Abstract

Recently, a novel protocol named round-robin differential phase-shift (RRDPS) quantum key distribution [Nature 509, 475(2014)] has been proposed. It can estimate information leakage without monitoring bit error rate. In this paper, we study the performance of RRDPS using heralded single photon source (HSPS) without and with decoy-state method, then compare it with the performance of weak coherent pulses (WCPs). From numerical simulation, we can see that HSPS performs better especially for shorter packet and higher bit error rate. Moreover, we propose a general theory of decoy-state method for RRDPS protocol based on only three decoy states and one signal state. Taking WCPs as an example, the three-intensity decoy-state protocol can distribute secret keys over a distance of 128 km when the length of pulses packet is 32, which confirms great practical interest of our method.

© 2016 Optical Society of America

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  5. C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” Cryptology 5, 3 (1992).
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    [Crossref]
  7. D. Bacco, M. Canale, N. Laurenti, G. Vallone, and P. Villoresi, “Experimental quantum key distribution with finite-key security analysis for noisy channels,” Nat. Commun. 4, 2363 (2013).
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  9. C. Wang, X.-T. Song, W. Chen, C.-M. Zhang, G.-C. Guo, and Z.-F. Han, “Phase-reference-free experiment of measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 115, 160502 (2015).
    [Crossref] [PubMed]
  10. W.-Y. Liang, M. Li, Z.-Q. Yin, W. Chen, S. Wang, W.-B. An, G.-C. Guo, and Z.-F. Han, “Simple implementation of quantum key distribution based on single-photon Bell-state measurement,” Phys. Rev. A 92, 012319 (2015).
    [Crossref]
  11. L. C. Comandar, M. Lucamarini, B. Fröhlich, J. F. Dynes, A. W. Sharpe, S. W.-B. Tam, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Quantum key distribution without detector vulnerabilities using optically seeded lasers,” Nat. Photonics 10, 312–315 (2016).
    [Crossref]
  12. T. Sasaki, Y. Yamamoto, and M. Koashi, “Practical quantum key distribution protocol without mointoring signal distutbance,” Nature 509, 475–478 (2014).
    [Crossref] [PubMed]
  13. Z. Zhang, X. Yuan, Z. Cao, and X. F. Ma, “Round-robin differential-phase-shift quantum key distribution,” ar” Xiv:1505.02481(2015).
  14. H. Takesue, T. Sasaki, K. Tamaki, and M. Koashi, “Experimental quantum key distribution without monitoring signal disturbance,” Nat. Photonics 9, 827 (2015).
    [Crossref]
  15. 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]
  16. J. Y. Guan, Z. Cao, and Y. Liu, “Experimental passive round-robin differential phase-shift quantum key distribution,” Phys. Rev. Lett. 114, 180502 (2015).
    [Crossref] [PubMed]
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    [Crossref]
  18. N. Lütkenhaus, “Security against individual attacks for realistic quantum key distribution,” Phys. Rev. A 61, 052304 (2000).
    [Crossref]
  19. 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]
  20. W. Y. Hwang, “Quantum key distribution with high loss: toward global secure communication,” Phys. Rev. Lett. 91, 057901 (2003).
    [Crossref] [PubMed]
  21. H.-K. Lo, X. F. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94, 230504 (2005).
    [Crossref] [PubMed]
  22. X.-B. Wang, “Beating the photon-number-splitting attack in practical quantum cryptography,” Phys. Rev. Lett. 94, 230503 (2005).
    [Crossref] [PubMed]
  23. X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A 72, 012326 (2005).
    [Crossref]
  24. C. Zhou, W. S. Bao, H. W. Li, Y. Wang, Y. Li, Z. Q. Yin, W. Chen, and Z. F. Han, “Tight finite-key analysis for passive decoy-state quantum key distribution under general attacks,” Phys. Rev. A 89, 052328 (2014).
    [Crossref]
  25. X. Ma, C. Fung, J. C. Boileau, and H. F. Chau, “Universally composable and customizable post-processing for practical quantum key distribution,” Comput. Security 30, 172–177 (2011).
    [Crossref]

2016 (3)

Y.-L. Tang, H.-L. Yin, Q. Zhao, H. Liu, X.-X. Sun, M.-Q. Huang, W.-J. Zhang, S.-J. Chen, L. Zhang, L.-X. You, Z. Wang, Y. Liu, C.-Y. Lu, X. Jiang, X. F. Ma, Q. Zhang, T.-Y. Chen, and J.-W. Pan, “Measurement-device-independent quantum key distribution over untrustful metropolitan network,” Phys. Rev. X 6, 011024 (2016).

L. C. Comandar, M. Lucamarini, B. Fröhlich, J. F. Dynes, A. W. Sharpe, S. W.-B. Tam, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Quantum key distribution without detector vulnerabilities using optically seeded lasers,” Nat. Photonics 10, 312–315 (2016).
[Crossref]

Y. H. Li, Y. Cao, H. Dai, J. Lin, Z. Zhang, W. Chen, Y. Xu, J. Y. Guan, S. K. Liao, J. Yin, Q. Zhang, X. Ma, C. Z. Peng, and J. W. Pan, “Experimental round-robin differential phase-shift quantum key distribution,” Phys. Rev. A 93, 030302 (2016).
[Crossref]

2015 (5)

H. Takesue, T. Sasaki, K. Tamaki, and M. Koashi, “Experimental quantum key distribution without monitoring signal disturbance,” Nat. Photonics 9, 827 (2015).
[Crossref]

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]

J. Y. Guan, Z. Cao, and Y. Liu, “Experimental passive round-robin differential phase-shift quantum key distribution,” Phys. Rev. Lett. 114, 180502 (2015).
[Crossref] [PubMed]

C. Wang, X.-T. Song, W. Chen, C.-M. Zhang, G.-C. Guo, and Z.-F. Han, “Phase-reference-free experiment of measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 115, 160502 (2015).
[Crossref] [PubMed]

W.-Y. Liang, M. Li, Z.-Q. Yin, W. Chen, S. Wang, W.-B. An, G.-C. Guo, and Z.-F. Han, “Simple implementation of quantum key distribution based on single-photon Bell-state measurement,” Phys. Rev. A 92, 012319 (2015).
[Crossref]

2014 (3)

T. Sasaki, Y. Yamamoto, and M. Koashi, “Practical quantum key distribution protocol without mointoring signal distutbance,” Nature 509, 475–478 (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]

C. Zhou, W. S. Bao, H. W. Li, Y. Wang, Y. Li, Z. Q. Yin, W. Chen, and Z. F. Han, “Tight finite-key analysis for passive decoy-state quantum key distribution under general attacks,” Phys. Rev. A 89, 052328 (2014).
[Crossref]

2013 (1)

D. Bacco, M. Canale, N. Laurenti, G. Vallone, and P. Villoresi, “Experimental quantum key distribution with finite-key security analysis for noisy channels,” Nat. Commun. 4, 2363 (2013).
[Crossref] [PubMed]

2011 (1)

X. Ma, C. Fung, J. C. Boileau, and H. F. Chau, “Universally composable and customizable post-processing for practical quantum key distribution,” Comput. Security 30, 172–177 (2011).
[Crossref]

2005 (3)

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

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

2004 (1)

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

2000 (2)

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

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

1999 (1)

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

1992 (1)

C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” Cryptology 5, 3 (1992).

1991 (1)

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661 (1991).
[Crossref] [PubMed]

An, W.-B.

W.-Y. Liang, M. Li, Z.-Q. Yin, W. Chen, S. Wang, W.-B. An, G.-C. Guo, and Z.-F. Han, “Simple implementation of quantum key distribution based on single-photon Bell-state measurement,” Phys. Rev. A 92, 012319 (2015).
[Crossref]

Bacco, D.

D. Bacco, M. Canale, N. Laurenti, G. Vallone, and P. Villoresi, “Experimental quantum key distribution with finite-key security analysis for noisy channels,” Nat. Commun. 4, 2363 (2013).
[Crossref] [PubMed]

Bao, W. S.

C. Zhou, W. S. Bao, H. W. Li, Y. Wang, Y. Li, Z. Q. Yin, W. Chen, and Z. F. Han, “Tight finite-key analysis for passive decoy-state quantum key distribution under general attacks,” Phys. Rev. A 89, 052328 (2014).
[Crossref]

Bennett, C. H.

C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” Cryptology 5, 3 (1992).

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

Bessette, F.

C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” Cryptology 5, 3 (1992).

Boileau, J. C.

X. Ma, C. Fung, J. C. Boileau, and H. F. Chau, “Universally composable and customizable post-processing for practical quantum key distribution,” Comput. Security 30, 172–177 (2011).
[Crossref]

Brassard, G.

C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” Cryptology 5, 3 (1992).

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

Canale, M.

D. Bacco, M. Canale, N. Laurenti, G. Vallone, and P. Villoresi, “Experimental quantum key distribution with finite-key security analysis for noisy channels,” Nat. Commun. 4, 2363 (2013).
[Crossref] [PubMed]

Cao, Y.

Y. H. Li, Y. Cao, H. Dai, J. Lin, Z. Zhang, W. Chen, Y. Xu, J. Y. Guan, S. K. Liao, J. Yin, Q. Zhang, X. Ma, C. Z. Peng, and J. W. Pan, “Experimental round-robin differential phase-shift quantum key distribution,” Phys. Rev. A 93, 030302 (2016).
[Crossref]

Cao, Z.

J. Y. Guan, Z. Cao, and Y. Liu, “Experimental passive round-robin differential phase-shift quantum key distribution,” Phys. Rev. Lett. 114, 180502 (2015).
[Crossref] [PubMed]

Z. Zhang, X. Yuan, Z. Cao, and X. F. Ma, “Round-robin differential-phase-shift quantum key distribution,” ar” Xiv:1505.02481(2015).

Chau, H. F.

X. Ma, C. Fung, J. C. Boileau, and H. F. Chau, “Universally composable and customizable post-processing for practical quantum key distribution,” Comput. Security 30, 172–177 (2011).
[Crossref]

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

Chen, K.

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

Chen, S.-J.

Y.-L. Tang, H.-L. Yin, Q. Zhao, H. Liu, X.-X. Sun, M.-Q. Huang, W.-J. Zhang, S.-J. Chen, L. Zhang, L.-X. You, Z. Wang, Y. Liu, C.-Y. Lu, X. Jiang, X. F. Ma, Q. Zhang, T.-Y. Chen, and J.-W. Pan, “Measurement-device-independent quantum key distribution over untrustful metropolitan network,” Phys. Rev. X 6, 011024 (2016).

Chen, T.-Y.

Y.-L. Tang, H.-L. Yin, Q. Zhao, H. Liu, X.-X. Sun, M.-Q. Huang, W.-J. Zhang, S.-J. Chen, L. Zhang, L.-X. You, Z. Wang, Y. Liu, C.-Y. Lu, X. Jiang, X. F. Ma, Q. Zhang, T.-Y. Chen, and J.-W. Pan, “Measurement-device-independent quantum key distribution over untrustful metropolitan network,” Phys. Rev. X 6, 011024 (2016).

Chen, W.

Y. H. Li, Y. Cao, H. Dai, J. Lin, Z. Zhang, W. Chen, Y. Xu, J. Y. Guan, S. K. Liao, J. Yin, Q. Zhang, X. Ma, C. Z. Peng, and J. W. Pan, “Experimental round-robin differential phase-shift quantum key distribution,” Phys. Rev. A 93, 030302 (2016).
[Crossref]

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]

C. Wang, X.-T. Song, W. Chen, C.-M. Zhang, G.-C. Guo, and Z.-F. Han, “Phase-reference-free experiment of measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 115, 160502 (2015).
[Crossref] [PubMed]

W.-Y. Liang, M. Li, Z.-Q. Yin, W. Chen, S. Wang, W.-B. An, G.-C. Guo, and Z.-F. Han, “Simple implementation of quantum key distribution based on single-photon Bell-state measurement,” Phys. Rev. A 92, 012319 (2015).
[Crossref]

C. Zhou, W. S. Bao, H. W. Li, Y. Wang, Y. Li, Z. Q. Yin, W. Chen, and Z. F. Han, “Tight finite-key analysis for passive decoy-state quantum key distribution under general attacks,” Phys. Rev. A 89, 052328 (2014).
[Crossref]

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]

Comandar, L. C.

L. C. Comandar, M. Lucamarini, B. Fröhlich, J. F. Dynes, A. W. Sharpe, S. W.-B. Tam, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Quantum key distribution without detector vulnerabilities using optically seeded lasers,” Nat. Photonics 10, 312–315 (2016).
[Crossref]

Dai, H.

Y. H. Li, Y. Cao, H. Dai, J. Lin, Z. Zhang, W. Chen, Y. Xu, J. Y. Guan, S. K. Liao, J. Yin, Q. Zhang, X. Ma, C. Z. Peng, and J. W. Pan, “Experimental round-robin differential phase-shift quantum key distribution,” Phys. Rev. A 93, 030302 (2016).
[Crossref]

Dynes, J. F.

L. C. Comandar, M. Lucamarini, B. Fröhlich, J. F. Dynes, A. W. Sharpe, S. W.-B. Tam, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Quantum key distribution without detector vulnerabilities using optically seeded lasers,” Nat. Photonics 10, 312–315 (2016).
[Crossref]

Ekert, A. K.

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661 (1991).
[Crossref] [PubMed]

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]

Fröhlich, B.

L. C. Comandar, M. Lucamarini, B. Fröhlich, J. F. Dynes, A. W. Sharpe, S. W.-B. Tam, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Quantum key distribution without detector vulnerabilities using optically seeded lasers,” Nat. Photonics 10, 312–315 (2016).
[Crossref]

Fung, C.

X. Ma, C. Fung, J. C. Boileau, and H. F. Chau, “Universally composable and customizable post-processing for practical quantum key distribution,” Comput. Security 30, 172–177 (2011).
[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 (2004).
[Crossref]

Guan, J. Y.

Y. H. Li, Y. Cao, H. Dai, J. Lin, Z. Zhang, W. Chen, Y. Xu, J. Y. Guan, S. K. Liao, J. Yin, Q. Zhang, X. Ma, C. Z. Peng, and J. W. Pan, “Experimental round-robin differential phase-shift quantum key distribution,” Phys. Rev. A 93, 030302 (2016).
[Crossref]

J. Y. Guan, Z. Cao, and Y. Liu, “Experimental passive round-robin differential phase-shift quantum key distribution,” Phys. Rev. Lett. 114, 180502 (2015).
[Crossref] [PubMed]

Guo, G. C.

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]

Guo, G.-C.

W.-Y. Liang, M. Li, Z.-Q. Yin, W. Chen, S. Wang, W.-B. An, G.-C. Guo, and Z.-F. Han, “Simple implementation of quantum key distribution based on single-photon Bell-state measurement,” Phys. Rev. A 92, 012319 (2015).
[Crossref]

C. Wang, X.-T. Song, W. Chen, C.-M. Zhang, G.-C. Guo, and Z.-F. Han, “Phase-reference-free experiment of measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 115, 160502 (2015).
[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]

C. Zhou, W. S. Bao, H. W. Li, Y. Wang, Y. Li, Z. Q. Yin, W. Chen, and Z. F. Han, “Tight finite-key analysis for passive decoy-state quantum key distribution under general attacks,” Phys. Rev. A 89, 052328 (2014).
[Crossref]

Han, Z.-F.

C. Wang, X.-T. Song, W. Chen, C.-M. Zhang, G.-C. Guo, and Z.-F. Han, “Phase-reference-free experiment of measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 115, 160502 (2015).
[Crossref] [PubMed]

W.-Y. Liang, M. Li, Z.-Q. Yin, W. Chen, S. Wang, W.-B. An, G.-C. Guo, and Z.-F. Han, “Simple implementation of quantum key distribution based on single-photon Bell-state measurement,” Phys. Rev. A 92, 012319 (2015).
[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]

Huang, M.-Q.

Y.-L. Tang, H.-L. Yin, Q. Zhao, H. Liu, X.-X. Sun, M.-Q. Huang, W.-J. Zhang, S.-J. Chen, L. Zhang, L.-X. You, Z. Wang, Y. Liu, C.-Y. Lu, X. Jiang, X. F. Ma, Q. Zhang, T.-Y. Chen, and J.-W. Pan, “Measurement-device-independent quantum key distribution over untrustful metropolitan network,” Phys. Rev. X 6, 011024 (2016).

Hwang, W. Y.

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

Jiang, X.

Y.-L. Tang, H.-L. Yin, Q. Zhao, H. Liu, X.-X. Sun, M.-Q. Huang, W.-J. Zhang, S.-J. Chen, L. Zhang, L.-X. You, Z. Wang, Y. Liu, C.-Y. Lu, X. Jiang, X. F. Ma, Q. Zhang, T.-Y. Chen, and J.-W. Pan, “Measurement-device-independent quantum key distribution over untrustful metropolitan network,” Phys. Rev. X 6, 011024 (2016).

Koashi, M.

H. Takesue, T. Sasaki, K. Tamaki, and M. Koashi, “Experimental quantum key distribution without monitoring signal disturbance,” Nat. Photonics 9, 827 (2015).
[Crossref]

T. Sasaki, Y. Yamamoto, and M. Koashi, “Practical quantum key distribution protocol without mointoring signal distutbance,” Nature 509, 475–478 (2014).
[Crossref] [PubMed]

Laurenti, N.

D. Bacco, M. Canale, N. Laurenti, G. Vallone, and P. Villoresi, “Experimental quantum key distribution with finite-key security analysis for noisy channels,” Nat. Commun. 4, 2363 (2013).
[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]

C. Zhou, W. S. Bao, H. W. Li, Y. Wang, Y. Li, Z. Q. Yin, W. Chen, and Z. F. Han, “Tight finite-key analysis for passive decoy-state quantum key distribution under general attacks,” Phys. Rev. A 89, 052328 (2014).
[Crossref]

Li, M.

W.-Y. Liang, M. Li, Z.-Q. Yin, W. Chen, S. Wang, W.-B. An, G.-C. Guo, and Z.-F. Han, “Simple implementation of quantum key distribution based on single-photon Bell-state measurement,” Phys. Rev. A 92, 012319 (2015).
[Crossref]

Li, Y.

C. Zhou, W. S. Bao, H. W. Li, Y. Wang, Y. Li, Z. Q. Yin, W. Chen, and Z. F. Han, “Tight finite-key analysis for passive decoy-state quantum key distribution under general attacks,” Phys. Rev. A 89, 052328 (2014).
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Liu, Y.

Y.-L. Tang, H.-L. Yin, Q. Zhao, H. Liu, X.-X. Sun, M.-Q. Huang, W.-J. Zhang, S.-J. Chen, L. Zhang, L.-X. You, Z. Wang, Y. Liu, C.-Y. Lu, X. Jiang, X. F. Ma, Q. Zhang, T.-Y. Chen, and J.-W. Pan, “Measurement-device-independent quantum key distribution over untrustful metropolitan network,” Phys. Rev. X 6, 011024 (2016).

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X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A 72, 012326 (2005).
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H.-K. Lo, X. F. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94, 230504 (2005).
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L. C. Comandar, M. Lucamarini, B. Fröhlich, J. F. Dynes, A. W. Sharpe, S. W.-B. Tam, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Quantum key distribution without detector vulnerabilities using optically seeded lasers,” Nat. Photonics 10, 312–315 (2016).
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X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A 72, 012326 (2005).
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Ma, X. F.

Y.-L. Tang, H.-L. Yin, Q. Zhao, H. Liu, X.-X. Sun, M.-Q. Huang, W.-J. Zhang, S.-J. Chen, L. Zhang, L.-X. You, Z. Wang, Y. Liu, C.-Y. Lu, X. Jiang, X. F. Ma, Q. Zhang, T.-Y. Chen, and J.-W. Pan, “Measurement-device-independent quantum key distribution over untrustful metropolitan network,” Phys. Rev. X 6, 011024 (2016).

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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).
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Y. H. Li, Y. Cao, H. Dai, J. Lin, Z. Zhang, W. Chen, Y. Xu, J. Y. Guan, S. K. Liao, J. Yin, Q. Zhang, X. Ma, C. Z. Peng, and J. W. Pan, “Experimental round-robin differential phase-shift quantum key distribution,” Phys. Rev. A 93, 030302 (2016).
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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).
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Pan, J.-W.

Y.-L. Tang, H.-L. Yin, Q. Zhao, H. Liu, X.-X. Sun, M.-Q. Huang, W.-J. Zhang, S.-J. Chen, L. Zhang, L.-X. You, Z. Wang, Y. Liu, C.-Y. Lu, X. Jiang, X. F. Ma, Q. Zhang, T.-Y. Chen, and J.-W. Pan, “Measurement-device-independent quantum key distribution over untrustful metropolitan network,” Phys. Rev. X 6, 011024 (2016).

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).
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Y. H. Li, Y. Cao, H. Dai, J. Lin, Z. Zhang, W. Chen, Y. Xu, J. Y. Guan, S. K. Liao, J. Yin, Q. Zhang, X. Ma, C. Z. Peng, and J. W. Pan, “Experimental round-robin differential phase-shift quantum key distribution,” Phys. Rev. A 93, 030302 (2016).
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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).
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L. C. Comandar, M. Lucamarini, B. Fröhlich, J. F. Dynes, A. W. Sharpe, S. W.-B. Tam, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Quantum key distribution without detector vulnerabilities using optically seeded lasers,” Nat. Photonics 10, 312–315 (2016).
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X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A 72, 012326 (2005).
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C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” Cryptology 5, 3 (1992).

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H. Takesue, T. Sasaki, K. Tamaki, and M. Koashi, “Experimental quantum key distribution without monitoring signal disturbance,” Nat. Photonics 9, 827 (2015).
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T. Sasaki, Y. Yamamoto, and M. Koashi, “Practical quantum key distribution protocol without mointoring signal distutbance,” Nature 509, 475–478 (2014).
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L. C. Comandar, M. Lucamarini, B. Fröhlich, J. F. Dynes, A. W. Sharpe, S. W.-B. Tam, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Quantum key distribution without detector vulnerabilities using optically seeded lasers,” Nat. Photonics 10, 312–315 (2016).
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Shields, A. J.

L. C. Comandar, M. Lucamarini, B. Fröhlich, J. F. Dynes, A. W. Sharpe, S. W.-B. Tam, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Quantum key distribution without detector vulnerabilities using optically seeded lasers,” Nat. Photonics 10, 312–315 (2016).
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P. W. Shor and J. Preskill, “Simple proof of security of the BB84 quantum key distribution protocol,” Phys. Rev. Lett. 85, 441 (2000).
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C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” Cryptology 5, 3 (1992).

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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).
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Song, X.-T.

C. Wang, X.-T. Song, W. Chen, C.-M. Zhang, G.-C. Guo, and Z.-F. Han, “Phase-reference-free experiment of measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 115, 160502 (2015).
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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).
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Sun, X.-X.

Y.-L. Tang, H.-L. Yin, Q. Zhao, H. Liu, X.-X. Sun, M.-Q. Huang, W.-J. Zhang, S.-J. Chen, L. Zhang, L.-X. You, Z. Wang, Y. Liu, C.-Y. Lu, X. Jiang, X. F. Ma, Q. Zhang, T.-Y. Chen, and J.-W. Pan, “Measurement-device-independent quantum key distribution over untrustful metropolitan network,” Phys. Rev. X 6, 011024 (2016).

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H. Takesue, T. Sasaki, K. Tamaki, and M. Koashi, “Experimental quantum key distribution without monitoring signal disturbance,” Nat. Photonics 9, 827 (2015).
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Tam, S. W.-B.

L. C. Comandar, M. Lucamarini, B. Fröhlich, J. F. Dynes, A. W. Sharpe, S. W.-B. Tam, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Quantum key distribution without detector vulnerabilities using optically seeded lasers,” Nat. Photonics 10, 312–315 (2016).
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Tamaki, K.

H. Takesue, T. Sasaki, K. Tamaki, and M. Koashi, “Experimental quantum key distribution without monitoring signal disturbance,” Nat. Photonics 9, 827 (2015).
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Tang, Y.-L.

Y.-L. Tang, H.-L. Yin, Q. Zhao, H. Liu, X.-X. Sun, M.-Q. Huang, W.-J. Zhang, S.-J. Chen, L. Zhang, L.-X. You, Z. Wang, Y. Liu, C.-Y. Lu, X. Jiang, X. F. Ma, Q. Zhang, T.-Y. Chen, and J.-W. Pan, “Measurement-device-independent quantum key distribution over untrustful metropolitan network,” Phys. Rev. X 6, 011024 (2016).

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D. Bacco, M. Canale, N. Laurenti, G. Vallone, and P. Villoresi, “Experimental quantum key distribution with finite-key security analysis for noisy channels,” Nat. Commun. 4, 2363 (2013).
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D. Bacco, M. Canale, N. Laurenti, G. Vallone, and P. Villoresi, “Experimental quantum key distribution with finite-key security analysis for noisy channels,” Nat. Commun. 4, 2363 (2013).
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C. Wang, X.-T. Song, W. Chen, C.-M. Zhang, G.-C. Guo, and Z.-F. Han, “Phase-reference-free experiment of measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 115, 160502 (2015).
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Wang, S.

W.-Y. Liang, M. Li, Z.-Q. Yin, W. Chen, S. Wang, W.-B. An, G.-C. Guo, and Z.-F. Han, “Simple implementation of quantum key distribution based on single-photon Bell-state measurement,” Phys. Rev. A 92, 012319 (2015).
[Crossref]

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).
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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).
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C. Zhou, W. S. Bao, H. W. Li, Y. Wang, Y. Li, Z. Q. Yin, W. Chen, and Z. F. Han, “Tight finite-key analysis for passive decoy-state quantum key distribution under general attacks,” Phys. Rev. A 89, 052328 (2014).
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Wang, Z.

Y.-L. Tang, H.-L. Yin, Q. Zhao, H. Liu, X.-X. Sun, M.-Q. Huang, W.-J. Zhang, S.-J. Chen, L. Zhang, L.-X. You, Z. Wang, Y. Liu, C.-Y. Lu, X. Jiang, X. F. Ma, Q. Zhang, T.-Y. Chen, and J.-W. Pan, “Measurement-device-independent quantum key distribution over untrustful metropolitan network,” Phys. Rev. X 6, 011024 (2016).

Xu, Y.

Y. H. Li, Y. Cao, H. Dai, J. Lin, Z. Zhang, W. Chen, Y. Xu, J. Y. Guan, S. K. Liao, J. Yin, Q. Zhang, X. Ma, C. Z. Peng, and J. W. Pan, “Experimental round-robin differential phase-shift quantum key distribution,” Phys. Rev. A 93, 030302 (2016).
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T. Sasaki, Y. Yamamoto, and M. Koashi, “Practical quantum key distribution protocol without mointoring signal distutbance,” Nature 509, 475–478 (2014).
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Y.-L. Tang, H.-L. Yin, Q. Zhao, H. Liu, X.-X. Sun, M.-Q. Huang, W.-J. Zhang, S.-J. Chen, L. Zhang, L.-X. You, Z. Wang, Y. Liu, C.-Y. Lu, X. Jiang, X. F. Ma, Q. Zhang, T.-Y. Chen, and J.-W. Pan, “Measurement-device-independent quantum key distribution over untrustful metropolitan network,” Phys. Rev. X 6, 011024 (2016).

Yin, J.

Y. H. Li, Y. Cao, H. Dai, J. Lin, Z. Zhang, W. Chen, Y. Xu, J. Y. Guan, S. K. Liao, J. Yin, Q. Zhang, X. Ma, C. Z. Peng, and J. W. Pan, “Experimental round-robin differential phase-shift quantum key distribution,” Phys. Rev. A 93, 030302 (2016).
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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).
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C. Zhou, W. S. Bao, H. W. Li, Y. Wang, Y. Li, Z. Q. Yin, W. Chen, and Z. F. Han, “Tight finite-key analysis for passive decoy-state quantum key distribution under general attacks,” Phys. Rev. A 89, 052328 (2014).
[Crossref]

Yin, Z.-Q.

W.-Y. Liang, M. Li, Z.-Q. Yin, W. Chen, S. Wang, W.-B. An, G.-C. Guo, and Z.-F. Han, “Simple implementation of quantum key distribution based on single-photon Bell-state measurement,” Phys. Rev. A 92, 012319 (2015).
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You, L.-X.

Y.-L. Tang, H.-L. Yin, Q. Zhao, H. Liu, X.-X. Sun, M.-Q. Huang, W.-J. Zhang, S.-J. Chen, L. Zhang, L.-X. You, Z. Wang, Y. Liu, C.-Y. Lu, X. Jiang, X. F. Ma, Q. Zhang, T.-Y. Chen, and J.-W. Pan, “Measurement-device-independent quantum key distribution over untrustful metropolitan network,” Phys. Rev. X 6, 011024 (2016).

Yuan, X.

Z. Zhang, X. Yuan, Z. Cao, and X. F. Ma, “Round-robin differential-phase-shift quantum key distribution,” ar” Xiv:1505.02481(2015).

Yuan, Z. L.

L. C. Comandar, M. Lucamarini, B. Fröhlich, J. F. Dynes, A. W. Sharpe, S. W.-B. Tam, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Quantum key distribution without detector vulnerabilities using optically seeded lasers,” Nat. Photonics 10, 312–315 (2016).
[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 (2004).
[Crossref]

Zhang, C.-M.

C. Wang, X.-T. Song, W. Chen, C.-M. Zhang, G.-C. Guo, and Z.-F. Han, “Phase-reference-free experiment of measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 115, 160502 (2015).
[Crossref] [PubMed]

Zhang, L.

Y.-L. Tang, H.-L. Yin, Q. Zhao, H. Liu, X.-X. Sun, M.-Q. Huang, W.-J. Zhang, S.-J. Chen, L. Zhang, L.-X. You, Z. Wang, Y. Liu, C.-Y. Lu, X. Jiang, X. F. Ma, Q. Zhang, T.-Y. Chen, and J.-W. Pan, “Measurement-device-independent quantum key distribution over untrustful metropolitan network,” Phys. Rev. X 6, 011024 (2016).

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.

Y. H. Li, Y. Cao, H. Dai, J. Lin, Z. Zhang, W. Chen, Y. Xu, J. Y. Guan, S. K. Liao, J. Yin, Q. Zhang, X. Ma, C. Z. Peng, and J. W. Pan, “Experimental round-robin differential phase-shift quantum key distribution,” Phys. Rev. A 93, 030302 (2016).
[Crossref]

Y.-L. Tang, H.-L. Yin, Q. Zhao, H. Liu, X.-X. Sun, M.-Q. Huang, W.-J. Zhang, S.-J. Chen, L. Zhang, L.-X. You, Z. Wang, Y. Liu, C.-Y. Lu, X. Jiang, X. F. Ma, Q. Zhang, T.-Y. Chen, and J.-W. Pan, “Measurement-device-independent quantum key distribution over untrustful metropolitan network,” Phys. Rev. X 6, 011024 (2016).

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, W.-J.

Y.-L. Tang, H.-L. Yin, Q. Zhao, H. Liu, X.-X. Sun, M.-Q. Huang, W.-J. Zhang, S.-J. Chen, L. Zhang, L.-X. You, Z. Wang, Y. Liu, C.-Y. Lu, X. Jiang, X. F. Ma, Q. Zhang, T.-Y. Chen, and J.-W. Pan, “Measurement-device-independent quantum key distribution over untrustful metropolitan network,” Phys. Rev. X 6, 011024 (2016).

Zhang, Z.

Y. H. Li, Y. Cao, H. Dai, J. Lin, Z. Zhang, W. Chen, Y. Xu, J. Y. Guan, S. K. Liao, J. Yin, Q. Zhang, X. Ma, C. Z. Peng, and J. W. Pan, “Experimental round-robin differential phase-shift quantum key distribution,” Phys. Rev. A 93, 030302 (2016).
[Crossref]

Z. Zhang, X. Yuan, Z. Cao, and X. F. Ma, “Round-robin differential-phase-shift quantum key distribution,” ar” Xiv:1505.02481(2015).

Zhao, Q.

Y.-L. Tang, H.-L. Yin, Q. Zhao, H. Liu, X.-X. Sun, M.-Q. Huang, W.-J. Zhang, S.-J. Chen, L. Zhang, L.-X. You, Z. Wang, Y. Liu, C.-Y. Lu, X. Jiang, X. F. Ma, Q. Zhang, T.-Y. Chen, and J.-W. Pan, “Measurement-device-independent quantum key distribution over untrustful metropolitan network,” Phys. Rev. X 6, 011024 (2016).

Zhao, Y.

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, C.

C. Zhou, W. S. Bao, H. W. Li, Y. Wang, Y. Li, Z. Q. Yin, W. Chen, and Z. F. Han, “Tight finite-key analysis for passive decoy-state quantum key distribution under general attacks,” Phys. Rev. A 89, 052328 (2014).
[Crossref]

Zhou, 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]

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]

Appl. Phys. Lett. (1)

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

Comput. Security (1)

X. Ma, C. Fung, J. C. Boileau, and H. F. Chau, “Universally composable and customizable post-processing for practical quantum key distribution,” Comput. Security 30, 172–177 (2011).
[Crossref]

Cryptology (1)

C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” Cryptology 5, 3 (1992).

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)

D. Bacco, M. Canale, N. Laurenti, G. Vallone, and P. Villoresi, “Experimental quantum key distribution with finite-key security analysis for noisy channels,” Nat. Commun. 4, 2363 (2013).
[Crossref] [PubMed]

Nat. Photonics (3)

L. C. Comandar, M. Lucamarini, B. Fröhlich, J. F. Dynes, A. W. Sharpe, S. W.-B. Tam, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Quantum key distribution without detector vulnerabilities using optically seeded lasers,” Nat. Photonics 10, 312–315 (2016).
[Crossref]

H. Takesue, T. Sasaki, K. Tamaki, and M. Koashi, “Experimental quantum key distribution without monitoring signal disturbance,” Nat. Photonics 9, 827 (2015).
[Crossref]

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).
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Nature (1)

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Figures (6)

Fig. 1
Fig. 1 Diagram of RRDPS protocol
Fig. 2
Fig. 2 Key rates versus mean photon number and threshold of photons in a packet.
Fig. 3
Fig. 3 Comparison for RRDPS protocol using WCPs and HSPS. (a) Bit error rate, e, is equal to 0.03. (b) Bit error rate, e, is equal to 0.06. The solid curves represent the key rates per pulse for using WCPs, the dashed curves stand for key rates for using HSPS. Lines labeled (i)-(iii) characterize the protocol with L = 128, 64, 32. The choices of vth and the mean photon number μ are optimized.
Fig. 4
Fig. 4 Final key rate without and with decoy states. The solid curves represent the key rates per pulse for using WCPs, and the dashed curves stand for key rates for using HSPS. The length of each packet is fixed at 32. The left two curves are the key rates of RRDPS protocol with no decoy states, and the other two are those of the protocol with decoy states.
Fig. 5
Fig. 5 The estimated bounds and asymptotic bounds of yields and error rates. (a) The lower bound of the yields. (b) The upper bound of the error rate. The solid lines represent estimated bounds of yields and error rates, and the dashed lines stand for asymptotic bounds of yields and error rates.
Fig. 6
Fig. 6 Final key rate for using infinite and finite decoy states. The dotted curve accounts for the key rate per packet for infinite decoy-state, and the solid curve stands for the four-intensity decoy-state method. The dashed curve represents for three-intensity decoy-state method and the dash-dotted one is on behalf of the two-intensity decoy-state method. The choices of the mean photon number μ are optimized. The optimal signal-state intensity μ = 0.025, decoy-state intensities v1 = 0.09μ, v2 = 0.05μ, v3 = 0.03μ, v4 = 0.01μ.

Tables (1)

Tables Icon

Table 1 Experimental parameters for simulation

Equations (19)

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| ψ > = 1 L k = 1 L ( 1 ) s k | k > ,
G = N [ 1 f h ( e b i t ) h ( e p h a s e ) ]
E L μ Q L μ = e n Y n ( L μ ) n ( 1 + L μ ) n + 1 = e 0 Y 0 + e d ( 1 Y 0 ) ( 1 e L η μ )
= Y 0 d A ( 1 + L μ ) P p o s t ( L μ ) + n = 1 [ 1 ( 1 Y 0 ) ( 1 η ) n ] [ 1 ( 1 η A ) n ] ( L μ ) n ( 1 + L μ ) n + 1 P p o s t ( L μ ) = d A Y 0 ( 1 + L μ η A ) + L μ η A ( 1 + L μ ) d A ( 1 + L μ η A ) + L μ η A ( 1 + L μ ) L μ ( 1 Y 0 ) ( 1 + L μ η A ) ( 1 η ) [ d A ( 1 + L μ η A ) + L μ η A ( 1 + L μ ) ] ( 1 + L μ η ) + L μ ( 1 Y 0 ) ( 1 + L μ η A ) ( 1 η ) ( 1 η A ) [ d A ( 1 + L μ η A ) + L μ η A ( 1 + L μ ) ] ( 1 + L μ η + L μ η A L μ η η A ) E L μ Q L μ = e n Y n P μ ( n ) = e 0 Y 0 d A ( 1 + L μ ) P p o s t ( L μ ) + n = 1 { [ 1 ( 1 η ) n ] } [ 1 ( 1 η A ) n ] ( L μ ) n ( 1 + L μ ) n + 1 P p o s t ( L μ ) = d A e 0 Y 0 ( 1 + L μ η A ) + L μ η A ( 1 + L μ ) [ e 0 Y 0 + e d ( 1 Y 0 ) ] d A ( 1 + L μ η A ) + L μ η A ( 1 + L μ ) e d L μ ( 1 Y 0 ) ( 1 + L μ η A ) ( 1 η ) ( d A ( 1 + L μ η A ) + L μ η A ( 1 + L μ ) ) ( 1 + L μ η ) + e d L μ ( 1 Y 0 ) ( 1 + L μ η A ) ( 1 η ) ( 1 η A ) ( d A ( 1 + L μ η A ) + L μ η A ( 1 + L μ ) ) ( 1 + L μ η + L μ η A L μ η η A )
R = Q L μ [ 1 f h ( e b i t ) H P A ] .
Q L μ H P A = n = 0 Y n P L μ ( n ) h ( e p h n ) .
Y n = 1 ( 1 Y 0 ) ( 1 η ) n .
R = n = 0 n t h Y n P L μ ( n ) ( 1 f h ( e b i t n ) h ( e p h n ) )
Q L μ e L μ = n = 0 Y n ( L μ ) n n ! E L μ Q L μ e L μ = n = 0 e n Y n ( L μ ) n n ! Q L ν 1 e L ν 1 = n = 0 Y n ( L ν 1 ) n n ! E L ν 1 Q L ν 1 e L ν 1 = n = 0 e n Y n ( L ν 1 ) n n ! Q L ν 2 e L ν 2 = n = 0 Y n ( L ν 2 ) n n ! E L ν 2 Q L ν 2 e L ν 2 = n = 0 e n Y n ( L ν 2 ) n n ! Q L ν 3 e L ν 3 = n = 0 Y n ( L ν 3 ) n n ! E L ν 3 Q L ν 3 e L ν 3 = n = 0 e n Y n ( L ν 3 ) n n ! Q L ν 4 e L ν 4 = n = 0 Y n ( L ν 4 ) n n ! E L ν 4 Q L ν 4 e L ν 4 = n = 0 e n Y n ( L ν 4 ) n n !
Q L ν 1 e L ν 1 Q L ν 2 e L ν 2 = Y 1 ( L v 1 L v 2 ) + Y 2 2 ! ( ( L v 1 ) 2 ( L v 2 ) 2 ) + Y 3 3 ! ( ( L v 1 ) 3 ( L v 2 ) 3 ) +
Q L ν 2 e L ν 2 Q L ν 3 e L ν 3 = Y 1 ( L v 2 L v 3 ) + Y 2 2 ! ( ( L v 2 ) 2 ( L v 3 ) 2 ) + Y 3 3 ! ( ( L v 2 ) 3 ( L v 3 ) 3 ) +
Y 2 Y 2 L = 2 μ [ ( ν 2 ν 3 ) Q L ν 1 e L ν 1 ( ν 1 ν 3 ) Q L ν 2 e L ν 2 + ( ν 1 + ν 2 ) Q L ν 3 e L ν 3 ] L 2 ( μ ν 1 ν 2 ν 3 ) ( ν 1 ν 3 ) ( v 1 v 2 ) ν 1 + ν 2 + ν 3 ( L μ ) 2 ( μ ν 1 ν 2 ν 3 ) ( Q L μ e L μ Y 0 L Y 1 L L μ )
( v 2 v 3 ) Q L ν 1 e L ν 1 ( v 1 v 3 ) Q L ν 2 e L ν 2 + ( v 1 v 2 ) Q L ν 3 e L ν 3 = Y 2 2 ! L 2 ( v 2 v 3 ) ( v 1 v 3 ) ( v 1 v 2 ) + Y 3 3 ! L 3 ( v 2 v 3 ) ( v 1 v 2 ) ( v 1 v 3 ) ( v 1 + v 2 + v 3 ) + Y 4 4 ! L 4 ( v 2 v 3 ) ( v 1 v 2 ) ( v 1 v 3 ) ( v 1 2 + v 2 2 + v 3 2 + v 1 v 2 + v 1 v 3 + v 2 v 3 ) + ( v 3 v 4 ) Q L ν 2 e L ν 2 ( v 2 v 4 ) Q L ν 3 e L ν 3 + ( v 2 v 3 ) Q L ν 4 e L ν 4 = Y 2 2 ! L 2 ( v 3 v 4 ) ( v 2 v 4 ) ( v 2 v 3 ) + Y 3 3 ! L 3 ( v 3 v 4 ) ( v 2 v 3 ) ( v 2 v 4 ) ( v 2 + v 3 + v 4 ) = Y 4 4 ! L 4 ( v 3 v 4 ) ( v 2 v 3 ) ( v 2 v 4 ) ( v 2 2 + v 3 2 + v 4 2 + v 2 v 3 + v 2 v 4 + v 3 v 4 ) +
Y 3 Y 3 L = 3 ! μ L 3 ( μ ν 1 ν 2 ν 3 ν 4 ) [ Q L ν 1 e L ν 1 ( ν 1 ν 2 ) ( ν 1 ν 3 ) ( ν 1 ν 4 ) Q L ν 2 e L ν 2 ( ν 2 ν 3 ) ( ν 1 ν 2 ) ( ν 2 ν 4 ) + Q L ν 3 e L ν 3 ( ν 1 ν 3 ) ( ν 2 ν 3 ) ( ν 3 ν 4 ) Q L ν 4 e L ν 4 ( ν 1 ν 4 ) ( ν 2 ν 4 ) ( ν 3 ν 4 ) ] 3 ! ( ν 1 + ν 2 + ν 3 + ν 4 ) μ ν 1 ν 2 ν 3 ν 4 Q L μ e L μ Y 0 L Y 1 L L μ Y 2 L ( L μ ) 2 2 ! ( L μ ) 3
E L ν 2 Q L ν 2 e L v 2 = e 0 Y 0 + e 1 L ν 2 Y 1 + n = 2 e n Y n ( L ν 2 ) n n !
e 1 e 1 U = E L ν 1 Q L ν 1 e L ν 1 E L ν 2 Q L ν 2 e L ν 2 ( L ν 1 L ν 2 ) Y 1 L
e 2 e 2 U = 2 [ ( ν 2 ν 3 ) E L ν 1 Q L ν 1 e L ν 1 ( ν 1 ν 3 ) E L ν 2 Q L ν 2 e L ν 2 + ( ν 1 ν 2 ) E L ν 3 Q L ν 3 e L ν 3 ] L 2 Y 2 L ( ν 2 ν 3 ) ( ν 1 ν 3 ) ( ν 1 ν 2 )
( v 2 v 3 ) E L ν 1 Q L ν 1 e L ν 1 ( v 1 v 3 ) E L ν 2 Q L ν 2 e L ν 2 + ( v 1 v 2 ) E L ν 3 Q L ν 3 e L ν 3 = e 2 Y 2 L 2 2 ( v 2 v 3 ) ( v 1 v 3 ) ( v 1 v 2 ) + e 3 Y 3 L 3 3 ! ( v 2 v 3 ) ( v 1 v 3 ) ( v 1 v 2 ) ( v 1 + v 2 + v 3 ) + ( v 3 v 4 ) E L ν 2 Q L ν 2 e L ν 2 ( v 2 v 4 ) E L ν 3 Q L ν 3 e L ν 3 + ( v 2 v 3 ) E L ν 4 Q L ν 4 e L ν 4 = e 2 Y 2 L 2 2 ( v 3 v 4 ) ( v 2 v 4 ) ( v 2 v 3 ) + e 3 Y 3 L 3 3 ! ( v 3 v 4 ) ( v 2 v 4 ) ( v 2 v 3 ) ( v 2 + v 3 + v 4 ) +
e 3 e 3 U = 3 ! Y 3 L L 3 [ E L ν 1 Q L v 1 e L ν 1 ( ν 1 ν 2 ) ( ν 1 ν 3 ) ( ν 1 ν 4 ) E L ν 2 Q L v 2 e L ν 2 ( ν 2 ν 3 ) ( ν 1 ν 2 ) ( ν 2 ν 4 ) + E L ν 3 Q L v 3 e L ν 3 ( ν 1 ν 3 ) ( ν 2 ν 3 ) ( ν 3 ν 4 ) E L ν 3 Q L v 4 e L ν 4 ( ν 1 ν 4 ) ( ν 2 ν 4 ) ( ν 3 ν 4 ) ]

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