Abstract

Quantum key distribution (QKD) offers information-theoretic security verified by quantum mechanics to share keys between legitimate users. Most of the existing QKD systems employ active decoy states based on weak coherent sources (WCS). Meanwhile, parametric down-conversion (PDC) sources are seldom used due to several of their shortcomings. In the present work, to show the superiority of PDC sources, we have accomplished a proof-of-principle demonstration of a PDC source-based QKD with over 40 dB based on the one-way BB84 protocol. In this QKD system, a novel passive decoy-state scheme—secure to coherent attacks—is proposed, using several built-in decoy states for parameter estimation. This not only avoids intensity modulating errors, but also diminishes all possible information leakage from the intensity modulating process. The experimental results show a significantly enhanced performance compared with existing PDC source-based QKD systems. In addition, it exhibits some superiority even over active decoy-state QKD systems based on WCS.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Biased three-intensity decoy-state scheme on the measurement-device-independent quantum key distribution using heralded single-photon sources

Chun-Hui Zhang, Chun-Mei Zhang, Guang-Can Guo, and Qin Wang
Opt. Express 26(4) 4219-4229 (2018)

Fast optical source for quantum key distribution based on semiconductor optical amplifiers

M. Jofre, A. Gardelein, G. Anzolin, W. Amaya, J. Capmany, R. Ursin, L. Peñate, D. Lopez, J. L. San Juan, J. A. Carrasco, F. Garcia, F. J. Torcal-Milla, L. M. Sanchez-Brea, E. Bernabeu, J. M. Perdigues, T. Jennewein, J. P. Torres, M. W. Mitchell, and V. Pruneri
Opt. Express 19(5) 3825-3834 (2011)

Finite-key analysis of practical decoy-state measurement-device-independent quantum key distribution with unstable sources

Yang Wang, Wan-Su Bao, Chun Zhou, Mu-Sheng Jiang, and Hong-Wei Li
J. Opt. Soc. Am. B 36(3) B83-B91 (2019)

References

  • View by:
  • |
  • |
  • |

  1. H.-K. Lo and H. F. Chau, “Unconditional security of quantum key distribution over arbitrarily long distances,” Science 283, 2050–2056 (1999).
    [Crossref] [PubMed]
  2. P. W. Shor and J. Preskill, “Simple proof of security of the BB84 quantum key distribution protocol,” Phys. Rev. Lett. 85, 441–444 (2000).
    [Crossref] [PubMed]
  3. D. Mayers, “Unconditional security in quantum cryptography,” J. ACM 48, 351–406 (2001).
    [Crossref]
  4. C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” in Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India (IEEE, New York, 1984), pp. 175–179.
  5. V. Makarov, A. Anisimov, and J. Skaar, “Effects of detector efficiency mismatch on security of quantum cryptosystems,” Phys. Rev. A 74, 022313 (2006).
    [Crossref]
  6. B. Qi, C.-H. F. Fung, H.-K. Lo, and X. Ma, “Time-shift attack in practical quantum cryptosystems,” Quantum Inf. Comput. 7, 073 (2007).
  7. Y. Zhao, C.-H. F. Fung, B. Qi, C. Chen, and H.-K. Lo, “Quantum hacking: Experimental demonstration of time-shift attack against practical quantum-key-distribution systems,” Phys. Rev. A 78, 042333 (2008).
    [Crossref]
  8. G. Brassard, N. Lütkenhaus, T. Mor, and B. Sanders, “Limitations on practical quantum cryptography,” Phys. Rev. Lett. 85, 1330–1333 (2000).
    [Crossref] [PubMed]
  9. N. Lütkenhaus, “Security against individual attacks for realistic quantum key distribution,” Phys. Rev. A 61, 052304 (2000).
    [Crossref]
  10. N. Lütkenhaus and M. Jahma, “Quantum key distribution with realistic states: photon-number statistics in the photon-number splitting attack,” New J. Phys. 4, 44 (2002).
    [Crossref]
  11. J. C. Boileau, D. Gottesman, R. Laflamme, D. Poulin, and R. W. Spekkens, “Robust polarization-based quantum key distribution over a collective-noise channel,” Phys. Rev. Lett. 92, 017901 (2004).
    [Crossref] [PubMed]
  12. W. Y. Hwang, “Quantum key distribution with high loss: Toward global secure communication,” Phys. Rev. Lett. 91, 057901 (2003).
    [Crossref] [PubMed]
  13. X. B. Wang, “Beating the photon-number-splitting attack in practical quantum cryptography,” Phys. Rev. Lett. 94, 230503 (2005).
    [Crossref] [PubMed]
  14. H.-K. Lo, X. F. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94, 230504 (2005).
    [Crossref] [PubMed]
  15. Y. Zhao, B. Qi, X. F. Ma, H.-K. Lo, and L. Qian, “Experimental quantum key distribution with decoy states,” Phys. Rev. Lett. 96, 070502 (2006).
    [Crossref] [PubMed]
  16. C.-Z. Peng, J. Zhang, D. Yang, W.-B. Gao, H.-X. Ma, H. Yin, H.-P. Zeng, T. Yang, X.B. Wang, and J. W. Pan, “Experimental long-distance decoy-state quantum key distribution based on polarization encoding,” Phys. Rev. Lett. 98, 010505 (2007).
    [Crossref] [PubMed]
  17. D. Rosenberg, J. W. Harrington, P. R. Rice, P. A. Hiskett, C. G. Peterson, R. J. Hughes, A. E. Lita, S. W. Nam, and J. E. Nordholt, “Long-distance decoy-state quantum key distribution in optical fibe, r,” Phys. Rev. Lett. 98, 010503 (2007).
    [Crossref]
  18. Q. Wang, X. B. Wang, and G. C. Guo, “Practical decoy-state method in quantum key distribution with a heralded single-photon source,” Phys. Rev. A 75, 012312 (2007).
    [Crossref]
  19. Q. Wang and A. karlsson, “Performance enhancement of a decoy-state quantum key distribution using a conditionally prepared downconversion source in the Poisson distribution,” Phys. Rev. A 76, 014309 (2007).
    [Crossref]
  20. Y. Adachi, T. Yamamoto, M. Koashi, and N. Imoto, “Simple and efficient quantum key distribution with parametric down-conversion,” Phys. Rev. Lett. 99, 180503 (2007).
    [Crossref] [PubMed]
  21. Q. Wang, W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z. F. Han, G. C. Guo, and A. Karlsson, “Experimental decoy-state quantum key distribution with a sub-poissionian heralded single-photon source,” Phys. Rev. Lett. 100, 090501 (2008).
    [Crossref] [PubMed]
  22. Q.-C. Sun, W.-L. Wang, Y. Liu, F. Zhou, J. S. Pelc, M. M. Fejer, C.-Z. Peng, X.-F. Chen, X.-F. Ma, Q. Zhang, and J.-W. Pan, “Experimental passive decoy-state quantum key distribution,” Laser Phys. Lett.,  11, 085202 (2014).
    [Crossref]
  23. Q. Wang, C.-H. Zhang, and X.-B. Wang, “Scheme for realizing passive quantum key distribution with heralded single-photon sources,” Phys. Rev. A 93, 032312 (2016).
    [Crossref]
  24. Y. Liu, T.-Y. Chen, J. Wang, W.-Q. Cai, X. Wan, L.-K. Chen, J.-H. Wang, S.-B. Liu, H. Liang, L. Yang, C.-Z. Peng, K. Chen, Z.-B. Chen, and J.-W. Pan, “Decoy-state quantum key distribution with polarized photons over 200 km,” Opt. Expr. 8, 8587–8594 (2010).
    [Crossref]
  25. B. Frohlich, M. Lucamarini, J. F. Dynes, L. C. Comandar, W. W.-S. Tam, A. Plews, A. W. Sharpe, Z.-L. Yuan, and A. J. Shields, “Long-distance quantum key distribution secure against coherent attacks,” Optica,  4, 163–167 (2017).
    [Crossref]
  26. B. Korzh, C. C. W. Lim, R. Houlmann, N. Gisin, M. J. Li, D. Nolan, B. Sanguinetti, R. Thew, and H. Zbinden, “Provably secure and practical quantum key distribution over 307 km of optical fibre,” Nature Photon. 9, 163–168 (2015).
    [Crossref]
  27. H.-L. Yin, T.-Y. Chen, Z.-W. Yu, H. Liu, L.-X. You, Y.-H. Zhou, S.-J. Chen, Y.-Q. Mao, M.-Q. Huang, W.-J. Zhang, H. Chen, M.-J. Li, D. Nolan, F. Zhou, X. Jiang, Z. Wang, Q. Zhang, X.-B. Wang, and J.-W. Pan, “Measurement-Device-Independent Quantum Key Distribution Over a 404 km Optical Fiber,” Phys. Rev. Lett. 117190501 (2016).
    [Crossref]
  28. T. Scheidl, R. Ursin, A. Fedrizzi, S. Ramelow, X.-S. Ma, T. Herbst, R. Prevedel, L. Ratschbacher, J. Kofler, T. Jennewein, and A. Zeilinger, “Feasibility of 300 km quantum key distribution with entangled states,” New J. Phys. 11, 085002 (2009).
    [Crossref]
  29. Y. Adachi, T. Yamamoto, M. Koashi, and N. Imoto, “Boosting up quantum key distribution by learning statistics of practical single-photon sources,” New J. Phys. 11, 113033 (2009).
    [Crossref]
  30. C. Gobby, Z. L. Yuan, and A. J. Shields, “Quantum key distribution over 122 km of standard telecom fiber,” Appl. Phys. Lett. 84, 3762–3764 (2004).
    [Crossref]
  31. X.-F. Mo, B. Zhu, Z.-F. Han, Y.-Z. Gui, and G.-C. Guo, “Faraday-Michelson system for quantum cryptography,” Opt. Lett. 30, 2632–2634 (2005).
    [Crossref] [PubMed]
  32. Z.-F. Han, X.-F. Mo, Y.-Z. Gui, and G.-C. Guo, “Stability of phase-modulated quantum key distribution systems,” Appl. Phys. Lett. 86, 221103 (2005).
    [Crossref]
  33. C.-H. F. Fung, X. Ma, and H. F. Chau, “Practical issues in quantum-key-distribution postprocessing,” Phys. Rev. A 81, 012318 (2010).
    [Crossref]
  34. Z. Zhang, Q. Zhao, M. Razavi, and X. Ma, “Improved key-rate bounds for practical decoy-state quantum-key-distribution systems,” Phys. Rev. A 95, 012333 (2017).
    [Crossref]
  35. C. C. W. Lim, M. Curty, N. Walenta, F. Xu, and H. Zbinden, “Concise security bounds for practical decoy-state quantum key distribution,” Phys. Rev. A 89, 022307 (2014).
    [Crossref]
  36. M. Curty, F. Xu, W. Cui, C. C. W. Lim, K. Tamaki, and H.-K. Lo, “Finite-key analysis for measurement-device-independent quantum key distribution,” Nat. Commun. 5, 3732 (2014).
    [Crossref] [PubMed]
  37. Digital cellular telecommunications system; Full rate speech; Transcoding (GSM 06.10 RPE-LTP), ETS 300 961, V8.1.1 (2000).
  38. Q. Wang, X.-Y. Zhou, and G.-C. Guo, “Realizing the measure-device-independent quantum-key-distribution with passive heralded-single photon sources,” Sci. Rep. 6, 35394 (2016).
    [Crossref] [PubMed]
  39. S. Wang, Z.-Q. Yin, W. Chen, D.-Y. He, X.-T. Song, H.-W. Li, L.-J. Zhang, Z. Zhou, G.-C. Guo, and Z.-F. Han,”Experimental demonstration of a quantum key distribution without signal disturbance monitoring,” Nat. Photonics 9, 832 (2015).
    [Crossref]
  40. X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A,  72, 012326 (2005).
    [Crossref]

2017 (2)

2016 (3)

Q. Wang, C.-H. Zhang, and X.-B. Wang, “Scheme for realizing passive quantum key distribution with heralded single-photon sources,” Phys. Rev. A 93, 032312 (2016).
[Crossref]

H.-L. Yin, T.-Y. Chen, Z.-W. Yu, H. Liu, L.-X. You, Y.-H. Zhou, S.-J. Chen, Y.-Q. Mao, M.-Q. Huang, W.-J. Zhang, H. Chen, M.-J. Li, D. Nolan, F. Zhou, X. Jiang, Z. Wang, Q. Zhang, X.-B. Wang, and J.-W. Pan, “Measurement-Device-Independent Quantum Key Distribution Over a 404 km Optical Fiber,” Phys. Rev. Lett. 117190501 (2016).
[Crossref]

Q. Wang, X.-Y. Zhou, and G.-C. Guo, “Realizing the measure-device-independent quantum-key-distribution with passive heralded-single photon sources,” Sci. Rep. 6, 35394 (2016).
[Crossref] [PubMed]

2015 (2)

S. Wang, Z.-Q. Yin, W. Chen, D.-Y. He, X.-T. Song, H.-W. Li, L.-J. Zhang, Z. Zhou, G.-C. Guo, and Z.-F. Han,”Experimental demonstration of a quantum key distribution without signal disturbance monitoring,” Nat. Photonics 9, 832 (2015).
[Crossref]

B. Korzh, C. C. W. Lim, R. Houlmann, N. Gisin, M. J. Li, D. Nolan, B. Sanguinetti, R. Thew, and H. Zbinden, “Provably secure and practical quantum key distribution over 307 km of optical fibre,” Nature Photon. 9, 163–168 (2015).
[Crossref]

2014 (3)

C. C. W. Lim, M. Curty, N. Walenta, F. Xu, and H. Zbinden, “Concise security bounds for practical decoy-state quantum key distribution,” Phys. Rev. A 89, 022307 (2014).
[Crossref]

M. Curty, F. Xu, W. Cui, C. C. W. Lim, K. Tamaki, and H.-K. Lo, “Finite-key analysis for measurement-device-independent quantum key distribution,” Nat. Commun. 5, 3732 (2014).
[Crossref] [PubMed]

Q.-C. Sun, W.-L. Wang, Y. Liu, F. Zhou, J. S. Pelc, M. M. Fejer, C.-Z. Peng, X.-F. Chen, X.-F. Ma, Q. Zhang, and J.-W. Pan, “Experimental passive decoy-state quantum key distribution,” Laser Phys. Lett.,  11, 085202 (2014).
[Crossref]

2010 (2)

C.-H. F. Fung, X. Ma, and H. F. Chau, “Practical issues in quantum-key-distribution postprocessing,” Phys. Rev. A 81, 012318 (2010).
[Crossref]

Y. Liu, T.-Y. Chen, J. Wang, W.-Q. Cai, X. Wan, L.-K. Chen, J.-H. Wang, S.-B. Liu, H. Liang, L. Yang, C.-Z. Peng, K. Chen, Z.-B. Chen, and J.-W. Pan, “Decoy-state quantum key distribution with polarized photons over 200 km,” Opt. Expr. 8, 8587–8594 (2010).
[Crossref]

2009 (2)

T. Scheidl, R. Ursin, A. Fedrizzi, S. Ramelow, X.-S. Ma, T. Herbst, R. Prevedel, L. Ratschbacher, J. Kofler, T. Jennewein, and A. Zeilinger, “Feasibility of 300 km quantum key distribution with entangled states,” New J. Phys. 11, 085002 (2009).
[Crossref]

Y. Adachi, T. Yamamoto, M. Koashi, and N. Imoto, “Boosting up quantum key distribution by learning statistics of practical single-photon sources,” New J. Phys. 11, 113033 (2009).
[Crossref]

2008 (2)

Q. Wang, W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z. F. Han, G. C. Guo, and A. Karlsson, “Experimental decoy-state quantum key distribution with a sub-poissionian heralded single-photon source,” Phys. Rev. Lett. 100, 090501 (2008).
[Crossref] [PubMed]

Y. Zhao, C.-H. F. Fung, B. Qi, C. Chen, and H.-K. Lo, “Quantum hacking: Experimental demonstration of time-shift attack against practical quantum-key-distribution systems,” Phys. Rev. A 78, 042333 (2008).
[Crossref]

2007 (6)

B. Qi, C.-H. F. Fung, H.-K. Lo, and X. Ma, “Time-shift attack in practical quantum cryptosystems,” Quantum Inf. Comput. 7, 073 (2007).

C.-Z. Peng, J. Zhang, D. Yang, W.-B. Gao, H.-X. Ma, H. Yin, H.-P. Zeng, T. Yang, X.B. Wang, and J. W. Pan, “Experimental long-distance decoy-state quantum key distribution based on polarization encoding,” Phys. Rev. Lett. 98, 010505 (2007).
[Crossref] [PubMed]

D. Rosenberg, J. W. Harrington, P. R. Rice, P. A. Hiskett, C. G. Peterson, R. J. Hughes, A. E. Lita, S. W. Nam, and J. E. Nordholt, “Long-distance decoy-state quantum key distribution in optical fibe, r,” Phys. Rev. Lett. 98, 010503 (2007).
[Crossref]

Q. Wang, X. B. Wang, and G. C. Guo, “Practical decoy-state method in quantum key distribution with a heralded single-photon source,” Phys. Rev. A 75, 012312 (2007).
[Crossref]

Q. Wang and A. karlsson, “Performance enhancement of a decoy-state quantum key distribution using a conditionally prepared downconversion source in the Poisson distribution,” Phys. Rev. A 76, 014309 (2007).
[Crossref]

Y. Adachi, T. Yamamoto, M. Koashi, and N. Imoto, “Simple and efficient quantum key distribution with parametric down-conversion,” Phys. Rev. Lett. 99, 180503 (2007).
[Crossref] [PubMed]

2006 (2)

V. Makarov, A. Anisimov, and J. Skaar, “Effects of detector efficiency mismatch on security of quantum cryptosystems,” Phys. Rev. A 74, 022313 (2006).
[Crossref]

Y. Zhao, B. Qi, X. F. Ma, H.-K. Lo, and L. Qian, “Experimental quantum key distribution with decoy states,” Phys. Rev. Lett. 96, 070502 (2006).
[Crossref] [PubMed]

2005 (5)

Z.-F. Han, X.-F. Mo, Y.-Z. Gui, and G.-C. Guo, “Stability of phase-modulated quantum key distribution systems,” Appl. Phys. Lett. 86, 221103 (2005).
[Crossref]

X.-F. Mo, B. Zhu, Z.-F. Han, Y.-Z. Gui, and G.-C. Guo, “Faraday-Michelson system for quantum cryptography,” Opt. Lett. 30, 2632–2634 (2005).
[Crossref] [PubMed]

X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A,  72, 012326 (2005).
[Crossref]

X. B. Wang, “Beating the photon-number-splitting attack in practical quantum cryptography,” Phys. Rev. Lett. 94, 230503 (2005).
[Crossref] [PubMed]

H.-K. Lo, X. F. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94, 230504 (2005).
[Crossref] [PubMed]

2004 (2)

J. C. Boileau, D. Gottesman, R. Laflamme, D. Poulin, and R. W. Spekkens, “Robust polarization-based quantum key distribution over a collective-noise channel,” Phys. Rev. Lett. 92, 017901 (2004).
[Crossref] [PubMed]

C. Gobby, Z. L. Yuan, and A. J. Shields, “Quantum key distribution over 122 km of standard telecom fiber,” Appl. Phys. Lett. 84, 3762–3764 (2004).
[Crossref]

2003 (1)

W. Y. Hwang, “Quantum key distribution with high loss: Toward global secure communication,” Phys. Rev. Lett. 91, 057901 (2003).
[Crossref] [PubMed]

2002 (1)

N. Lütkenhaus and M. Jahma, “Quantum key distribution with realistic states: photon-number statistics in the photon-number splitting attack,” New J. Phys. 4, 44 (2002).
[Crossref]

2001 (1)

D. Mayers, “Unconditional security in quantum cryptography,” J. ACM 48, 351–406 (2001).
[Crossref]

2000 (3)

P. W. Shor and J. Preskill, “Simple proof of security of the BB84 quantum key distribution protocol,” Phys. Rev. Lett. 85, 441–444 (2000).
[Crossref] [PubMed]

G. Brassard, N. Lütkenhaus, T. Mor, and B. Sanders, “Limitations on practical quantum cryptography,” Phys. Rev. Lett. 85, 1330–1333 (2000).
[Crossref] [PubMed]

N. Lütkenhaus, “Security against individual attacks for realistic quantum key distribution,” Phys. Rev. A 61, 052304 (2000).
[Crossref]

1999 (1)

H.-K. Lo and H. F. Chau, “Unconditional security of quantum key distribution over arbitrarily long distances,” Science 283, 2050–2056 (1999).
[Crossref] [PubMed]

Adachi, Y.

Y. Adachi, T. Yamamoto, M. Koashi, and N. Imoto, “Boosting up quantum key distribution by learning statistics of practical single-photon sources,” New J. Phys. 11, 113033 (2009).
[Crossref]

Y. Adachi, T. Yamamoto, M. Koashi, and N. Imoto, “Simple and efficient quantum key distribution with parametric down-conversion,” Phys. Rev. Lett. 99, 180503 (2007).
[Crossref] [PubMed]

Anisimov, A.

V. Makarov, A. Anisimov, and J. Skaar, “Effects of detector efficiency mismatch on security of quantum cryptosystems,” Phys. Rev. A 74, 022313 (2006).
[Crossref]

Bennett, C. H.

C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” in Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India (IEEE, New York, 1984), pp. 175–179.

Boileau, J. C.

J. C. Boileau, D. Gottesman, R. Laflamme, D. Poulin, and R. W. Spekkens, “Robust polarization-based quantum key distribution over a collective-noise channel,” Phys. Rev. Lett. 92, 017901 (2004).
[Crossref] [PubMed]

Brassard, G.

G. Brassard, N. Lütkenhaus, T. Mor, and B. Sanders, “Limitations on practical quantum cryptography,” Phys. Rev. Lett. 85, 1330–1333 (2000).
[Crossref] [PubMed]

C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” in Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India (IEEE, New York, 1984), pp. 175–179.

Cai, W.-Q.

Y. Liu, T.-Y. Chen, J. Wang, W.-Q. Cai, X. Wan, L.-K. Chen, J.-H. Wang, S.-B. Liu, H. Liang, L. Yang, C.-Z. Peng, K. Chen, Z.-B. Chen, and J.-W. Pan, “Decoy-state quantum key distribution with polarized photons over 200 km,” Opt. Expr. 8, 8587–8594 (2010).
[Crossref]

Chau, H. F.

C.-H. F. Fung, X. Ma, and H. F. Chau, “Practical issues in quantum-key-distribution postprocessing,” Phys. Rev. A 81, 012318 (2010).
[Crossref]

H.-K. Lo and H. F. Chau, “Unconditional security of quantum key distribution over arbitrarily long distances,” Science 283, 2050–2056 (1999).
[Crossref] [PubMed]

Chen, C.

Y. Zhao, C.-H. F. Fung, B. Qi, C. Chen, and H.-K. Lo, “Quantum hacking: Experimental demonstration of time-shift attack against practical quantum-key-distribution systems,” Phys. Rev. A 78, 042333 (2008).
[Crossref]

Chen, H.

H.-L. Yin, T.-Y. Chen, Z.-W. Yu, H. Liu, L.-X. You, Y.-H. Zhou, S.-J. Chen, Y.-Q. Mao, M.-Q. Huang, W.-J. Zhang, H. Chen, M.-J. Li, D. Nolan, F. Zhou, X. Jiang, Z. Wang, Q. Zhang, X.-B. Wang, and J.-W. Pan, “Measurement-Device-Independent Quantum Key Distribution Over a 404 km Optical Fiber,” Phys. Rev. Lett. 117190501 (2016).
[Crossref]

Chen, K.

Y. Liu, T.-Y. Chen, J. Wang, W.-Q. Cai, X. Wan, L.-K. Chen, J.-H. Wang, S.-B. Liu, H. Liang, L. Yang, C.-Z. Peng, K. Chen, Z.-B. Chen, and J.-W. Pan, “Decoy-state quantum key distribution with polarized photons over 200 km,” Opt. Expr. 8, 8587–8594 (2010).
[Crossref]

H.-K. Lo, X. F. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94, 230504 (2005).
[Crossref] [PubMed]

Chen, L.-K.

Y. Liu, T.-Y. Chen, J. Wang, W.-Q. Cai, X. Wan, L.-K. Chen, J.-H. Wang, S.-B. Liu, H. Liang, L. Yang, C.-Z. Peng, K. Chen, Z.-B. Chen, and J.-W. Pan, “Decoy-state quantum key distribution with polarized photons over 200 km,” Opt. Expr. 8, 8587–8594 (2010).
[Crossref]

Chen, S.-J.

H.-L. Yin, T.-Y. Chen, Z.-W. Yu, H. Liu, L.-X. You, Y.-H. Zhou, S.-J. Chen, Y.-Q. Mao, M.-Q. Huang, W.-J. Zhang, H. Chen, M.-J. Li, D. Nolan, F. Zhou, X. Jiang, Z. Wang, Q. Zhang, X.-B. Wang, and J.-W. Pan, “Measurement-Device-Independent Quantum Key Distribution Over a 404 km Optical Fiber,” Phys. Rev. Lett. 117190501 (2016).
[Crossref]

Chen, T.-Y.

H.-L. Yin, T.-Y. Chen, Z.-W. Yu, H. Liu, L.-X. You, Y.-H. Zhou, S.-J. Chen, Y.-Q. Mao, M.-Q. Huang, W.-J. Zhang, H. Chen, M.-J. Li, D. Nolan, F. Zhou, X. Jiang, Z. Wang, Q. Zhang, X.-B. Wang, and J.-W. Pan, “Measurement-Device-Independent Quantum Key Distribution Over a 404 km Optical Fiber,” Phys. Rev. Lett. 117190501 (2016).
[Crossref]

Y. Liu, T.-Y. Chen, J. Wang, W.-Q. Cai, X. Wan, L.-K. Chen, J.-H. Wang, S.-B. Liu, H. Liang, L. Yang, C.-Z. Peng, K. Chen, Z.-B. Chen, and J.-W. Pan, “Decoy-state quantum key distribution with polarized photons over 200 km,” Opt. Expr. 8, 8587–8594 (2010).
[Crossref]

Chen, W.

S. Wang, Z.-Q. Yin, W. Chen, D.-Y. He, X.-T. Song, H.-W. Li, L.-J. Zhang, Z. Zhou, G.-C. Guo, and Z.-F. Han,”Experimental demonstration of a quantum key distribution without signal disturbance monitoring,” Nat. Photonics 9, 832 (2015).
[Crossref]

Q. Wang, W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z. F. Han, G. C. Guo, and A. Karlsson, “Experimental decoy-state quantum key distribution with a sub-poissionian heralded single-photon source,” Phys. Rev. Lett. 100, 090501 (2008).
[Crossref] [PubMed]

Chen, X.-F.

Q.-C. Sun, W.-L. Wang, Y. Liu, F. Zhou, J. S. Pelc, M. M. Fejer, C.-Z. Peng, X.-F. Chen, X.-F. Ma, Q. Zhang, and J.-W. Pan, “Experimental passive decoy-state quantum key distribution,” Laser Phys. Lett.,  11, 085202 (2014).
[Crossref]

Chen, Z.-B.

Y. Liu, T.-Y. Chen, J. Wang, W.-Q. Cai, X. Wan, L.-K. Chen, J.-H. Wang, S.-B. Liu, H. Liang, L. Yang, C.-Z. Peng, K. Chen, Z.-B. Chen, and J.-W. Pan, “Decoy-state quantum key distribution with polarized photons over 200 km,” Opt. Expr. 8, 8587–8594 (2010).
[Crossref]

Comandar, L. C.

Cui, W.

M. Curty, F. Xu, W. Cui, C. C. W. Lim, K. Tamaki, and H.-K. Lo, “Finite-key analysis for measurement-device-independent quantum key distribution,” Nat. Commun. 5, 3732 (2014).
[Crossref] [PubMed]

Curty, M.

M. Curty, F. Xu, W. Cui, C. C. W. Lim, K. Tamaki, and H.-K. Lo, “Finite-key analysis for measurement-device-independent quantum key distribution,” Nat. Commun. 5, 3732 (2014).
[Crossref] [PubMed]

C. C. W. Lim, M. Curty, N. Walenta, F. Xu, and H. Zbinden, “Concise security bounds for practical decoy-state quantum key distribution,” Phys. Rev. A 89, 022307 (2014).
[Crossref]

Dynes, J. F.

Fedrizzi, A.

T. Scheidl, R. Ursin, A. Fedrizzi, S. Ramelow, X.-S. Ma, T. Herbst, R. Prevedel, L. Ratschbacher, J. Kofler, T. Jennewein, and A. Zeilinger, “Feasibility of 300 km quantum key distribution with entangled states,” New J. Phys. 11, 085002 (2009).
[Crossref]

Fejer, M. M.

Q.-C. Sun, W.-L. Wang, Y. Liu, F. Zhou, J. S. Pelc, M. M. Fejer, C.-Z. Peng, X.-F. Chen, X.-F. Ma, Q. Zhang, and J.-W. Pan, “Experimental passive decoy-state quantum key distribution,” Laser Phys. Lett.,  11, 085202 (2014).
[Crossref]

Frohlich, B.

Fung, C.-H. F.

C.-H. F. Fung, X. Ma, and H. F. Chau, “Practical issues in quantum-key-distribution postprocessing,” Phys. Rev. A 81, 012318 (2010).
[Crossref]

Y. Zhao, C.-H. F. Fung, B. Qi, C. Chen, and H.-K. Lo, “Quantum hacking: Experimental demonstration of time-shift attack against practical quantum-key-distribution systems,” Phys. Rev. A 78, 042333 (2008).
[Crossref]

B. Qi, C.-H. F. Fung, H.-K. Lo, and X. Ma, “Time-shift attack in practical quantum cryptosystems,” Quantum Inf. Comput. 7, 073 (2007).

Gao, W.-B.

C.-Z. Peng, J. Zhang, D. Yang, W.-B. Gao, H.-X. Ma, H. Yin, H.-P. Zeng, T. Yang, X.B. Wang, and J. W. Pan, “Experimental long-distance decoy-state quantum key distribution based on polarization encoding,” Phys. Rev. Lett. 98, 010505 (2007).
[Crossref] [PubMed]

Gisin, N.

B. Korzh, C. C. W. Lim, R. Houlmann, N. Gisin, M. J. Li, D. Nolan, B. Sanguinetti, R. Thew, and H. Zbinden, “Provably secure and practical quantum key distribution over 307 km of optical fibre,” Nature Photon. 9, 163–168 (2015).
[Crossref]

Gobby, C.

C. Gobby, Z. L. Yuan, and A. J. Shields, “Quantum key distribution over 122 km of standard telecom fiber,” Appl. Phys. Lett. 84, 3762–3764 (2004).
[Crossref]

Gottesman, D.

J. C. Boileau, D. Gottesman, R. Laflamme, D. Poulin, and R. W. Spekkens, “Robust polarization-based quantum key distribution over a collective-noise channel,” Phys. Rev. Lett. 92, 017901 (2004).
[Crossref] [PubMed]

Gui, Y.-Z.

Z.-F. Han, X.-F. Mo, Y.-Z. Gui, and G.-C. Guo, “Stability of phase-modulated quantum key distribution systems,” Appl. Phys. Lett. 86, 221103 (2005).
[Crossref]

X.-F. Mo, B. Zhu, Z.-F. Han, Y.-Z. Gui, and G.-C. Guo, “Faraday-Michelson system for quantum cryptography,” Opt. Lett. 30, 2632–2634 (2005).
[Crossref] [PubMed]

Guo, G. C.

Q. Wang, W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z. F. Han, G. C. Guo, and A. Karlsson, “Experimental decoy-state quantum key distribution with a sub-poissionian heralded single-photon source,” Phys. Rev. Lett. 100, 090501 (2008).
[Crossref] [PubMed]

Q. Wang, X. B. Wang, and G. C. Guo, “Practical decoy-state method in quantum key distribution with a heralded single-photon source,” Phys. Rev. A 75, 012312 (2007).
[Crossref]

Guo, G.-C.

Q. Wang, X.-Y. Zhou, and G.-C. Guo, “Realizing the measure-device-independent quantum-key-distribution with passive heralded-single photon sources,” Sci. Rep. 6, 35394 (2016).
[Crossref] [PubMed]

S. Wang, Z.-Q. Yin, W. Chen, D.-Y. He, X.-T. Song, H.-W. Li, L.-J. Zhang, Z. Zhou, G.-C. Guo, and Z.-F. Han,”Experimental demonstration of a quantum key distribution without signal disturbance monitoring,” Nat. Photonics 9, 832 (2015).
[Crossref]

X.-F. Mo, B. Zhu, Z.-F. Han, Y.-Z. Gui, and G.-C. Guo, “Faraday-Michelson system for quantum cryptography,” Opt. Lett. 30, 2632–2634 (2005).
[Crossref] [PubMed]

Z.-F. Han, X.-F. Mo, Y.-Z. Gui, and G.-C. Guo, “Stability of phase-modulated quantum key distribution systems,” Appl. Phys. Lett. 86, 221103 (2005).
[Crossref]

Han, Z. F.

Q. Wang, W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z. F. Han, G. C. Guo, and A. Karlsson, “Experimental decoy-state quantum key distribution with a sub-poissionian heralded single-photon source,” Phys. Rev. Lett. 100, 090501 (2008).
[Crossref] [PubMed]

Han, Z.-F.

S. Wang, Z.-Q. Yin, W. Chen, D.-Y. He, X.-T. Song, H.-W. Li, L.-J. Zhang, Z. Zhou, G.-C. Guo, and Z.-F. Han,”Experimental demonstration of a quantum key distribution without signal disturbance monitoring,” Nat. Photonics 9, 832 (2015).
[Crossref]

X.-F. Mo, B. Zhu, Z.-F. Han, Y.-Z. Gui, and G.-C. Guo, “Faraday-Michelson system for quantum cryptography,” Opt. Lett. 30, 2632–2634 (2005).
[Crossref] [PubMed]

Z.-F. Han, X.-F. Mo, Y.-Z. Gui, and G.-C. Guo, “Stability of phase-modulated quantum key distribution systems,” Appl. Phys. Lett. 86, 221103 (2005).
[Crossref]

Harrington, J. W.

D. Rosenberg, J. W. Harrington, P. R. Rice, P. A. Hiskett, C. G. Peterson, R. J. Hughes, A. E. Lita, S. W. Nam, and J. E. Nordholt, “Long-distance decoy-state quantum key distribution in optical fibe, r,” Phys. Rev. Lett. 98, 010503 (2007).
[Crossref]

He, D.-Y.

S. Wang, Z.-Q. Yin, W. Chen, D.-Y. He, X.-T. Song, H.-W. Li, L.-J. Zhang, Z. Zhou, G.-C. Guo, and Z.-F. Han,”Experimental demonstration of a quantum key distribution without signal disturbance monitoring,” Nat. Photonics 9, 832 (2015).
[Crossref]

Herbst, T.

T. Scheidl, R. Ursin, A. Fedrizzi, S. Ramelow, X.-S. Ma, T. Herbst, R. Prevedel, L. Ratschbacher, J. Kofler, T. Jennewein, and A. Zeilinger, “Feasibility of 300 km quantum key distribution with entangled states,” New J. Phys. 11, 085002 (2009).
[Crossref]

Hiskett, P. A.

D. Rosenberg, J. W. Harrington, P. R. Rice, P. A. Hiskett, C. G. Peterson, R. J. Hughes, A. E. Lita, S. W. Nam, and J. E. Nordholt, “Long-distance decoy-state quantum key distribution in optical fibe, r,” Phys. Rev. Lett. 98, 010503 (2007).
[Crossref]

Houlmann, R.

B. Korzh, C. C. W. Lim, R. Houlmann, N. Gisin, M. J. Li, D. Nolan, B. Sanguinetti, R. Thew, and H. Zbinden, “Provably secure and practical quantum key distribution over 307 km of optical fibre,” Nature Photon. 9, 163–168 (2015).
[Crossref]

Huang, M.-Q.

H.-L. Yin, T.-Y. Chen, Z.-W. Yu, H. Liu, L.-X. You, Y.-H. Zhou, S.-J. Chen, Y.-Q. Mao, M.-Q. Huang, W.-J. Zhang, H. Chen, M.-J. Li, D. Nolan, F. Zhou, X. Jiang, Z. Wang, Q. Zhang, X.-B. Wang, and J.-W. Pan, “Measurement-Device-Independent Quantum Key Distribution Over a 404 km Optical Fiber,” Phys. Rev. Lett. 117190501 (2016).
[Crossref]

Hughes, R. J.

D. Rosenberg, J. W. Harrington, P. R. Rice, P. A. Hiskett, C. G. Peterson, R. J. Hughes, A. E. Lita, S. W. Nam, and J. E. Nordholt, “Long-distance decoy-state quantum key distribution in optical fibe, r,” Phys. Rev. Lett. 98, 010503 (2007).
[Crossref]

Hwang, W. Y.

W. Y. Hwang, “Quantum key distribution with high loss: Toward global secure communication,” Phys. Rev. Lett. 91, 057901 (2003).
[Crossref] [PubMed]

Imoto, N.

Y. Adachi, T. Yamamoto, M. Koashi, and N. Imoto, “Boosting up quantum key distribution by learning statistics of practical single-photon sources,” New J. Phys. 11, 113033 (2009).
[Crossref]

Y. Adachi, T. Yamamoto, M. Koashi, and N. Imoto, “Simple and efficient quantum key distribution with parametric down-conversion,” Phys. Rev. Lett. 99, 180503 (2007).
[Crossref] [PubMed]

Jahma, M.

N. Lütkenhaus and M. Jahma, “Quantum key distribution with realistic states: photon-number statistics in the photon-number splitting attack,” New J. Phys. 4, 44 (2002).
[Crossref]

Jennewein, T.

T. Scheidl, R. Ursin, A. Fedrizzi, S. Ramelow, X.-S. Ma, T. Herbst, R. Prevedel, L. Ratschbacher, J. Kofler, T. Jennewein, and A. Zeilinger, “Feasibility of 300 km quantum key distribution with entangled states,” New J. Phys. 11, 085002 (2009).
[Crossref]

Jiang, X.

H.-L. Yin, T.-Y. Chen, Z.-W. Yu, H. Liu, L.-X. You, Y.-H. Zhou, S.-J. Chen, Y.-Q. Mao, M.-Q. Huang, W.-J. Zhang, H. Chen, M.-J. Li, D. Nolan, F. Zhou, X. Jiang, Z. Wang, Q. Zhang, X.-B. Wang, and J.-W. Pan, “Measurement-Device-Independent Quantum Key Distribution Over a 404 km Optical Fiber,” Phys. Rev. Lett. 117190501 (2016).
[Crossref]

Karlsson, A.

Q. Wang, W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z. F. Han, G. C. Guo, and A. Karlsson, “Experimental decoy-state quantum key distribution with a sub-poissionian heralded single-photon source,” Phys. Rev. Lett. 100, 090501 (2008).
[Crossref] [PubMed]

Q. Wang and A. karlsson, “Performance enhancement of a decoy-state quantum key distribution using a conditionally prepared downconversion source in the Poisson distribution,” Phys. Rev. A 76, 014309 (2007).
[Crossref]

Koashi, M.

Y. Adachi, T. Yamamoto, M. Koashi, and N. Imoto, “Boosting up quantum key distribution by learning statistics of practical single-photon sources,” New J. Phys. 11, 113033 (2009).
[Crossref]

Y. Adachi, T. Yamamoto, M. Koashi, and N. Imoto, “Simple and efficient quantum key distribution with parametric down-conversion,” Phys. Rev. Lett. 99, 180503 (2007).
[Crossref] [PubMed]

Kofler, J.

T. Scheidl, R. Ursin, A. Fedrizzi, S. Ramelow, X.-S. Ma, T. Herbst, R. Prevedel, L. Ratschbacher, J. Kofler, T. Jennewein, and A. Zeilinger, “Feasibility of 300 km quantum key distribution with entangled states,” New J. Phys. 11, 085002 (2009).
[Crossref]

Korzh, B.

B. Korzh, C. C. W. Lim, R. Houlmann, N. Gisin, M. J. Li, D. Nolan, B. Sanguinetti, R. Thew, and H. Zbinden, “Provably secure and practical quantum key distribution over 307 km of optical fibre,” Nature Photon. 9, 163–168 (2015).
[Crossref]

Laflamme, R.

J. C. Boileau, D. Gottesman, R. Laflamme, D. Poulin, and R. W. Spekkens, “Robust polarization-based quantum key distribution over a collective-noise channel,” Phys. Rev. Lett. 92, 017901 (2004).
[Crossref] [PubMed]

Li, H.-W.

S. Wang, Z.-Q. Yin, W. Chen, D.-Y. He, X.-T. Song, H.-W. Li, L.-J. Zhang, Z. Zhou, G.-C. Guo, and Z.-F. Han,”Experimental demonstration of a quantum key distribution without signal disturbance monitoring,” Nat. Photonics 9, 832 (2015).
[Crossref]

Li, M. J.

B. Korzh, C. C. W. Lim, R. Houlmann, N. Gisin, M. J. Li, D. Nolan, B. Sanguinetti, R. Thew, and H. Zbinden, “Provably secure and practical quantum key distribution over 307 km of optical fibre,” Nature Photon. 9, 163–168 (2015).
[Crossref]

Li, M.-J.

H.-L. Yin, T.-Y. Chen, Z.-W. Yu, H. Liu, L.-X. You, Y.-H. Zhou, S.-J. Chen, Y.-Q. Mao, M.-Q. Huang, W.-J. Zhang, H. Chen, M.-J. Li, D. Nolan, F. Zhou, X. Jiang, Z. Wang, Q. Zhang, X.-B. Wang, and J.-W. Pan, “Measurement-Device-Independent Quantum Key Distribution Over a 404 km Optical Fiber,” Phys. Rev. Lett. 117190501 (2016).
[Crossref]

Liang, H.

Y. Liu, T.-Y. Chen, J. Wang, W.-Q. Cai, X. Wan, L.-K. Chen, J.-H. Wang, S.-B. Liu, H. Liang, L. Yang, C.-Z. Peng, K. Chen, Z.-B. Chen, and J.-W. Pan, “Decoy-state quantum key distribution with polarized photons over 200 km,” Opt. Expr. 8, 8587–8594 (2010).
[Crossref]

Lim, C. C. W.

B. Korzh, C. C. W. Lim, R. Houlmann, N. Gisin, M. J. Li, D. Nolan, B. Sanguinetti, R. Thew, and H. Zbinden, “Provably secure and practical quantum key distribution over 307 km of optical fibre,” Nature Photon. 9, 163–168 (2015).
[Crossref]

C. C. W. Lim, M. Curty, N. Walenta, F. Xu, and H. Zbinden, “Concise security bounds for practical decoy-state quantum key distribution,” Phys. Rev. A 89, 022307 (2014).
[Crossref]

M. Curty, F. Xu, W. Cui, C. C. W. Lim, K. Tamaki, and H.-K. Lo, “Finite-key analysis for measurement-device-independent quantum key distribution,” Nat. Commun. 5, 3732 (2014).
[Crossref] [PubMed]

Lita, A. E.

D. Rosenberg, J. W. Harrington, P. R. Rice, P. A. Hiskett, C. G. Peterson, R. J. Hughes, A. E. Lita, S. W. Nam, and J. E. Nordholt, “Long-distance decoy-state quantum key distribution in optical fibe, r,” Phys. Rev. Lett. 98, 010503 (2007).
[Crossref]

Liu, H.

H.-L. Yin, T.-Y. Chen, Z.-W. Yu, H. Liu, L.-X. You, Y.-H. Zhou, S.-J. Chen, Y.-Q. Mao, M.-Q. Huang, W.-J. Zhang, H. Chen, M.-J. Li, D. Nolan, F. Zhou, X. Jiang, Z. Wang, Q. Zhang, X.-B. Wang, and J.-W. Pan, “Measurement-Device-Independent Quantum Key Distribution Over a 404 km Optical Fiber,” Phys. Rev. Lett. 117190501 (2016).
[Crossref]

Liu, S.-B.

Y. Liu, T.-Y. Chen, J. Wang, W.-Q. Cai, X. Wan, L.-K. Chen, J.-H. Wang, S.-B. Liu, H. Liang, L. Yang, C.-Z. Peng, K. Chen, Z.-B. Chen, and J.-W. Pan, “Decoy-state quantum key distribution with polarized photons over 200 km,” Opt. Expr. 8, 8587–8594 (2010).
[Crossref]

Liu, Y.

Q.-C. Sun, W.-L. Wang, Y. Liu, F. Zhou, J. S. Pelc, M. M. Fejer, C.-Z. Peng, X.-F. Chen, X.-F. Ma, Q. Zhang, and J.-W. Pan, “Experimental passive decoy-state quantum key distribution,” Laser Phys. Lett.,  11, 085202 (2014).
[Crossref]

Y. Liu, T.-Y. Chen, J. Wang, W.-Q. Cai, X. Wan, L.-K. Chen, J.-H. Wang, S.-B. Liu, H. Liang, L. Yang, C.-Z. Peng, K. Chen, Z.-B. Chen, and J.-W. Pan, “Decoy-state quantum key distribution with polarized photons over 200 km,” Opt. Expr. 8, 8587–8594 (2010).
[Crossref]

Lo, H.-K.

M. Curty, F. Xu, W. Cui, C. C. W. Lim, K. Tamaki, and H.-K. Lo, “Finite-key analysis for measurement-device-independent quantum key distribution,” Nat. Commun. 5, 3732 (2014).
[Crossref] [PubMed]

Y. Zhao, C.-H. F. Fung, B. Qi, C. Chen, and H.-K. Lo, “Quantum hacking: Experimental demonstration of time-shift attack against practical quantum-key-distribution systems,” Phys. Rev. A 78, 042333 (2008).
[Crossref]

B. Qi, C.-H. F. Fung, H.-K. Lo, and X. Ma, “Time-shift attack in practical quantum cryptosystems,” Quantum Inf. Comput. 7, 073 (2007).

Y. Zhao, B. Qi, X. F. Ma, H.-K. Lo, and L. Qian, “Experimental quantum key distribution with decoy states,” Phys. Rev. Lett. 96, 070502 (2006).
[Crossref] [PubMed]

H.-K. Lo, X. F. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94, 230504 (2005).
[Crossref] [PubMed]

X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A,  72, 012326 (2005).
[Crossref]

H.-K. Lo and H. F. Chau, “Unconditional security of quantum key distribution over arbitrarily long distances,” Science 283, 2050–2056 (1999).
[Crossref] [PubMed]

Lucamarini, M.

Lütkenhaus, N.

N. Lütkenhaus and M. Jahma, “Quantum key distribution with realistic states: photon-number statistics in the photon-number splitting attack,” New J. Phys. 4, 44 (2002).
[Crossref]

N. Lütkenhaus, “Security against individual attacks for realistic quantum key distribution,” Phys. Rev. A 61, 052304 (2000).
[Crossref]

G. Brassard, N. Lütkenhaus, T. Mor, and B. Sanders, “Limitations on practical quantum cryptography,” Phys. Rev. Lett. 85, 1330–1333 (2000).
[Crossref] [PubMed]

Ma, H.-X.

C.-Z. Peng, J. Zhang, D. Yang, W.-B. Gao, H.-X. Ma, H. Yin, H.-P. Zeng, T. Yang, X.B. Wang, and J. W. Pan, “Experimental long-distance decoy-state quantum key distribution based on polarization encoding,” Phys. Rev. Lett. 98, 010505 (2007).
[Crossref] [PubMed]

Ma, X.

Z. Zhang, Q. Zhao, M. Razavi, and X. Ma, “Improved key-rate bounds for practical decoy-state quantum-key-distribution systems,” Phys. Rev. A 95, 012333 (2017).
[Crossref]

C.-H. F. Fung, X. Ma, and H. F. Chau, “Practical issues in quantum-key-distribution postprocessing,” Phys. Rev. A 81, 012318 (2010).
[Crossref]

B. Qi, C.-H. F. Fung, H.-K. Lo, and X. Ma, “Time-shift attack in practical quantum cryptosystems,” Quantum Inf. Comput. 7, 073 (2007).

X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A,  72, 012326 (2005).
[Crossref]

Ma, X. F.

Y. Zhao, B. Qi, X. F. Ma, H.-K. Lo, and L. Qian, “Experimental quantum key distribution with decoy states,” Phys. Rev. Lett. 96, 070502 (2006).
[Crossref] [PubMed]

H.-K. Lo, X. F. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94, 230504 (2005).
[Crossref] [PubMed]

Ma, X.-F.

Q.-C. Sun, W.-L. Wang, Y. Liu, F. Zhou, J. S. Pelc, M. M. Fejer, C.-Z. Peng, X.-F. Chen, X.-F. Ma, Q. Zhang, and J.-W. Pan, “Experimental passive decoy-state quantum key distribution,” Laser Phys. Lett.,  11, 085202 (2014).
[Crossref]

Ma, X.-S.

T. Scheidl, R. Ursin, A. Fedrizzi, S. Ramelow, X.-S. Ma, T. Herbst, R. Prevedel, L. Ratschbacher, J. Kofler, T. Jennewein, and A. Zeilinger, “Feasibility of 300 km quantum key distribution with entangled states,” New J. Phys. 11, 085002 (2009).
[Crossref]

Makarov, V.

V. Makarov, A. Anisimov, and J. Skaar, “Effects of detector efficiency mismatch on security of quantum cryptosystems,” Phys. Rev. A 74, 022313 (2006).
[Crossref]

Mao, Y.-Q.

H.-L. Yin, T.-Y. Chen, Z.-W. Yu, H. Liu, L.-X. You, Y.-H. Zhou, S.-J. Chen, Y.-Q. Mao, M.-Q. Huang, W.-J. Zhang, H. Chen, M.-J. Li, D. Nolan, F. Zhou, X. Jiang, Z. Wang, Q. Zhang, X.-B. Wang, and J.-W. Pan, “Measurement-Device-Independent Quantum Key Distribution Over a 404 km Optical Fiber,” Phys. Rev. Lett. 117190501 (2016).
[Crossref]

Mayers, D.

D. Mayers, “Unconditional security in quantum cryptography,” J. ACM 48, 351–406 (2001).
[Crossref]

Mo, X.-F.

X.-F. Mo, B. Zhu, Z.-F. Han, Y.-Z. Gui, and G.-C. Guo, “Faraday-Michelson system for quantum cryptography,” Opt. Lett. 30, 2632–2634 (2005).
[Crossref] [PubMed]

Z.-F. Han, X.-F. Mo, Y.-Z. Gui, and G.-C. Guo, “Stability of phase-modulated quantum key distribution systems,” Appl. Phys. Lett. 86, 221103 (2005).
[Crossref]

Mor, T.

G. Brassard, N. Lütkenhaus, T. Mor, and B. Sanders, “Limitations on practical quantum cryptography,” Phys. Rev. Lett. 85, 1330–1333 (2000).
[Crossref] [PubMed]

Nam, S. W.

D. Rosenberg, J. W. Harrington, P. R. Rice, P. A. Hiskett, C. G. Peterson, R. J. Hughes, A. E. Lita, S. W. Nam, and J. E. Nordholt, “Long-distance decoy-state quantum key distribution in optical fibe, r,” Phys. Rev. Lett. 98, 010503 (2007).
[Crossref]

Nolan, D.

H.-L. Yin, T.-Y. Chen, Z.-W. Yu, H. Liu, L.-X. You, Y.-H. Zhou, S.-J. Chen, Y.-Q. Mao, M.-Q. Huang, W.-J. Zhang, H. Chen, M.-J. Li, D. Nolan, F. Zhou, X. Jiang, Z. Wang, Q. Zhang, X.-B. Wang, and J.-W. Pan, “Measurement-Device-Independent Quantum Key Distribution Over a 404 km Optical Fiber,” Phys. Rev. Lett. 117190501 (2016).
[Crossref]

B. Korzh, C. C. W. Lim, R. Houlmann, N. Gisin, M. J. Li, D. Nolan, B. Sanguinetti, R. Thew, and H. Zbinden, “Provably secure and practical quantum key distribution over 307 km of optical fibre,” Nature Photon. 9, 163–168 (2015).
[Crossref]

Nordholt, J. E.

D. Rosenberg, J. W. Harrington, P. R. Rice, P. A. Hiskett, C. G. Peterson, R. J. Hughes, A. E. Lita, S. W. Nam, and J. E. Nordholt, “Long-distance decoy-state quantum key distribution in optical fibe, r,” Phys. Rev. Lett. 98, 010503 (2007).
[Crossref]

Pan, J. W.

C.-Z. Peng, J. Zhang, D. Yang, W.-B. Gao, H.-X. Ma, H. Yin, H.-P. Zeng, T. Yang, X.B. Wang, and J. W. Pan, “Experimental long-distance decoy-state quantum key distribution based on polarization encoding,” Phys. Rev. Lett. 98, 010505 (2007).
[Crossref] [PubMed]

Pan, J.-W.

H.-L. Yin, T.-Y. Chen, Z.-W. Yu, H. Liu, L.-X. You, Y.-H. Zhou, S.-J. Chen, Y.-Q. Mao, M.-Q. Huang, W.-J. Zhang, H. Chen, M.-J. Li, D. Nolan, F. Zhou, X. Jiang, Z. Wang, Q. Zhang, X.-B. Wang, and J.-W. Pan, “Measurement-Device-Independent Quantum Key Distribution Over a 404 km Optical Fiber,” Phys. Rev. Lett. 117190501 (2016).
[Crossref]

Q.-C. Sun, W.-L. Wang, Y. Liu, F. Zhou, J. S. Pelc, M. M. Fejer, C.-Z. Peng, X.-F. Chen, X.-F. Ma, Q. Zhang, and J.-W. Pan, “Experimental passive decoy-state quantum key distribution,” Laser Phys. Lett.,  11, 085202 (2014).
[Crossref]

Y. Liu, T.-Y. Chen, J. Wang, W.-Q. Cai, X. Wan, L.-K. Chen, J.-H. Wang, S.-B. Liu, H. Liang, L. Yang, C.-Z. Peng, K. Chen, Z.-B. Chen, and J.-W. Pan, “Decoy-state quantum key distribution with polarized photons over 200 km,” Opt. Expr. 8, 8587–8594 (2010).
[Crossref]

Pelc, J. S.

Q.-C. Sun, W.-L. Wang, Y. Liu, F. Zhou, J. S. Pelc, M. M. Fejer, C.-Z. Peng, X.-F. Chen, X.-F. Ma, Q. Zhang, and J.-W. Pan, “Experimental passive decoy-state quantum key distribution,” Laser Phys. Lett.,  11, 085202 (2014).
[Crossref]

Peng, C.-Z.

Q.-C. Sun, W.-L. Wang, Y. Liu, F. Zhou, J. S. Pelc, M. M. Fejer, C.-Z. Peng, X.-F. Chen, X.-F. Ma, Q. Zhang, and J.-W. Pan, “Experimental passive decoy-state quantum key distribution,” Laser Phys. Lett.,  11, 085202 (2014).
[Crossref]

Y. Liu, T.-Y. Chen, J. Wang, W.-Q. Cai, X. Wan, L.-K. Chen, J.-H. Wang, S.-B. Liu, H. Liang, L. Yang, C.-Z. Peng, K. Chen, Z.-B. Chen, and J.-W. Pan, “Decoy-state quantum key distribution with polarized photons over 200 km,” Opt. Expr. 8, 8587–8594 (2010).
[Crossref]

C.-Z. Peng, J. Zhang, D. Yang, W.-B. Gao, H.-X. Ma, H. Yin, H.-P. Zeng, T. Yang, X.B. Wang, and J. W. Pan, “Experimental long-distance decoy-state quantum key distribution based on polarization encoding,” Phys. Rev. Lett. 98, 010505 (2007).
[Crossref] [PubMed]

Peterson, C. G.

D. Rosenberg, J. W. Harrington, P. R. Rice, P. A. Hiskett, C. G. Peterson, R. J. Hughes, A. E. Lita, S. W. Nam, and J. E. Nordholt, “Long-distance decoy-state quantum key distribution in optical fibe, r,” Phys. Rev. Lett. 98, 010503 (2007).
[Crossref]

Plews, A.

Poulin, D.

J. C. Boileau, D. Gottesman, R. Laflamme, D. Poulin, and R. W. Spekkens, “Robust polarization-based quantum key distribution over a collective-noise channel,” Phys. Rev. Lett. 92, 017901 (2004).
[Crossref] [PubMed]

Preskill, J.

P. W. Shor and J. Preskill, “Simple proof of security of the BB84 quantum key distribution protocol,” Phys. Rev. Lett. 85, 441–444 (2000).
[Crossref] [PubMed]

Prevedel, R.

T. Scheidl, R. Ursin, A. Fedrizzi, S. Ramelow, X.-S. Ma, T. Herbst, R. Prevedel, L. Ratschbacher, J. Kofler, T. Jennewein, and A. Zeilinger, “Feasibility of 300 km quantum key distribution with entangled states,” New J. Phys. 11, 085002 (2009).
[Crossref]

Qi, B.

Y. Zhao, C.-H. F. Fung, B. Qi, C. Chen, and H.-K. Lo, “Quantum hacking: Experimental demonstration of time-shift attack against practical quantum-key-distribution systems,” Phys. Rev. A 78, 042333 (2008).
[Crossref]

B. Qi, C.-H. F. Fung, H.-K. Lo, and X. Ma, “Time-shift attack in practical quantum cryptosystems,” Quantum Inf. Comput. 7, 073 (2007).

Y. Zhao, B. Qi, X. F. Ma, H.-K. Lo, and L. Qian, “Experimental quantum key distribution with decoy states,” Phys. Rev. Lett. 96, 070502 (2006).
[Crossref] [PubMed]

X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A,  72, 012326 (2005).
[Crossref]

Qian, L.

Y. Zhao, B. Qi, X. F. Ma, H.-K. Lo, and L. Qian, “Experimental quantum key distribution with decoy states,” Phys. Rev. Lett. 96, 070502 (2006).
[Crossref] [PubMed]

Ramelow, S.

T. Scheidl, R. Ursin, A. Fedrizzi, S. Ramelow, X.-S. Ma, T. Herbst, R. Prevedel, L. Ratschbacher, J. Kofler, T. Jennewein, and A. Zeilinger, “Feasibility of 300 km quantum key distribution with entangled states,” New J. Phys. 11, 085002 (2009).
[Crossref]

Ratschbacher, L.

T. Scheidl, R. Ursin, A. Fedrizzi, S. Ramelow, X.-S. Ma, T. Herbst, R. Prevedel, L. Ratschbacher, J. Kofler, T. Jennewein, and A. Zeilinger, “Feasibility of 300 km quantum key distribution with entangled states,” New J. Phys. 11, 085002 (2009).
[Crossref]

Razavi, M.

Z. Zhang, Q. Zhao, M. Razavi, and X. Ma, “Improved key-rate bounds for practical decoy-state quantum-key-distribution systems,” Phys. Rev. A 95, 012333 (2017).
[Crossref]

Rice, P. R.

D. Rosenberg, J. W. Harrington, P. R. Rice, P. A. Hiskett, C. G. Peterson, R. J. Hughes, A. E. Lita, S. W. Nam, and J. E. Nordholt, “Long-distance decoy-state quantum key distribution in optical fibe, r,” Phys. Rev. Lett. 98, 010503 (2007).
[Crossref]

Rosenberg, D.

D. Rosenberg, J. W. Harrington, P. R. Rice, P. A. Hiskett, C. G. Peterson, R. J. Hughes, A. E. Lita, S. W. Nam, and J. E. Nordholt, “Long-distance decoy-state quantum key distribution in optical fibe, r,” Phys. Rev. Lett. 98, 010503 (2007).
[Crossref]

Sanders, B.

G. Brassard, N. Lütkenhaus, T. Mor, and B. Sanders, “Limitations on practical quantum cryptography,” Phys. Rev. Lett. 85, 1330–1333 (2000).
[Crossref] [PubMed]

Sanguinetti, B.

B. Korzh, C. C. W. Lim, R. Houlmann, N. Gisin, M. J. Li, D. Nolan, B. Sanguinetti, R. Thew, and H. Zbinden, “Provably secure and practical quantum key distribution over 307 km of optical fibre,” Nature Photon. 9, 163–168 (2015).
[Crossref]

Sauge, S.

Q. Wang, W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z. F. Han, G. C. Guo, and A. Karlsson, “Experimental decoy-state quantum key distribution with a sub-poissionian heralded single-photon source,” Phys. Rev. Lett. 100, 090501 (2008).
[Crossref] [PubMed]

Scheidl, T.

T. Scheidl, R. Ursin, A. Fedrizzi, S. Ramelow, X.-S. Ma, T. Herbst, R. Prevedel, L. Ratschbacher, J. Kofler, T. Jennewein, and A. Zeilinger, “Feasibility of 300 km quantum key distribution with entangled states,” New J. Phys. 11, 085002 (2009).
[Crossref]

Sharpe, A. W.

Shields, A. J.

Shor, P. W.

P. W. Shor and J. Preskill, “Simple proof of security of the BB84 quantum key distribution protocol,” Phys. Rev. Lett. 85, 441–444 (2000).
[Crossref] [PubMed]

Skaar, J.

V. Makarov, A. Anisimov, and J. Skaar, “Effects of detector efficiency mismatch on security of quantum cryptosystems,” Phys. Rev. A 74, 022313 (2006).
[Crossref]

Song, X.-T.

S. Wang, Z.-Q. Yin, W. Chen, D.-Y. He, X.-T. Song, H.-W. Li, L.-J. Zhang, Z. Zhou, G.-C. Guo, and Z.-F. Han,”Experimental demonstration of a quantum key distribution without signal disturbance monitoring,” Nat. Photonics 9, 832 (2015).
[Crossref]

Spekkens, R. W.

J. C. Boileau, D. Gottesman, R. Laflamme, D. Poulin, and R. W. Spekkens, “Robust polarization-based quantum key distribution over a collective-noise channel,” Phys. Rev. Lett. 92, 017901 (2004).
[Crossref] [PubMed]

Sun, Q.-C.

Q.-C. Sun, W.-L. Wang, Y. Liu, F. Zhou, J. S. Pelc, M. M. Fejer, C.-Z. Peng, X.-F. Chen, X.-F. Ma, Q. Zhang, and J.-W. Pan, “Experimental passive decoy-state quantum key distribution,” Laser Phys. Lett.,  11, 085202 (2014).
[Crossref]

Swillo, M.

Q. Wang, W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z. F. Han, G. C. Guo, and A. Karlsson, “Experimental decoy-state quantum key distribution with a sub-poissionian heralded single-photon source,” Phys. Rev. Lett. 100, 090501 (2008).
[Crossref] [PubMed]

Tam, W. W.-S.

Tamaki, K.

M. Curty, F. Xu, W. Cui, C. C. W. Lim, K. Tamaki, and H.-K. Lo, “Finite-key analysis for measurement-device-independent quantum key distribution,” Nat. Commun. 5, 3732 (2014).
[Crossref] [PubMed]

Tengner, M.

Q. Wang, W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z. F. Han, G. C. Guo, and A. Karlsson, “Experimental decoy-state quantum key distribution with a sub-poissionian heralded single-photon source,” Phys. Rev. Lett. 100, 090501 (2008).
[Crossref] [PubMed]

Thew, R.

B. Korzh, C. C. W. Lim, R. Houlmann, N. Gisin, M. J. Li, D. Nolan, B. Sanguinetti, R. Thew, and H. Zbinden, “Provably secure and practical quantum key distribution over 307 km of optical fibre,” Nature Photon. 9, 163–168 (2015).
[Crossref]

Ursin, R.

T. Scheidl, R. Ursin, A. Fedrizzi, S. Ramelow, X.-S. Ma, T. Herbst, R. Prevedel, L. Ratschbacher, J. Kofler, T. Jennewein, and A. Zeilinger, “Feasibility of 300 km quantum key distribution with entangled states,” New J. Phys. 11, 085002 (2009).
[Crossref]

Walenta, N.

C. C. W. Lim, M. Curty, N. Walenta, F. Xu, and H. Zbinden, “Concise security bounds for practical decoy-state quantum key distribution,” Phys. Rev. A 89, 022307 (2014).
[Crossref]

Wan, X.

Y. Liu, T.-Y. Chen, J. Wang, W.-Q. Cai, X. Wan, L.-K. Chen, J.-H. Wang, S.-B. Liu, H. Liang, L. Yang, C.-Z. Peng, K. Chen, Z.-B. Chen, and J.-W. Pan, “Decoy-state quantum key distribution with polarized photons over 200 km,” Opt. Expr. 8, 8587–8594 (2010).
[Crossref]

Wang, J.

Y. Liu, T.-Y. Chen, J. Wang, W.-Q. Cai, X. Wan, L.-K. Chen, J.-H. Wang, S.-B. Liu, H. Liang, L. Yang, C.-Z. Peng, K. Chen, Z.-B. Chen, and J.-W. Pan, “Decoy-state quantum key distribution with polarized photons over 200 km,” Opt. Expr. 8, 8587–8594 (2010).
[Crossref]

Wang, J.-H.

Y. Liu, T.-Y. Chen, J. Wang, W.-Q. Cai, X. Wan, L.-K. Chen, J.-H. Wang, S.-B. Liu, H. Liang, L. Yang, C.-Z. Peng, K. Chen, Z.-B. Chen, and J.-W. Pan, “Decoy-state quantum key distribution with polarized photons over 200 km,” Opt. Expr. 8, 8587–8594 (2010).
[Crossref]

Wang, Q.

Q. Wang, C.-H. Zhang, and X.-B. Wang, “Scheme for realizing passive quantum key distribution with heralded single-photon sources,” Phys. Rev. A 93, 032312 (2016).
[Crossref]

Q. Wang, X.-Y. Zhou, and G.-C. Guo, “Realizing the measure-device-independent quantum-key-distribution with passive heralded-single photon sources,” Sci. Rep. 6, 35394 (2016).
[Crossref] [PubMed]

Q. Wang, W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z. F. Han, G. C. Guo, and A. Karlsson, “Experimental decoy-state quantum key distribution with a sub-poissionian heralded single-photon source,” Phys. Rev. Lett. 100, 090501 (2008).
[Crossref] [PubMed]

Q. Wang, X. B. Wang, and G. C. Guo, “Practical decoy-state method in quantum key distribution with a heralded single-photon source,” Phys. Rev. A 75, 012312 (2007).
[Crossref]

Q. Wang and A. karlsson, “Performance enhancement of a decoy-state quantum key distribution using a conditionally prepared downconversion source in the Poisson distribution,” Phys. Rev. A 76, 014309 (2007).
[Crossref]

Wang, S.

S. Wang, Z.-Q. Yin, W. Chen, D.-Y. He, X.-T. Song, H.-W. Li, L.-J. Zhang, Z. Zhou, G.-C. Guo, and Z.-F. Han,”Experimental demonstration of a quantum key distribution without signal disturbance monitoring,” Nat. Photonics 9, 832 (2015).
[Crossref]

Wang, W.-L.

Q.-C. Sun, W.-L. Wang, Y. Liu, F. Zhou, J. S. Pelc, M. M. Fejer, C.-Z. Peng, X.-F. Chen, X.-F. Ma, Q. Zhang, and J.-W. Pan, “Experimental passive decoy-state quantum key distribution,” Laser Phys. Lett.,  11, 085202 (2014).
[Crossref]

Wang, X. B.

Q. Wang, X. B. Wang, and G. C. Guo, “Practical decoy-state method in quantum key distribution with a heralded single-photon source,” Phys. Rev. A 75, 012312 (2007).
[Crossref]

X. B. Wang, “Beating the photon-number-splitting attack in practical quantum cryptography,” Phys. Rev. Lett. 94, 230503 (2005).
[Crossref] [PubMed]

Wang, X.B.

C.-Z. Peng, J. Zhang, D. Yang, W.-B. Gao, H.-X. Ma, H. Yin, H.-P. Zeng, T. Yang, X.B. Wang, and J. W. Pan, “Experimental long-distance decoy-state quantum key distribution based on polarization encoding,” Phys. Rev. Lett. 98, 010505 (2007).
[Crossref] [PubMed]

Wang, X.-B.

Q. Wang, C.-H. Zhang, and X.-B. Wang, “Scheme for realizing passive quantum key distribution with heralded single-photon sources,” Phys. Rev. A 93, 032312 (2016).
[Crossref]

H.-L. Yin, T.-Y. Chen, Z.-W. Yu, H. Liu, L.-X. You, Y.-H. Zhou, S.-J. Chen, Y.-Q. Mao, M.-Q. Huang, W.-J. Zhang, H. Chen, M.-J. Li, D. Nolan, F. Zhou, X. Jiang, Z. Wang, Q. Zhang, X.-B. Wang, and J.-W. Pan, “Measurement-Device-Independent Quantum Key Distribution Over a 404 km Optical Fiber,” Phys. Rev. Lett. 117190501 (2016).
[Crossref]

Wang, Z.

H.-L. Yin, T.-Y. Chen, Z.-W. Yu, H. Liu, L.-X. You, Y.-H. Zhou, S.-J. Chen, Y.-Q. Mao, M.-Q. Huang, W.-J. Zhang, H. Chen, M.-J. Li, D. Nolan, F. Zhou, X. Jiang, Z. Wang, Q. Zhang, X.-B. Wang, and J.-W. Pan, “Measurement-Device-Independent Quantum Key Distribution Over a 404 km Optical Fiber,” Phys. Rev. Lett. 117190501 (2016).
[Crossref]

Xavier, G.

Q. Wang, W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z. F. Han, G. C. Guo, and A. Karlsson, “Experimental decoy-state quantum key distribution with a sub-poissionian heralded single-photon source,” Phys. Rev. Lett. 100, 090501 (2008).
[Crossref] [PubMed]

Xu, F.

M. Curty, F. Xu, W. Cui, C. C. W. Lim, K. Tamaki, and H.-K. Lo, “Finite-key analysis for measurement-device-independent quantum key distribution,” Nat. Commun. 5, 3732 (2014).
[Crossref] [PubMed]

C. C. W. Lim, M. Curty, N. Walenta, F. Xu, and H. Zbinden, “Concise security bounds for practical decoy-state quantum key distribution,” Phys. Rev. A 89, 022307 (2014).
[Crossref]

Yamamoto, T.

Y. Adachi, T. Yamamoto, M. Koashi, and N. Imoto, “Boosting up quantum key distribution by learning statistics of practical single-photon sources,” New J. Phys. 11, 113033 (2009).
[Crossref]

Y. Adachi, T. Yamamoto, M. Koashi, and N. Imoto, “Simple and efficient quantum key distribution with parametric down-conversion,” Phys. Rev. Lett. 99, 180503 (2007).
[Crossref] [PubMed]

Yang, D.

C.-Z. Peng, J. Zhang, D. Yang, W.-B. Gao, H.-X. Ma, H. Yin, H.-P. Zeng, T. Yang, X.B. Wang, and J. W. Pan, “Experimental long-distance decoy-state quantum key distribution based on polarization encoding,” Phys. Rev. Lett. 98, 010505 (2007).
[Crossref] [PubMed]

Yang, L.

Y. Liu, T.-Y. Chen, J. Wang, W.-Q. Cai, X. Wan, L.-K. Chen, J.-H. Wang, S.-B. Liu, H. Liang, L. Yang, C.-Z. Peng, K. Chen, Z.-B. Chen, and J.-W. Pan, “Decoy-state quantum key distribution with polarized photons over 200 km,” Opt. Expr. 8, 8587–8594 (2010).
[Crossref]

Yang, T.

C.-Z. Peng, J. Zhang, D. Yang, W.-B. Gao, H.-X. Ma, H. Yin, H.-P. Zeng, T. Yang, X.B. Wang, and J. W. Pan, “Experimental long-distance decoy-state quantum key distribution based on polarization encoding,” Phys. Rev. Lett. 98, 010505 (2007).
[Crossref] [PubMed]

Yin, H.

C.-Z. Peng, J. Zhang, D. Yang, W.-B. Gao, H.-X. Ma, H. Yin, H.-P. Zeng, T. Yang, X.B. Wang, and J. W. Pan, “Experimental long-distance decoy-state quantum key distribution based on polarization encoding,” Phys. Rev. Lett. 98, 010505 (2007).
[Crossref] [PubMed]

Yin, H.-L.

H.-L. Yin, T.-Y. Chen, Z.-W. Yu, H. Liu, L.-X. You, Y.-H. Zhou, S.-J. Chen, Y.-Q. Mao, M.-Q. Huang, W.-J. Zhang, H. Chen, M.-J. Li, D. Nolan, F. Zhou, X. Jiang, Z. Wang, Q. Zhang, X.-B. Wang, and J.-W. Pan, “Measurement-Device-Independent Quantum Key Distribution Over a 404 km Optical Fiber,” Phys. Rev. Lett. 117190501 (2016).
[Crossref]

Yin, Z.-Q.

S. Wang, Z.-Q. Yin, W. Chen, D.-Y. He, X.-T. Song, H.-W. Li, L.-J. Zhang, Z. Zhou, G.-C. Guo, and Z.-F. Han,”Experimental demonstration of a quantum key distribution without signal disturbance monitoring,” Nat. Photonics 9, 832 (2015).
[Crossref]

You, L.-X.

H.-L. Yin, T.-Y. Chen, Z.-W. Yu, H. Liu, L.-X. You, Y.-H. Zhou, S.-J. Chen, Y.-Q. Mao, M.-Q. Huang, W.-J. Zhang, H. Chen, M.-J. Li, D. Nolan, F. Zhou, X. Jiang, Z. Wang, Q. Zhang, X.-B. Wang, and J.-W. Pan, “Measurement-Device-Independent Quantum Key Distribution Over a 404 km Optical Fiber,” Phys. Rev. Lett. 117190501 (2016).
[Crossref]

Yu, Z.-W.

H.-L. Yin, T.-Y. Chen, Z.-W. Yu, H. Liu, L.-X. You, Y.-H. Zhou, S.-J. Chen, Y.-Q. Mao, M.-Q. Huang, W.-J. Zhang, H. Chen, M.-J. Li, D. Nolan, F. Zhou, X. Jiang, Z. Wang, Q. Zhang, X.-B. Wang, and J.-W. Pan, “Measurement-Device-Independent Quantum Key Distribution Over a 404 km Optical Fiber,” Phys. Rev. Lett. 117190501 (2016).
[Crossref]

Yuan, Z. L.

C. Gobby, Z. L. Yuan, and A. J. Shields, “Quantum key distribution over 122 km of standard telecom fiber,” Appl. Phys. Lett. 84, 3762–3764 (2004).
[Crossref]

Yuan, Z.-L.

Zbinden, H.

B. Korzh, C. C. W. Lim, R. Houlmann, N. Gisin, M. J. Li, D. Nolan, B. Sanguinetti, R. Thew, and H. Zbinden, “Provably secure and practical quantum key distribution over 307 km of optical fibre,” Nature Photon. 9, 163–168 (2015).
[Crossref]

C. C. W. Lim, M. Curty, N. Walenta, F. Xu, and H. Zbinden, “Concise security bounds for practical decoy-state quantum key distribution,” Phys. Rev. A 89, 022307 (2014).
[Crossref]

Zeilinger, A.

T. Scheidl, R. Ursin, A. Fedrizzi, S. Ramelow, X.-S. Ma, T. Herbst, R. Prevedel, L. Ratschbacher, J. Kofler, T. Jennewein, and A. Zeilinger, “Feasibility of 300 km quantum key distribution with entangled states,” New J. Phys. 11, 085002 (2009).
[Crossref]

Zeng, H.-P.

C.-Z. Peng, J. Zhang, D. Yang, W.-B. Gao, H.-X. Ma, H. Yin, H.-P. Zeng, T. Yang, X.B. Wang, and J. W. Pan, “Experimental long-distance decoy-state quantum key distribution based on polarization encoding,” Phys. Rev. Lett. 98, 010505 (2007).
[Crossref] [PubMed]

Zhang, C.-H.

Q. Wang, C.-H. Zhang, and X.-B. Wang, “Scheme for realizing passive quantum key distribution with heralded single-photon sources,” Phys. Rev. A 93, 032312 (2016).
[Crossref]

Zhang, J.

C.-Z. Peng, J. Zhang, D. Yang, W.-B. Gao, H.-X. Ma, H. Yin, H.-P. Zeng, T. Yang, X.B. Wang, and J. W. Pan, “Experimental long-distance decoy-state quantum key distribution based on polarization encoding,” Phys. Rev. Lett. 98, 010505 (2007).
[Crossref] [PubMed]

Zhang, L.-J.

S. Wang, Z.-Q. Yin, W. Chen, D.-Y. He, X.-T. Song, H.-W. Li, L.-J. Zhang, Z. Zhou, G.-C. Guo, and Z.-F. Han,”Experimental demonstration of a quantum key distribution without signal disturbance monitoring,” Nat. Photonics 9, 832 (2015).
[Crossref]

Zhang, Q.

H.-L. Yin, T.-Y. Chen, Z.-W. Yu, H. Liu, L.-X. You, Y.-H. Zhou, S.-J. Chen, Y.-Q. Mao, M.-Q. Huang, W.-J. Zhang, H. Chen, M.-J. Li, D. Nolan, F. Zhou, X. Jiang, Z. Wang, Q. Zhang, X.-B. Wang, and J.-W. Pan, “Measurement-Device-Independent Quantum Key Distribution Over a 404 km Optical Fiber,” Phys. Rev. Lett. 117190501 (2016).
[Crossref]

Q.-C. Sun, W.-L. Wang, Y. Liu, F. Zhou, J. S. Pelc, M. M. Fejer, C.-Z. Peng, X.-F. Chen, X.-F. Ma, Q. Zhang, and J.-W. Pan, “Experimental passive decoy-state quantum key distribution,” Laser Phys. Lett.,  11, 085202 (2014).
[Crossref]

Zhang, T.

Q. Wang, W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z. F. Han, G. C. Guo, and A. Karlsson, “Experimental decoy-state quantum key distribution with a sub-poissionian heralded single-photon source,” Phys. Rev. Lett. 100, 090501 (2008).
[Crossref] [PubMed]

Zhang, W.-J.

H.-L. Yin, T.-Y. Chen, Z.-W. Yu, H. Liu, L.-X. You, Y.-H. Zhou, S.-J. Chen, Y.-Q. Mao, M.-Q. Huang, W.-J. Zhang, H. Chen, M.-J. Li, D. Nolan, F. Zhou, X. Jiang, Z. Wang, Q. Zhang, X.-B. Wang, and J.-W. Pan, “Measurement-Device-Independent Quantum Key Distribution Over a 404 km Optical Fiber,” Phys. Rev. Lett. 117190501 (2016).
[Crossref]

Zhang, Z.

Z. Zhang, Q. Zhao, M. Razavi, and X. Ma, “Improved key-rate bounds for practical decoy-state quantum-key-distribution systems,” Phys. Rev. A 95, 012333 (2017).
[Crossref]

Zhao, Q.

Z. Zhang, Q. Zhao, M. Razavi, and X. Ma, “Improved key-rate bounds for practical decoy-state quantum-key-distribution systems,” Phys. Rev. A 95, 012333 (2017).
[Crossref]

Zhao, Y.

Y. Zhao, C.-H. F. Fung, B. Qi, C. Chen, and H.-K. Lo, “Quantum hacking: Experimental demonstration of time-shift attack against practical quantum-key-distribution systems,” Phys. Rev. A 78, 042333 (2008).
[Crossref]

Y. Zhao, B. Qi, X. F. Ma, H.-K. Lo, and L. Qian, “Experimental quantum key distribution with decoy states,” Phys. Rev. Lett. 96, 070502 (2006).
[Crossref] [PubMed]

X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A,  72, 012326 (2005).
[Crossref]

Zhou, F.

H.-L. Yin, T.-Y. Chen, Z.-W. Yu, H. Liu, L.-X. You, Y.-H. Zhou, S.-J. Chen, Y.-Q. Mao, M.-Q. Huang, W.-J. Zhang, H. Chen, M.-J. Li, D. Nolan, F. Zhou, X. Jiang, Z. Wang, Q. Zhang, X.-B. Wang, and J.-W. Pan, “Measurement-Device-Independent Quantum Key Distribution Over a 404 km Optical Fiber,” Phys. Rev. Lett. 117190501 (2016).
[Crossref]

Q.-C. Sun, W.-L. Wang, Y. Liu, F. Zhou, J. S. Pelc, M. M. Fejer, C.-Z. Peng, X.-F. Chen, X.-F. Ma, Q. Zhang, and J.-W. Pan, “Experimental passive decoy-state quantum key distribution,” Laser Phys. Lett.,  11, 085202 (2014).
[Crossref]

Zhou, X.-Y.

Q. Wang, X.-Y. Zhou, and G.-C. Guo, “Realizing the measure-device-independent quantum-key-distribution with passive heralded-single photon sources,” Sci. Rep. 6, 35394 (2016).
[Crossref] [PubMed]

Zhou, Y.-H.

H.-L. Yin, T.-Y. Chen, Z.-W. Yu, H. Liu, L.-X. You, Y.-H. Zhou, S.-J. Chen, Y.-Q. Mao, M.-Q. Huang, W.-J. Zhang, H. Chen, M.-J. Li, D. Nolan, F. Zhou, X. Jiang, Z. Wang, Q. Zhang, X.-B. Wang, and J.-W. Pan, “Measurement-Device-Independent Quantum Key Distribution Over a 404 km Optical Fiber,” Phys. Rev. Lett. 117190501 (2016).
[Crossref]

Zhou, Z.

S. Wang, Z.-Q. Yin, W. Chen, D.-Y. He, X.-T. Song, H.-W. Li, L.-J. Zhang, Z. Zhou, G.-C. Guo, and Z.-F. Han,”Experimental demonstration of a quantum key distribution without signal disturbance monitoring,” Nat. Photonics 9, 832 (2015).
[Crossref]

Zhu, B.

Appl. Phys. Lett. (2)

Z.-F. Han, X.-F. Mo, Y.-Z. Gui, and G.-C. Guo, “Stability of phase-modulated quantum key distribution systems,” Appl. Phys. Lett. 86, 221103 (2005).
[Crossref]

C. Gobby, Z. L. Yuan, and A. J. Shields, “Quantum key distribution over 122 km of standard telecom fiber,” Appl. Phys. Lett. 84, 3762–3764 (2004).
[Crossref]

J. ACM (1)

D. Mayers, “Unconditional security in quantum cryptography,” J. ACM 48, 351–406 (2001).
[Crossref]

Laser Phys. Lett. (1)

Q.-C. Sun, W.-L. Wang, Y. Liu, F. Zhou, J. S. Pelc, M. M. Fejer, C.-Z. Peng, X.-F. Chen, X.-F. Ma, Q. Zhang, and J.-W. Pan, “Experimental passive decoy-state quantum key distribution,” Laser Phys. Lett.,  11, 085202 (2014).
[Crossref]

Nat. Commun. (1)

M. Curty, F. Xu, W. Cui, C. C. W. Lim, K. Tamaki, and H.-K. Lo, “Finite-key analysis for measurement-device-independent quantum key distribution,” Nat. Commun. 5, 3732 (2014).
[Crossref] [PubMed]

Nat. Photonics (1)

S. Wang, Z.-Q. Yin, W. Chen, D.-Y. He, X.-T. Song, H.-W. Li, L.-J. Zhang, Z. Zhou, G.-C. Guo, and Z.-F. Han,”Experimental demonstration of a quantum key distribution without signal disturbance monitoring,” Nat. Photonics 9, 832 (2015).
[Crossref]

Nature Photon. (1)

B. Korzh, C. C. W. Lim, R. Houlmann, N. Gisin, M. J. Li, D. Nolan, B. Sanguinetti, R. Thew, and H. Zbinden, “Provably secure and practical quantum key distribution over 307 km of optical fibre,” Nature Photon. 9, 163–168 (2015).
[Crossref]

New J. Phys. (3)

T. Scheidl, R. Ursin, A. Fedrizzi, S. Ramelow, X.-S. Ma, T. Herbst, R. Prevedel, L. Ratschbacher, J. Kofler, T. Jennewein, and A. Zeilinger, “Feasibility of 300 km quantum key distribution with entangled states,” New J. Phys. 11, 085002 (2009).
[Crossref]

Y. Adachi, T. Yamamoto, M. Koashi, and N. Imoto, “Boosting up quantum key distribution by learning statistics of practical single-photon sources,” New J. Phys. 11, 113033 (2009).
[Crossref]

N. Lütkenhaus and M. Jahma, “Quantum key distribution with realistic states: photon-number statistics in the photon-number splitting attack,” New J. Phys. 4, 44 (2002).
[Crossref]

Opt. Expr. (1)

Y. Liu, T.-Y. Chen, J. Wang, W.-Q. Cai, X. Wan, L.-K. Chen, J.-H. Wang, S.-B. Liu, H. Liang, L. Yang, C.-Z. Peng, K. Chen, Z.-B. Chen, and J.-W. Pan, “Decoy-state quantum key distribution with polarized photons over 200 km,” Opt. Expr. 8, 8587–8594 (2010).
[Crossref]

Opt. Lett. (1)

Optica (1)

Phys. Rev. A (10)

Q. Wang, C.-H. Zhang, and X.-B. Wang, “Scheme for realizing passive quantum key distribution with heralded single-photon sources,” Phys. Rev. A 93, 032312 (2016).
[Crossref]

Q. Wang, X. B. Wang, and G. C. Guo, “Practical decoy-state method in quantum key distribution with a heralded single-photon source,” Phys. Rev. A 75, 012312 (2007).
[Crossref]

Q. Wang and A. karlsson, “Performance enhancement of a decoy-state quantum key distribution using a conditionally prepared downconversion source in the Poisson distribution,” Phys. Rev. A 76, 014309 (2007).
[Crossref]

C.-H. F. Fung, X. Ma, and H. F. Chau, “Practical issues in quantum-key-distribution postprocessing,” Phys. Rev. A 81, 012318 (2010).
[Crossref]

Z. Zhang, Q. Zhao, M. Razavi, and X. Ma, “Improved key-rate bounds for practical decoy-state quantum-key-distribution systems,” Phys. Rev. A 95, 012333 (2017).
[Crossref]

C. C. W. Lim, M. Curty, N. Walenta, F. Xu, and H. Zbinden, “Concise security bounds for practical decoy-state quantum key distribution,” Phys. Rev. A 89, 022307 (2014).
[Crossref]

V. Makarov, A. Anisimov, and J. Skaar, “Effects of detector efficiency mismatch on security of quantum cryptosystems,” Phys. Rev. A 74, 022313 (2006).
[Crossref]

Y. Zhao, C.-H. F. Fung, B. Qi, C. Chen, and H.-K. Lo, “Quantum hacking: Experimental demonstration of time-shift attack against practical quantum-key-distribution systems,” Phys. Rev. A 78, 042333 (2008).
[Crossref]

X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A,  72, 012326 (2005).
[Crossref]

N. Lütkenhaus, “Security against individual attacks for realistic quantum key distribution,” Phys. Rev. A 61, 052304 (2000).
[Crossref]

Phys. Rev. Lett. (12)

G. Brassard, N. Lütkenhaus, T. Mor, and B. Sanders, “Limitations on practical quantum cryptography,” Phys. Rev. Lett. 85, 1330–1333 (2000).
[Crossref] [PubMed]

P. W. Shor and J. Preskill, “Simple proof of security of the BB84 quantum key distribution protocol,” Phys. Rev. Lett. 85, 441–444 (2000).
[Crossref] [PubMed]

J. C. Boileau, D. Gottesman, R. Laflamme, D. Poulin, and R. W. Spekkens, “Robust polarization-based quantum key distribution over a collective-noise channel,” Phys. Rev. Lett. 92, 017901 (2004).
[Crossref] [PubMed]

W. Y. Hwang, “Quantum key distribution with high loss: Toward global secure communication,” Phys. Rev. Lett. 91, 057901 (2003).
[Crossref] [PubMed]

X. B. Wang, “Beating the photon-number-splitting attack in practical quantum cryptography,” Phys. Rev. Lett. 94, 230503 (2005).
[Crossref] [PubMed]

H.-K. Lo, X. F. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94, 230504 (2005).
[Crossref] [PubMed]

Y. Zhao, B. Qi, X. F. Ma, H.-K. Lo, and L. Qian, “Experimental quantum key distribution with decoy states,” Phys. Rev. Lett. 96, 070502 (2006).
[Crossref] [PubMed]

C.-Z. Peng, J. Zhang, D. Yang, W.-B. Gao, H.-X. Ma, H. Yin, H.-P. Zeng, T. Yang, X.B. Wang, and J. W. Pan, “Experimental long-distance decoy-state quantum key distribution based on polarization encoding,” Phys. Rev. Lett. 98, 010505 (2007).
[Crossref] [PubMed]

D. Rosenberg, J. W. Harrington, P. R. Rice, P. A. Hiskett, C. G. Peterson, R. J. Hughes, A. E. Lita, S. W. Nam, and J. E. Nordholt, “Long-distance decoy-state quantum key distribution in optical fibe, r,” Phys. Rev. Lett. 98, 010503 (2007).
[Crossref]

H.-L. Yin, T.-Y. Chen, Z.-W. Yu, H. Liu, L.-X. You, Y.-H. Zhou, S.-J. Chen, Y.-Q. Mao, M.-Q. Huang, W.-J. Zhang, H. Chen, M.-J. Li, D. Nolan, F. Zhou, X. Jiang, Z. Wang, Q. Zhang, X.-B. Wang, and J.-W. Pan, “Measurement-Device-Independent Quantum Key Distribution Over a 404 km Optical Fiber,” Phys. Rev. Lett. 117190501 (2016).
[Crossref]

Y. Adachi, T. Yamamoto, M. Koashi, and N. Imoto, “Simple and efficient quantum key distribution with parametric down-conversion,” Phys. Rev. Lett. 99, 180503 (2007).
[Crossref] [PubMed]

Q. Wang, W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z. F. Han, G. C. Guo, and A. Karlsson, “Experimental decoy-state quantum key distribution with a sub-poissionian heralded single-photon source,” Phys. Rev. Lett. 100, 090501 (2008).
[Crossref] [PubMed]

Quantum Inf. Comput. (1)

B. Qi, C.-H. F. Fung, H.-K. Lo, and X. Ma, “Time-shift attack in practical quantum cryptosystems,” Quantum Inf. Comput. 7, 073 (2007).

Sci. Rep. (1)

Q. Wang, X.-Y. Zhou, and G.-C. Guo, “Realizing the measure-device-independent quantum-key-distribution with passive heralded-single photon sources,” Sci. Rep. 6, 35394 (2016).
[Crossref] [PubMed]

Science (1)

H.-K. Lo and H. F. Chau, “Unconditional security of quantum key distribution over arbitrarily long distances,” Science 283, 2050–2056 (1999).
[Crossref] [PubMed]

Other (2)

C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” in Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India (IEEE, New York, 1984), pp. 175–179.

Digital cellular telecommunications system; Full rate speech; Transcoding (GSM 06.10 RPE-LTP), ETS 300 961, V8.1.1 (2000).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1 Schematic of the passive heralded single-photon source at Alice’s side.
Fig. 2
Fig. 2 Schematic setup of the passive decoy-state QKD with HSPS. BBO: β−BaB2O4 crystal; PPLN: periodically poled LiNbO3 crystal; M: mirror; BPF: band-pass filter; LPF: long-pass filter; DM: dichroic mirror; BS: beam splitter; SAPD: silicon APD; PC: polarization controller; Filter: 3nm fiber filter with a variable central wavelength; FBS: fiber beam-splitter; FPBS: fiber polarization beam-splitter; PM: phase modulator; TDC: time to digital converter; CB: control board; SNSPD: superconducting nanowire single-photon detector.
Fig. 3
Fig. 3 Rt_passive and Re_passive represent the theoretical and experimental key generation rate by using our proposed passive scheme; Rt_2-intensity and Re_2-intensity correspond to the case of implementing two-intensity decoy states (μ and 0). The horizontal axis represents the total channel loss (or equivalent to using commercial standard single-mode fiber at a certain length, as marked in the figure by 100 km, 200 km, 250 km, respectively), and the vertical axis indicates the key generation rate per pulse with logarithmic coordinates.
Fig. 4
Fig. 4 The structure of QKD system based the low-loss AMZIs.

Tables (5)

Tables Icon

Table 1 Nomenclature and the corresponding probabilities of the signal states depending on the detection events in the idler mode, where “0” denotes the detector not clicking and “1” corresponds to a click.

Tables Icon

Table 2 Performance comparison between different works on QKD.

Tables Icon

Table 3 Probability for a Xi event to occur.

Tables Icon

Table 4 Parameters used in our experiments.

Tables Icon

Table 5 Final experimental results. η is the total loss. Ni corresponds to the number of pulses sent out for Xi (i = 1, 2, 3) event.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

a n l = m = n μ 0 m e μ 0 m ! C m n η s n ( 1 η s ) m n P X i | m ,
R l 1 2 { a 1 l Y 1 L [ 1 H ( e 1 U ) ] Q l f ( E l ) H ( E l ) } , R = R x + R y + R z ,
P s 1 s 2 | m = k = 0 m s 2 = 0 m k s 1 = 0 k ( C m k t k ( 1 t ) m k C k s 1 η 10 s 1 ( 1 η 10 ) k s 1 × C m k s 2 η 20 s 2 ( 1 η 20 ) m k s 2 ) = k = 0 m s 2 = 0 m k s 1 = 0 k m ! t k ( 1 t ) m k η 10 s 1 η 10 s 2 ( 1 η 10 ) k s 1 ( 1 η 20 ) m k s 2 s 1 ! s 2 ! ( k s 1 ) ! ( m k s 2 ) ! ,
P X i | m = s 1 s 2 P X i | s 1 s 2 P s 1 s 2 | m .
a n l = m = n μ 0 m e μ 0 m ! C m n η s n ( 1 η s ) m n P X i | m ,
a n x = ( 1 d 1 ) ( 1 d 2 ) e μ 0 ( η 1 + η 2 ) P n [ μ 0 η s ( 1 η 1 η 2 ) ] , a n y = ( 1 d 2 ) e μ 0 η 2 P n [ μ 0 η s ( 1 η 2 ) ] a n x , a n z = ( 1 d 1 ) e μ 0 η 1 P n [ μ 0 η s ( 1 η 1 ) ] a n x ,
a n z a n x a n 1 z a n 1 x = e μ 0 η 2 ( 1 η s ) 1 d 2 [ ( 1 η 1 1 η 1 η 2 ) n ( 1 η 1 1 η 1 η 2 ) n 1 ] = e μ 0 η 2 ( 1 η s ) 1 d 2 ( 1 η 1 1 η 1 η 2 ) n 1 η 2 1 η 1 η 2 0 ,
a n z a n x a 2 z a 2 x a 1 z a 1 x .
Y 1 L = a 2 z Δ L [ Q x N ] a 2 x Δ U [ Q z N ] ( a 2 z a 0 x a 2 x a 0 z ) Y 0 U N ( a 1 x a 2 z a 1 z a 2 x ) , e 1 U = Δ U [ E y Q y N ] e 0 a 0 y Y 0 L N ( a 1 y Y 1 L ) ,
Y 0 L = max { a 1 y Δ L [ Q x N ] a 1 x Δ U [ Q y N ] N ( a 0 x a 1 y a 0 y a 1 x ) , a 1 z Δ L [ Q x N ] a 1 x Δ U [ Q z N ] N ( a 0 x a 1 z a 0 z a 1 x ) , 0 } , Y 0 U = min { Δ U [ E x Q x N ] N a 0 x e 0 , Δ U [ E y Q y N ] N a 0 y e 0 , Δ U [ E z Q z N ] N a 0 z e 0 } .
Δ L [ χ ] = χ 1 + δ L , Δ U [ χ ] = χ 1 δ U .
[ e δ L ( 1 + δ L ) 1 + δ L ] χ 1 + δ L = 1 2 ε , [ e δ U ( 1 δ U ) 1 δ U ] χ 1 δ U = 1 2 ε ,
R l 1 2 { a 1 l Y 1 L [ 1 H ( e 1 U ) ] Q l f ( E l ) H ( E l ) } , R = R x + R y + R z ,

Metrics