiu, and F. G. Deng, Phys. Rev. A 93, 052324 (2016), arXiv: 1602.00050.

    ADS  Google Scholar 

  52. X. K. Song, H. Zhang, Q. Ai, J. Qiu, and F. G. Deng, New J. Phys. 18, 023001 (2016), arXiv: 1509.00097.

    ADS  Google Scholar 

  53. F. Flamini, N. Spagnolo, and F. Sciarrino, Rep. Prog. Phys. 82, 016001 (2019), arXiv: 1803.02790.

    ADS  Google Scholar 

  54. C. Kurtsiefer, P. Zarda, and M. Halder, Nature, 419, 450 (2002).

    ADS  Google Scholar 

  55. X. F. Mo, B. Zhu, Z. F. Han, Y. Z. Gui, and G. C. Guo, Opt. Lett. 30, 2632 (2005).

    ADS  Google Scholar 

  56. J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, Rev. Mod. Phys. 84, 777 (2012), arXiv: 0805.2853.

    ADS  Google Scholar 

  57. F. G. Deng, B. C. Ren, and X. H. Li, Sci. Bull. 62, 46 (2017).

    Google Scholar 

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

    ADS  Google Scholar 

  59. P. Zanardi, and M. Rasetti, Phys. Rev. Lett. 79, 3306 (1997).

    ADS  Google Scholar 

  60. T. Yamamoto, K. Hayashi, K. Özdemir, M. Koashi, and N. Imoto, Nat. Photon 2, 488 (2008).

    Google Scholar 

  61. M. Martinelli, Opt. Commun. 72, 341 (1989).

    ADS  Google Scholar 

  62. M. A. Nielsen, and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2010).

    MATH  Google Scholar 

  63. F. G. Deng, X. H. Li, and T. Li, Acta. Phys. Sin. 67, 130301 (2018).

    Google Scholar 

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

    ADS  Google Scholar 

  65. J. W. Pan, C. Simon, d. Brukner, and A. Zeilinger, Nature 410, 1067 (2001).

    ADS  Google Scholar 

  66. C. Simon, and J. W. Pan, Phys. Rev. Lett. 89, 257901 (2002).

    ADS  Google Scholar 

  67. Y. B. Sheng, F. G. Deng, and H. Y. Zhou, Phys. Rev. A 77, 042308 (2008), arXiv: 0805.0032.

    ADS  Google Scholar 

  68. Y. B. Sheng, and F. G. Deng, Phys. Rev. A 81, 032307 (2010), arXiv: 0912.0079.

    ADS  Google Scholar 

  69. Y. B. Sheng, and F. G. Deng, Phys. Rev. A 82, 044305 (2010), arXiv: 1008.3509.

    ADS  Google Scholar 

  70. C. Wang, Y. Zhang, and G. Jin, Phys. Rev. A 84, 032307 (2011).

    ADS  Google Scholar 

  71. T. Li, G. J. Yang, and F. G. Deng, Opt. Express 22, 23897 (2014), arXiv: 1403.4660.

    ADS  Google Scholar 

  72. Y. B. Sheng, and L. Zhou, Laser Phys. Lett. 11, 085203 (2014), arXiv: 1311.0470.

    ADS  Google Scholar 

  73. L. Zhou, and Y. B. Sheng, Sci. Rep. 6, 28813 (2016), arXiv: 1511.02344.

    ADS  Google Scholar 

  74. L. Zhou, and Y. B. Sheng, Ann. Phys. 385, 10 (2017).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  78. Y. B. Sheng, F. G. Deng, and H. Y. Zhou, Phys. Rev. A 77, 062325 (2008), arXiv: 0806.0115.

    ADS  Google Scholar 

  79. Y. B. Sheng, L. Zhou, S. M. Zhao, and B. Y. Zheng, Phys. Rev. A 85, 012307 (2012), arXiv: 1202.2190.

    ADS  Google Scholar 

  80. Y. B. Sheng, L. Zhou, and S. M. Zhao, Phys. Rev. A 85, 042302 (2012), arXiv: 1202.3019.

    ADS  Google Scholar 

  81. F. G. Deng, Phys. Rev. A 85, 022311 (2012), arXiv: 1112.1355.

    ADS  Google Scholar 

  82. C. Wang, T. J. Wang, Y. Zhang, R. Jiao, and G. Jin, Opt. Express 22, 1551 (2014).

    ADS  Google Scholar 

  83. S. M. Fei, Sci. China-Inf. Sci. 59, 128501 (2016).

    Google Scholar 

  84. C. Cao, X. Chen, Y. W. Duan, L. Fan, R. Zhang, T. J. Wang, and C. Wang, Sci. China-Phys. Mech. Astron. 59, 100315 (2016).

    Google Scholar 

  85. J. Liu, L. Zhou, W. Zhong, and Y. B. Sheng, Front. Phys. 14, 21601 (2019).

    Google Scholar 

  86. R. Laflamme, C. Miquel, J. P. Paz, and W. H. Zurek, Phys. Rev. Lett. 77, 198 (1996).

    ADS  Google Scholar 

  87. T. Aoki, G. Takahashi, T. Kajiya, J. Yoshikawa, S. L. Braunstein, P. van Loock, and A. Furusawa, Nat. Phys. 5, 541 (2009).

    Google Scholar 

  88. T. Y. Ye, Quantum Inf. Process. 14, 1487 (2015).

    ADS  Google Scholar 

  89. L. Zhou, and Y. B. Sheng, Phys. Rev. A 92, 042314 (2015).

    ADS  Google Scholar 

  90. L. Zhou, and Y. B. Sheng, Sci. Rep. 6, 20901 (2016), arXiv: 1511.05251.

    ADS  Google Scholar 

  91. N. M. Linke, M. Gutierrez, K. A. Landsman, C. Figgatt, S. Debnath, K. R. Brown, and C. Monroe, Sci. Adv. 3, e1701074 (2017), arXiv: 1611.06946.

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  94. Z. D. Walton, A. F. Abouraddy, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, Phys. Rev. Lett. 91, 087901 (2003).

    ADS  Google Scholar 

  95. J. B. Altepeter, P. G. Hadley, S. M. Wendelken, A. J. Berglund, and P. G. Kwiat, Phys. Rev. Lett. 92, 147901 (2004).

    ADS  Google Scholar 

  96. X. H. Li, F. G. Deng, and H. Y. Zhou, Phys. Rev. A 78, 022321 (2008), arXiv: 0808.0042.

    ADS  Google Scholar 

  97. Z. Q. Yin, Y. B. Zhao, Z. W. Zhou, Z. F. Han, and G. C. Guo, Phys. Rev. A 77, 062326 (2008), arXiv: 0803.1594.

    ADS  Google Scholar 

  98. H. F. Wang, S. Zhang, A. D. Zhu, X. X. Yi, and K. H. Yeon, Opt. Express 19, 25433 (2011).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  100. G. F. Xu, J. Zhang, D. M. Tong, E. Sjöqvist, and L. C. Kwek, Phys. Rev. Lett. 109, 170501 (2012), arXiv: 1210.6782.

    ADS  Google Scholar 

  101. T. Y. Ye, Sci. China-Phys. Mech. Astron. 57, 2266 (2014).

    ADS  Google Scholar 

  102. W. Qin, C. Wang, and X. Zhang, Phys. Rev. A 91, 042303 (2015), arXiv: 1503.08617.

    ADS  Google Scholar 

  103. L. Dong, J. X. Wang, Q. Y. Li, H. Z. Shen, H. K. Dong, X. M. Xiu, and Y. J. Gao, Opt. Lett. 41, 1030 (2016).

    ADS  Google Scholar 

  104. M. Wang, F. Yan, and T. Gao, Sci. Rep. 6, 38233 (2016).

    ADS  Google Scholar 

  105. M. Zwerger, B. P. Lanyon, T. E. Northup, C. A. Muschik, W. Dür, and N. Sangouard, Quantum Sci. Technol. 2, 044001 (2017), arXiv: 1611.07779.

    ADS  Google Scholar 

  106. S. L. Wu, X. L. Huang, H. Li, and X. X. Yi, Phys. Rev. A 96, 042104 (2017), arXiv: 1705.01695.

    ADS  Google Scholar 

  107. A. F. Kockum, G. Johansson, and F. Nori, Phys. Rev. Lett. 120, 140404 (2018).

    ADS  Google Scholar 

  108. N. Shammah, S. Ahmed, N. Lambert, S. De Liberato, and F. Nori, Phys. Rev. A 98, 063815 (2018), arXiv: 1805.05129.

    ADS  Google Scholar 

  109. J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, Phys. Rev. Lett. 82, 2594 (1999).

    ADS  Google Scholar 

  110. D. Bouwmeester, Phys. Rev. A 63, 040301(R) (2001).

    ADS  Google Scholar 

  111. D. Kalamidas, Phys. Lett. A 321, 87 (2004).

    ADS  MathSciNet  Google Scholar 

  112. X. B. Wang, Phys. Rev. A 69, 022320 (2004).

    ADS  Google Scholar 

  113. X. B. Wang, Phys. Rev. Lett. 92, 077902 (2004).

    ADS  Google Scholar 

  114. X. B. Wang, Phys. Rev. A 72, 050304(R) (2005).

    ADS  Google Scholar 

  115. Y. A. Chen, A. N. Zhang, Z. Zhao, X. Q. Zhou, and J. W. Pan, Phys. Rev. Lett. 96, 220504 (2006).

    ADS  Google Scholar 

  116. J. C. Boileau, R. Laflamme, M. Laforest, and C. Myers, Phys. Rev. Lett. 93, 220501 (2004).

    ADS  Google Scholar 

  117. T. Y. Chen, J. Zhang, J. C. Boileau, X. M. Jin, B. Yang, Q. Zhang, T. Yang, R. Laflamme, and J. W. Pan, Phys. Rev. Lett. 96, 150504 (2006).

    ADS  Google Scholar 

  118. M. Gao, L. M. Liang, C. Z. Li, and C. L. Tian, Phys. Lett. A 359, 126 (2006).

    ADS  Google Scholar 

  119. T. Yamamoto, J. Shimamura, K. Özdemir, M. Koashi, and N. Imoto, Phys. Rev. Lett. 95, 040503 (2005).

    ADS  Google Scholar 

  120. X. H. Li, B. K. Zhao, Y. B. Sheng, F. G. Deng, and H. Y. Zhou, Opt. Commun. 282, 4025 (2009), arXiv: 0907.0053.

    ADS  Google Scholar 

  121. T. Yamamoto, R. Nagase, J. Shimamura, K. Özdemir, M. Koashi, and N. Imoto, New J. Phys. 9, 191 (2007).

    ADS  Google Scholar 

  122. D. Kalamidas, Phys. Lett. A, 343, 331 (2005).

    ADS  Google Scholar 

  123. C. Han, Z. W. Zhou, and G. C. Guo, J. Phys. B-At. Mol. Opt. Phys. 39, 1677 (2006).

    ADS  Google Scholar 

  124. X. H. Li, F. G. Deng, and H. Y. Zhou, Appl. Phys. Lett. 91, 144101 (2007), arXiv: 0708.0068.

    ADS  Google Scholar 

  125. Y. B. Sheng, and F. G. Deng, Phys. Rev. A 81, 042332 (2010), arXiv: 1005.0050.

    ADS  Google Scholar 

  126. F. G. Deng, X. H. Li, and H. Y. Zhou, Quantum Info. Comput. 11, 0913 (2011).

    Google Scholar 

  127. J. Wu, X. B. An, Z. Q. Yin, F. X. Wang, W. Chen, S. Wang, G. C. Guo, and Z. F. Han, Opt. Lett. 43, 4707 (2018).

    ADS  Google Scholar 

  128. C. E. R. Souza, C. V. S. Borges, A. Z. Khoury, J. A. O. Huguenin, L. Aolita, and S. P. Walborn, Phys. Rev. A 77, 032345 (2008).

    ADS  MathSciNet  Google Scholar 

  129. T. Li, G. Y. Wang, F. G. Deng, and G. L. Long, Sci. Rep. 6, 20677 (2016).

    ADS  Google Scholar 

  130. Y. X. Jiang, P. L. Guo, C. Y. Gao, H. B. Wang, F. Alzahrani, A. Hobiny, and F. G. Deng, Sci. China-Phys. Mech. Astron. 60, 120312 (2017), arXiv: 1804.00873.

    ADS  Google Scholar 

  131. Y. F. Huang, B. H. Liu, L. Peng, Y. H. Li, L. Li, C. F. Li, and G. C. Guo, Nat. Commun. 2, 546 (2011).

    ADS  Google Scholar 

  132. X. C. Yao, T. X. Wang, P. Xu, H. Lu, G. S. Pan, X. H. Bao, C. Z. Peng, C. Y. Lu, Y. A. Chen, and J. W. Pan, Nat. Photon 6, 225 (2012), arXiv: 1105.6318.

    ADS  Google Scholar 

  133. H. Lu, L. K. Chen, C. Liu, P. Xu, X. C. Yao, L. Li, N. L. Liu, B. Zhao, Y. A. Chen, and J. W. Pan, Nat. Photon 8, 364 (2014).

    ADS  Google Scholar 

  134. N. Bergamasco, M. Menotti, J. E. Sipe, and M. Liscidini, Phys. Rev. Appl. 8, 054014 (2017), arXiv: 1704.03213.

    ADS  Google Scholar 

  135. M. Krenn, A. Hochrainer, M. Lahiri, and A. Zeilinger, Phys. Rev. Lett. 118, 080401 (2017), arXiv: 1610.00642.

    ADS  MathSciNet  Google Scholar 

  136. P. Walther, and A. Zeilinger, Phys. Rev. A 72, 010302(R) (2005).

    ADS  Google Scholar 

  137. J. A. W. van Houwelingen, N. Brunner, A. Beveratos, H. Zbinden, and N. Gisin, Phys. Rev. Lett. 96, 130502 (2006).

    MathSciNet  Google Scholar 

  138. M. Barbieri, G. Vallone, P. Mataloni, and F. De Martini, Phys. Rev. A 75, 042317 (2007).

    ADS  Google Scholar 

  139. Y. B. Sheng, F. G. Deng, and G. L. Long, Phys. Rev. A 82, 032318 (2010), arXiv: 1103.0230.

    ADS  Google Scholar 

  140. B. C. Ren, H. R. Wei, M. Hua, T. Li, and F. G. Deng, Opt. Express 20, 24664 (2012), arXiv: 1207.0168.

    ADS  Google Scholar 

  141. T. J. Wang, Y. Lu, and G. L. Long, Phys. Rev. A 86, 042337 (2012).

    ADS  Google Scholar 

  142. Q. Liu, and M. Zhang, Phys. Rev. A 91, 062321 (2015), arXiv: 1507.06108.

    ADS  Google Scholar 

  143. G. Y. Wang, Q. Ai, B. C. Ren, T. Li, and F. G. Deng, Opt. Express 24, 28444 (2016), arXiv: 1611.03352.

    ADS  Google Scholar 

  144. X. H. Li, and S. Ghose, Phys. Rev. A 93, 022302 (2016), arXiv: 1601.02029.

    ADS  Google Scholar 

  145. X. H. Li, and S. Ghose, Phys. Rev. A 96, 020303(R) (2017).

    ADS  Google Scholar 

  146. L. Xiao, C. Wang, W. Zhang, Y. Huang, J. Peng, and G. Long, Phys. Rev. A 77, 042315 (2008).

    ADS  Google Scholar 

  147. J. Zhang, Y. Liu, K. Özdemir, R. B. Wu, F. Gao, X. B. Wang, L. Yang, and F. Nori, Sci. Rep. 3, 2211 (2013), arXiv: 1204.1742.

    Google Scholar 

  148. M. Bloch, S. W. McLaughlin, J. M. Merolla, and F. Patois, Opt. Lett. 32, 301 (2007).

    ADS  Google Scholar 

  149. T. Zhang, Z. Q. Yin, Z. F. Han, and G. C. Guo, Opt. Commun. 281, 4800 (2008).

    ADS  Google Scholar 

  150. E. Huntington, and T. Ralph, Phys. Rev. A 69, 042318 (2004).

    ADS  Google Scholar 

  151. B. Li, P. B. Li, Y. Zhou, S. L. Ma, and F. L. Li, Phys. Rev. A 96, 032342 (2017), arXiv: 1709.04852.

    ADS  Google Scholar 

  152. C. Langrock, E. Diamanti, R. V. Roussev, Y. Yamamoto, M. M. Fejer, and H. Takesue, Opt. Lett. 30, 1725 (2005).

    ADS  Google Scholar 

  153. H. Takesue, E. Diamanti, T. Honjo, C. Langrock, M. M. Fejer, K. Inoue, and Y. Yamamoto, New J. Phys. 7, 232 (2005).

    ADS  Google Scholar 

  154. H. Wang, W. Li, X. Jiang, Y. M. He, Y. H. Li, X. Ding, M. C. Chen, J. Qin, C. Z. Peng, C. Schneider, M. Kamp, W. J. Zhang, H. Li, L. X. You, Z. Wang, J. P. Dowling, S. Höfling, C. Y. Lu, and J. W. Pan, Phys. Rev. Lett. 120, 230502 (2018), arXiv: 1801.08282.

    ADS  Google Scholar 

  155. L. Dong, Y. F. Lin, C. Cui, H. K. Dong, X. M. Xiu, and Y. J. Gao, Opt. Express 25, 18581 (2017).

    ADS  Google Scholar 

  156. L. Aolita, and S. P. Walborn, Phys. Rev. Lett. 98, 100501 (2007).

    ADS  Google Scholar 

  157. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).

    ADS  Google Scholar 

  158. V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, Nat. Commun. 3, 961 (2012), arXiv: 1203.6417.

    ADS  Google Scholar 

  159. G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, Phys. Rev. Lett. 113, 060503 (2014), arXiv: 1402.2932.

    ADS  Google Scholar 

  160. Z. S. Yuan, X. H. Bao, C. Y. Lu, J. Zhang, C. Z. Peng, and J. W. Pan, Phys. Rep. 497, 1 (2010).

    ADS  MathSciNet  Google Scholar 

  161. Z. Y. Zhou, Y. Li, D. S. Ding, W. Zhang, S. Shi, B. S. Shi, and G. C. Guo, Light Sci. Appl. 5, e16019 (2016).

    Google Scholar 

  162. A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, Adv. Opt. Photon. 7, 66 (2015).

    Google Scholar 

  163. L. Chen, and W. She, Phys. Rev. A 80, 063831 (2009).

    ADS  Google Scholar 

  164. L. Chen, J. Lei, and J. Romero, Light Sci. Appl. 3, e153 (2014).

    ADS  Google Scholar 

  165. S. M. Zhao, J. Leach, L. Y. Gong, J. Ding, and B. Y. Zheng, Opt. Express 20, 452 (2012).

    ADS  Google Scholar 

  166. M. Krenn, J. Handsteiner, M. Fink, R. Fickler, R. Ursin, M. Malik, and A. Zeilinger, Proc. Natl. Acad. Sci. USA 113, 13648 (2016), arXiv: 1606.01811.

    ADS  Google Scholar 

  167. P. G. Kwiat, J. Modern Opt. 44, 2173 (1997).

    ADS  MathSciNet  Google Scholar 

  168. B. C. Ren, and F. G. Deng, Laser Phys. Lett. 10, 115201 (2013), arXiv: 1309.0168.

    ADS  Google Scholar 

  169. B. C. Ren, F. F. Du, and F. G. Deng, Phys. Rev. A 90, 052309 (2014), arXiv: 1408.0048.

    ADS  Google Scholar 

  170. T. J. Wang, L. L. Liu, R. Zhang, C. Cao, and C. Wang, Opt. Express 23, 9284 (2015).

    ADS  Google Scholar 

  171. T. J. Wang, C. Cao, and C. Wang, Phys. Rev. A 89, 052303 (2014).

    ADS  Google Scholar 

  172. G. Y. Wang, Q. Liu, and F. G. Deng, Phys. Rev. A 94, 032319 (2016), arXiv: 1607.00082.

    ADS  Google Scholar 

  173. G. Y. Wang, T. Li, Q. Ai, A. Alsaedi, T. Hayat, and F. G. Deng, Phys. Rev. Appl. 10, 054058 (2018), arXiv: 1802.00111.

    ADS  Google Scholar 

  174. B. C. Ren, H. R. Wei, and F. G. Deng, Laser Phys. Lett. 10, 095202 (2013), arXiv: 1303.0056.

    ADS  Google Scholar 

  175. B. C. Ren, and F. G. Deng, Sci. Rep. 4, 4623 (2014).

    Google Scholar 

  176. B. C. Ren, G. Y. Wang, and F. G. Deng, Phys. Rev. A 91, 032328 (2015), arXiv: 1411.0274.

    ADS  Google Scholar 

  177. T. J. Wang, Y. Zhang, and C. Wang, Laser Phys. Lett. 11, 025203 (2014).

    ADS  Google Scholar 

  178. T. Li, and G. L. Long, Phys. Rev. A 94, 022343 (2016).

    ADS  Google Scholar 

  179. B. C. Ren, and F. G. Deng, Opt. Express 25, 10863 (2017).

    ADS  Google Scholar 

  180. G. Y. Wang, T. Li, Q. Ai, and F. G. Deng, Opt. Express 26, 23333 (2018), arXiv: 1802.00113.

    ADS  Google Scholar 

  181. A. I. Lvovsky, B. C. Sanders, and W. Tittel, Nat. Photon 3, 706 (2009).

    ADS  Google Scholar 

  182. T. Li, G. J. Yang, and F. G. Deng, Phys. Rev. A 93, 012302 (2016), arXiv: 1409.0270.

    ADS  Google Scholar 

  183. T. Li, A. Miranowicz, X. Hu, K. Xia, and F. Nori, Phys. Rev. A 97, 062318 (2018), arXiv: 1803.05626.

    ADS  Google Scholar 

  184. J. Jing, and L. A. Wu, Sci. Bull. 60, 328 (2015).

    Google Scholar 

  185. C. Y. Gao, G. Y. Wang, H. Zhang, and F. G. Deng, Quantum Inf. Process. 16, 11 (2017).

    ADS  Google Scholar 

  186. C. Y. Gao, G. Y. Wang, F. Alzahrani, A. Hobiny, and F. G. Deng, J. Phys. B-At. Mol. Opt. 50, 5 (2017).

    Google Scholar 

  187. C. H. Bennett, and S. J. Wiesner, Phys. Rev. Lett. 69, 2881 (1992).

    ADS  MathSciNet  Google Scholar 

  188. C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).

    ADS  MathSciNet  Google Scholar 

  189. D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, Nature 390, 575 (1997), arXiv: 1901.11004.

    ADS  Google Scholar 

  190. A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, Science 282, 706 (1998).

    ADS  Google Scholar 

  191. C. P. Yang, S. I. Chu, and S. Han, Phys. Rev. A 70, 022329 (2004).

    ADS  Google Scholar 

  192. E. Jung, M. R. Hwang, Y. H. Ju, M. S. Kim, S. K. Yoo, H. Kim, D. K. Park, J. W. Son, S. Tamaryan, and S. K. Cha, Phys. Rev. A 78, 012312 (2008), arXiv: 0801.1433.

    ADS  Google Scholar 

  193. S. Takeda, T. Mizuta, M. Fuwa, P. van Loock, and A. Furusawa, Nature 500, 315 (2013), arXiv: 1402.4895.

    ADS  Google Scholar 

  194. S. Pirandola, J. Eisert, C. Weedbrook, A. Furusawa, and S. L. Braunstein, Nat. Photon 9, 641 (2015), arXiv: 1505.07831.

    ADS  Google Scholar 

  195. D. V. Sychev, A. E. Ulanov, E. S. Tiunov, A. A. Pushkina, A. Kuzhamuratov, V. Novikov, and A. I. Lvovsky, Nat. Commun. 9, 3672 (2018), arXiv: 1712.10206.

    ADS  Google Scholar 

  196. J. I. Cirac, A. K. Ekert, S. F. Huelga, and C. Macchiavello, Phys. Rev. A 59, 4249 (1999).

    ADS  MathSciNet  Google Scholar 

  197. J. Borregaard, P. Kómár, E. M. Kessler, A. S. Sørensen, and M. D. Lukin, Phys. Rev. Lett. 114, 110502 (2015), arXiv: 1501.00956.

    ADS  Google Scholar 

  198. W. Qin, X. Wang, A. Miranowicz, Z. Zhong, and F. Nori, Phys. Rev. A 96, 012315 (2017), arXiv: 1608.04195.

    ADS  Google Scholar 

  199. W. Qin, A. Miranowicz, P. B. Li, X. Y. Lü, J. Q. You, and F. Nori, Phys. Rev. Lett. 120, 093601 (2018), arXiv: 1709.09555.

    ADS  Google Scholar 

  200. Y. Takeuchi, K. Fujii, R. Ikuta, T. Yamamoto, and N. Imoto, Phys. Rev. A 93, 052307 (2016), arXiv: 1505.04248.

    ADS  Google Scholar 

  201. H. L. Huang, Q. Zhao, X. Ma, C. Liu, Z. E. Su, X. L. Wang, L. Li, N. L. Liu, B. C. Sanders, C. Y. Lu, and J. W. Pan, Phys. Rev. Lett. 119, 050503 (2017), arXiv: 1707.00400.

    ADS  Google Scholar 

  202. Y. B. Sheng, and L. Zhou, Phys. Rev. A 98, 052343 (2018).

    ADS  Google Scholar 

  203. Y. B. Sheng, and L. Zhou, Sci. Bull. 62, 1025 (2017).

    Google Scholar 

  204. P. L. Guo, T. Li, Q. Ai, and F.-G. Deng, arXiv: 1809.00105.

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Authors and Affiliations

  1. Department of Physics, Applied Optics Beijing Area Major Laboratory, Beijing Normal University, Beijing, 100875, China

    Peng-Liang Guo, Cheng-Yan Gao & Fu-Guo Deng

  2. School of Science, Nanjing University of Science and Technology, Nanjing, 210094, China

    Tao Li

  3. Department of Physics, Chongqing University, Chongqing, 400044, China

    Xi-Han Li

  4. NAAM-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Fu-Guo Deng

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  1. Peng-Liang Guo
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Guo, PL., Gao, CY., Li, T. et al. Quantum error rejection for faithful quantum communication over noise channels. Sci. China Phys. Mech. Astron. 62, 110301 (2019). https://doi.org/10.1007/s11433-019-9396-8

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