Abstract

We analyse the finite-size security of the efficient Bennett-Brassard 1984 protocol implemented with decoy states and apply the results to a gigahertz-clocked quantum key distribution system. Despite the enhanced security level, the obtained secure key rates are the highest reported so far at all fibre distances.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Wiesner, “Conjugate coding,” Sigact News15(1), 78–88 (1983).
    [CrossRef]
  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 (Institute of Electrical and Electronics Engineers, New York, 1984), pp. 175–179.
  3. A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett.67(6), 661–663 (1991).
    [CrossRef] [PubMed]
  4. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys.74(1), 145–195 (2002).
    [CrossRef]
  5. V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys.81(3), 1301–1350 (2009).
    [CrossRef]
  6. P. D. Townsend, J. G. Rarity, and P. R. Tapster, “Enhanced single-photon fringe visibility in a 10 km-long prototype quantum cryptography,” Electron. Lett.29(14), 1291 (1993).
    [CrossRef]
  7. M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
    [CrossRef]
  8. M. Sasaki, M. Fujiwara, H. Ishizuka, W. Klaus, K. Wakui, M. Takeoka, S. Miki, T. Yamashita, Z. Wang, A. Tanaka, K. Yoshino, Y. Nambu, S. Takahashi, A. Tajima, A. Tomita, T. Domeki, T. Hasegawa, Y. Sakai, H. Kobayashi, T. Asai, K. Shimizu, T. Tokura, T. Tsurumaru, M. Matsui, T. Honjo, K. Tamaki, H. Takesue, Y. Tokura, J. F. Dynes, A. R. Dixon, A. W. Sharpe, Z. L. Yuan, A. J. Shields, S. Uchikoga, M. Legré, S. Robyr, P. Trinkler, L. Monat, J. B. Page, G. Ribordy, A. Poppe, A. Allacher, O. Maurhart, T. Länger, M. Peev, and A. Zeilinger, “Field test of quantum key distribution in the Tokyo QKD Network,” Opt. Express19(11), 10387–10409 (2011).
    [CrossRef] [PubMed]
  9. K. Patel, J. F. Dynes, I. Choi, A. W. Sharpe, A. R. Dixon, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Coexistence of high-bit-rate quantum key distribution and data on optical fiber,” Phys. Rev. X2(4), 041010 (2012).
    [CrossRef]
  10. B. Fröhlich, J. F. Dynes, M. Lucamarini, A. W. Sharpe, Z. Yuan, and A. J. Shields, “A quantum access network,” Nature501(7465), 69–72 (2013).
    [CrossRef] [PubMed]
  11. D. Mayers, D. Coppersmith, ed., in Advances in Cryptology:Proceedings of CRYPTO '95, vol. 963 of Lecture Notes in Computer Science, D. Coppersmith, Ed. (Springer-Verlag, 1995), pp. 124–135; in Advances in Cryptology: Proceedings of CRYPTO '96, vol. 1109 of Lecture Notes in Computer Science, N. Koblitz, Ed. (Springer-Verlag, 1996), pp. 343–357.
  12. H. Inamori, N. Lütkenhaus, and D. Mayers, “Unconditional security of practical quantum key distribution,” Eur. Phys. J. D41(3), 599–627 (2007).
    [CrossRef]
  13. S. Watanabe, R. Matsumoto, and T. Uyematsu, “Noise tolerance of the BB84 protocol with random privacy amplification,” Int. J. Quantum Inf.4(6), 935–946 (2006).
    [CrossRef]
  14. M. Hayashi, “Practical evaluation of security for quantum key distribution,” Phys. Rev. A74(2), 022307 (2006).
    [CrossRef]
  15. M. Hayashi, “Upper bounds of eavesdropper’s performances in finite-length code with the decoy method,” Phys. Rev. A76(1), 012329 (2007).
    [CrossRef]
  16. V. Scarani and R. Renner, “Quantum cryptography with finite resources: unconditional security bound for discrete-variable protocols with one-way postprocessing,” Phys. Rev. Lett.100(20), 200501 (2008).
    [CrossRef] [PubMed]
  17. V. Scarani and R. Renner, “Security bounds for quantum cryptography with finite resources,” in Theory of Quantum Computation, Communication, and Cryptography, vol. 5106 of Lecture Notes in Computer Science, (Berlin Springer, 2008), pp 83–95.
  18. M. Tomamichel, C. C. W. Lim, N. Gisin, and R. Renner, “Tight finite-key analysis for quantum cryptography,” Nat Commun3, 634 (2012).
    [CrossRef] [PubMed]
  19. R. Renner, N. Gisin, and B. Kraus, “Information-theoretic security proof for quantum-key-distribution protocols,” Phys. Rev. A72(1), 012332 (2005).
    [CrossRef]
  20. B. Kraus, N. Gisin, and R. Renner, “Lower and upper bounds on the secret-key rate for quantum key distribution protocols using one-way classical communication,” Phys. Rev. Lett.95(8), 080501 (2005).
    [CrossRef] [PubMed]
  21. H.-K. Lo, H. F. Chau, and M. Ardehali, “Efficient quantum key distribution scheme and proof of its unconditional security,” J. of Crypt.18(2), 133–165 (2005).
    [CrossRef]
  22. W.-Y. Hwang, “Quantum key distribution with high loss: toward global secure communication,” Phys. Rev. Lett.91(5), 057901 (2003).
    [CrossRef] [PubMed]
  23. X.-B. Wang, “Beating the photon-number-splitting attack in practical quantum cryptography,” Phys. Rev. Lett.94(23), 230503 (2005).
    [CrossRef] [PubMed]
  24. H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett.94(23), 230504 (2005).
    [CrossRef] [PubMed]
  25. X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A72(1), 012326 (2005).
    [CrossRef]
  26. R. Y. Q. Cai and V. Scarani, “Finite-key analysis for practical implementations of quantum key distribution,” New J. Phys.11(4), 045024 (2009).
    [CrossRef]
  27. M. Lucamarini, J. F. Dynes, Z. L. Yuan, and A. J. Shields, “Practical treatment of quantum bugs,” Proc. SPIE8542, Electro-Optical Remote Sensing, Photonic Technologies, and Applications VI (2012).
  28. M. Hayashi and R. Nakayama, “Security analysis of the decoy method with the Bennett-Brassard 1984 protocol for finite key lengths,” arXiv:1302.4139 (2013).
  29. Z. Wei, W. Wang, Z. Zhang, M. Gao, Z. Ma, and X. Ma, “Decoy-state quantum key distribution with biased basis choice,” Sci Rep3, 2453 (2013).
    [CrossRef] [PubMed]
  30. N. J. Beaudry, T. Moroder, and N. Lütkenhaus, “Squashing models for optical measurements in quantum communication,” Phys. Rev. Lett.101(9), 093601 (2008).
    [CrossRef] [PubMed]
  31. T. Tsurumaru and K. Tamaki, “Security proof for QKD systems with threshold detectors,” Phys. Rev. A78, 032302 (2008).
    [CrossRef]
  32. J. Hasegawa, M. Hayashi, T. Hiroshima, and A. Tomita, “Security analysis of decoy state quantum key distribution incorporating finite statistics,” arXiv:0707.3541 (2007).
  33. M. Koashi and J. Preskill, “Secure quantum key distribution with an uncharacterized source,” Phys. Rev. Lett.90(5), 057902 (2003).
    [CrossRef] [PubMed]
  34. H. K. Lo and J. Preskill, “Security of quantum key distribution using weak coherent states with nonrandom phases,” Quantum Inf. Comput.7, 431 (2007).
  35. M. Koashi, “Efficient quantum key distribution with practical sources and detectors,” arXiv:quant-ph/0609180 (2006).
  36. A. Wald, “Tests of statistical hypotheses concerning several parameters when the number of observations is large,” in Transactions of the American Mathematical Society, vol. 54 (1943), pp. 426–482.
  37. A. Agresti and B. A. Coull, “Approximate is better than ‘exact’ for interval estimation of binomial proportions,” Am. Stat.52, 119 (1998).
  38. J. W. Harrington, J. M. Ettinger, R. J. Hughes, and J. E. Nordholt, “Enhancing practical security of quantum key distribution with a few decoy states,” arXiv:quant-ph/0503002 (2005).
  39. P. Rice and J. W. Harrington, “Numerical analysis of decoy state quantum key distribution protocols,” arXiv:0901.0013 (2009).
  40. C. Clopper and E. S. Pearson, “The use of confidence or fiducial limits illustrated in the case of the binomial,” Biometrika26(4), 404–413 (1934).
    [CrossRef]
  41. R. Renner, “Symmetry of large physical systems implies independence of subsystems,” Nat. Phys.3(9), 645–649 (2007).
    [CrossRef]
  42. S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge University Press, 2004).
  43. Z. L. Yuan, B. E. Kardynal, A. W. Sharpe, and A. J. Shields, “High speed single photon detection in the near infrared,” Appl. Phys. Lett.91(4), 041114 (2007).
    [CrossRef]
  44. C. Erven, X. Ma, R. Laflamme, and G. Weihs, “Entangled quantum key distribution with a biased basis choice,” New J. Phys.11(4), 045025 (2009).
    [CrossRef]
  45. J. Hasegawa, M. Hayashi, T. Hiroshima, A. Tanaka, and A. Tomita, “Experimental decoy state quantum key distribution with unconditional security incorporating finite statistics,” arXiv:0705.3081 (2007).
  46. D. Rosenberg, C. G. Peterson, J. W. Harrington, P. R. Rice, N. Dallmann, K. T. Tyagi, K. P. McCabe, S. Nam, B. Baek, R. H. Hadfield, R. J. Hughes, and J. E. Nordholt, “Practical long-distance quantum key distribution system using decoy levels,” New J. Phys.11(4), 045009 (2009).
    [CrossRef]
  47. P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics7(5), 378–381 (2013).
    [CrossRef]

2013

B. Fröhlich, J. F. Dynes, M. Lucamarini, A. W. Sharpe, Z. Yuan, and A. J. Shields, “A quantum access network,” Nature501(7465), 69–72 (2013).
[CrossRef] [PubMed]

Z. Wei, W. Wang, Z. Zhang, M. Gao, Z. Ma, and X. Ma, “Decoy-state quantum key distribution with biased basis choice,” Sci Rep3, 2453 (2013).
[CrossRef] [PubMed]

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics7(5), 378–381 (2013).
[CrossRef]

2012

M. Tomamichel, C. C. W. Lim, N. Gisin, and R. Renner, “Tight finite-key analysis for quantum cryptography,” Nat Commun3, 634 (2012).
[CrossRef] [PubMed]

K. Patel, J. F. Dynes, I. Choi, A. W. Sharpe, A. R. Dixon, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Coexistence of high-bit-rate quantum key distribution and data on optical fiber,” Phys. Rev. X2(4), 041010 (2012).
[CrossRef]

2011

2009

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys.81(3), 1301–1350 (2009).
[CrossRef]

R. Y. Q. Cai and V. Scarani, “Finite-key analysis for practical implementations of quantum key distribution,” New J. Phys.11(4), 045024 (2009).
[CrossRef]

C. Erven, X. Ma, R. Laflamme, and G. Weihs, “Entangled quantum key distribution with a biased basis choice,” New J. Phys.11(4), 045025 (2009).
[CrossRef]

D. Rosenberg, C. G. Peterson, J. W. Harrington, P. R. Rice, N. Dallmann, K. T. Tyagi, K. P. McCabe, S. Nam, B. Baek, R. H. Hadfield, R. J. Hughes, and J. E. Nordholt, “Practical long-distance quantum key distribution system using decoy levels,” New J. Phys.11(4), 045009 (2009).
[CrossRef]

2008

N. J. Beaudry, T. Moroder, and N. Lütkenhaus, “Squashing models for optical measurements in quantum communication,” Phys. Rev. Lett.101(9), 093601 (2008).
[CrossRef] [PubMed]

T. Tsurumaru and K. Tamaki, “Security proof for QKD systems with threshold detectors,” Phys. Rev. A78, 032302 (2008).
[CrossRef]

V. Scarani and R. Renner, “Quantum cryptography with finite resources: unconditional security bound for discrete-variable protocols with one-way postprocessing,” Phys. Rev. Lett.100(20), 200501 (2008).
[CrossRef] [PubMed]

2007

M. Hayashi, “Upper bounds of eavesdropper’s performances in finite-length code with the decoy method,” Phys. Rev. A76(1), 012329 (2007).
[CrossRef]

H. K. Lo and J. Preskill, “Security of quantum key distribution using weak coherent states with nonrandom phases,” Quantum Inf. Comput.7, 431 (2007).

R. Renner, “Symmetry of large physical systems implies independence of subsystems,” Nat. Phys.3(9), 645–649 (2007).
[CrossRef]

Z. L. Yuan, B. E. Kardynal, A. W. Sharpe, and A. J. Shields, “High speed single photon detection in the near infrared,” Appl. Phys. Lett.91(4), 041114 (2007).
[CrossRef]

H. Inamori, N. Lütkenhaus, and D. Mayers, “Unconditional security of practical quantum key distribution,” Eur. Phys. J. D41(3), 599–627 (2007).
[CrossRef]

2006

S. Watanabe, R. Matsumoto, and T. Uyematsu, “Noise tolerance of the BB84 protocol with random privacy amplification,” Int. J. Quantum Inf.4(6), 935–946 (2006).
[CrossRef]

M. Hayashi, “Practical evaluation of security for quantum key distribution,” Phys. Rev. A74(2), 022307 (2006).
[CrossRef]

2005

R. Renner, N. Gisin, and B. Kraus, “Information-theoretic security proof for quantum-key-distribution protocols,” Phys. Rev. A72(1), 012332 (2005).
[CrossRef]

B. Kraus, N. Gisin, and R. Renner, “Lower and upper bounds on the secret-key rate for quantum key distribution protocols using one-way classical communication,” Phys. Rev. Lett.95(8), 080501 (2005).
[CrossRef] [PubMed]

H.-K. Lo, H. F. Chau, and M. Ardehali, “Efficient quantum key distribution scheme and proof of its unconditional security,” J. of Crypt.18(2), 133–165 (2005).
[CrossRef]

X.-B. Wang, “Beating the photon-number-splitting attack in practical quantum cryptography,” Phys. Rev. Lett.94(23), 230503 (2005).
[CrossRef] [PubMed]

H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett.94(23), 230504 (2005).
[CrossRef] [PubMed]

X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A72(1), 012326 (2005).
[CrossRef]

2003

M. Koashi and J. Preskill, “Secure quantum key distribution with an uncharacterized source,” Phys. Rev. Lett.90(5), 057902 (2003).
[CrossRef] [PubMed]

W.-Y. Hwang, “Quantum key distribution with high loss: toward global secure communication,” Phys. Rev. Lett.91(5), 057901 (2003).
[CrossRef] [PubMed]

2002

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys.74(1), 145–195 (2002).
[CrossRef]

1998

A. Agresti and B. A. Coull, “Approximate is better than ‘exact’ for interval estimation of binomial proportions,” Am. Stat.52, 119 (1998).

1993

P. D. Townsend, J. G. Rarity, and P. R. Tapster, “Enhanced single-photon fringe visibility in a 10 km-long prototype quantum cryptography,” Electron. Lett.29(14), 1291 (1993).
[CrossRef]

1991

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett.67(6), 661–663 (1991).
[CrossRef] [PubMed]

1983

S. Wiesner, “Conjugate coding,” Sigact News15(1), 78–88 (1983).
[CrossRef]

1934

C. Clopper and E. S. Pearson, “The use of confidence or fiducial limits illustrated in the case of the binomial,” Biometrika26(4), 404–413 (1934).
[CrossRef]

Agresti, A.

A. Agresti and B. A. Coull, “Approximate is better than ‘exact’ for interval estimation of binomial proportions,” Am. Stat.52, 119 (1998).

Allacher, A.

Alléaume, R.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Ardehali, M.

H.-K. Lo, H. F. Chau, and M. Ardehali, “Efficient quantum key distribution scheme and proof of its unconditional security,” J. of Crypt.18(2), 133–165 (2005).
[CrossRef]

Asai, T.

Baek, B.

D. Rosenberg, C. G. Peterson, J. W. Harrington, P. R. Rice, N. Dallmann, K. T. Tyagi, K. P. McCabe, S. Nam, B. Baek, R. H. Hadfield, R. J. Hughes, and J. E. Nordholt, “Practical long-distance quantum key distribution system using decoy levels,” New J. Phys.11(4), 045009 (2009).
[CrossRef]

Barreiro, C.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Beaudry, N. J.

N. J. Beaudry, T. Moroder, and N. Lütkenhaus, “Squashing models for optical measurements in quantum communication,” Phys. Rev. Lett.101(9), 093601 (2008).
[CrossRef] [PubMed]

Bechmann-Pasquinucci, H.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys.81(3), 1301–1350 (2009).
[CrossRef]

Bouda, J.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Boxleitner, W.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Cai, R. Y. Q.

R. Y. Q. Cai and V. Scarani, “Finite-key analysis for practical implementations of quantum key distribution,” New J. Phys.11(4), 045024 (2009).
[CrossRef]

Cerf, N. J.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys.81(3), 1301–1350 (2009).
[CrossRef]

Chau, H. F.

H.-K. Lo, H. F. Chau, and M. Ardehali, “Efficient quantum key distribution scheme and proof of its unconditional security,” J. of Crypt.18(2), 133–165 (2005).
[CrossRef]

Chen, K.

H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett.94(23), 230504 (2005).
[CrossRef] [PubMed]

Choi, I.

K. Patel, J. F. Dynes, I. Choi, A. W. Sharpe, A. R. Dixon, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Coexistence of high-bit-rate quantum key distribution and data on optical fiber,” Phys. Rev. X2(4), 041010 (2012).
[CrossRef]

Clopper, C.

C. Clopper and E. S. Pearson, “The use of confidence or fiducial limits illustrated in the case of the binomial,” Biometrika26(4), 404–413 (1934).
[CrossRef]

Coull, B. A.

A. Agresti and B. A. Coull, “Approximate is better than ‘exact’ for interval estimation of binomial proportions,” Am. Stat.52, 119 (1998).

Dallmann, N.

D. Rosenberg, C. G. Peterson, J. W. Harrington, P. R. Rice, N. Dallmann, K. T. Tyagi, K. P. McCabe, S. Nam, B. Baek, R. H. Hadfield, R. J. Hughes, and J. E. Nordholt, “Practical long-distance quantum key distribution system using decoy levels,” New J. Phys.11(4), 045009 (2009).
[CrossRef]

Debuisschert, T.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Diamanti, E.

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics7(5), 378–381 (2013).
[CrossRef]

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Dianati, M.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Dixon, A. R.

Domeki, T.

Dušek, M.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys.81(3), 1301–1350 (2009).
[CrossRef]

Dynes, J. F.

B. Fröhlich, J. F. Dynes, M. Lucamarini, A. W. Sharpe, Z. Yuan, and A. J. Shields, “A quantum access network,” Nature501(7465), 69–72 (2013).
[CrossRef] [PubMed]

K. Patel, J. F. Dynes, I. Choi, A. W. Sharpe, A. R. Dixon, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Coexistence of high-bit-rate quantum key distribution and data on optical fiber,” Phys. Rev. X2(4), 041010 (2012).
[CrossRef]

M. Sasaki, M. Fujiwara, H. Ishizuka, W. Klaus, K. Wakui, M. Takeoka, S. Miki, T. Yamashita, Z. Wang, A. Tanaka, K. Yoshino, Y. Nambu, S. Takahashi, A. Tajima, A. Tomita, T. Domeki, T. Hasegawa, Y. Sakai, H. Kobayashi, T. Asai, K. Shimizu, T. Tokura, T. Tsurumaru, M. Matsui, T. Honjo, K. Tamaki, H. Takesue, Y. Tokura, J. F. Dynes, A. R. Dixon, A. W. Sharpe, Z. L. Yuan, A. J. Shields, S. Uchikoga, M. Legré, S. Robyr, P. Trinkler, L. Monat, J. B. Page, G. Ribordy, A. Poppe, A. Allacher, O. Maurhart, T. Länger, M. Peev, and A. Zeilinger, “Field test of quantum key distribution in the Tokyo QKD Network,” Opt. Express19(11), 10387–10409 (2011).
[CrossRef] [PubMed]

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

M. Lucamarini, J. F. Dynes, Z. L. Yuan, and A. J. Shields, “Practical treatment of quantum bugs,” Proc. SPIE8542, Electro-Optical Remote Sensing, Photonic Technologies, and Applications VI (2012).

Ekert, A. K.

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett.67(6), 661–663 (1991).
[CrossRef] [PubMed]

Erven, C.

C. Erven, X. Ma, R. Laflamme, and G. Weihs, “Entangled quantum key distribution with a biased basis choice,” New J. Phys.11(4), 045025 (2009).
[CrossRef]

Fasel, S.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Fossier, S.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Fröhlich, B.

B. Fröhlich, J. F. Dynes, M. Lucamarini, A. W. Sharpe, Z. Yuan, and A. J. Shields, “A quantum access network,” Nature501(7465), 69–72 (2013).
[CrossRef] [PubMed]

Fujiwara, M.

Fürst, M.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Gao, M.

Z. Wei, W. Wang, Z. Zhang, M. Gao, Z. Ma, and X. Ma, “Decoy-state quantum key distribution with biased basis choice,” Sci Rep3, 2453 (2013).
[CrossRef] [PubMed]

Gautier, J.-D.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Gay, O.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Gisin, N.

M. Tomamichel, C. C. W. Lim, N. Gisin, and R. Renner, “Tight finite-key analysis for quantum cryptography,” Nat Commun3, 634 (2012).
[CrossRef] [PubMed]

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

R. Renner, N. Gisin, and B. Kraus, “Information-theoretic security proof for quantum-key-distribution protocols,” Phys. Rev. A72(1), 012332 (2005).
[CrossRef]

B. Kraus, N. Gisin, and R. Renner, “Lower and upper bounds on the secret-key rate for quantum key distribution protocols using one-way classical communication,” Phys. Rev. Lett.95(8), 080501 (2005).
[CrossRef] [PubMed]

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys.74(1), 145–195 (2002).
[CrossRef]

Grangier, P.

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics7(5), 378–381 (2013).
[CrossRef]

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Hadfield, R. H.

D. Rosenberg, C. G. Peterson, J. W. Harrington, P. R. Rice, N. Dallmann, K. T. Tyagi, K. P. McCabe, S. Nam, B. Baek, R. H. Hadfield, R. J. Hughes, and J. E. Nordholt, “Practical long-distance quantum key distribution system using decoy levels,” New J. Phys.11(4), 045009 (2009).
[CrossRef]

Happe, A.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Harrington, J. W.

D. Rosenberg, C. G. Peterson, J. W. Harrington, P. R. Rice, N. Dallmann, K. T. Tyagi, K. P. McCabe, S. Nam, B. Baek, R. H. Hadfield, R. J. Hughes, and J. E. Nordholt, “Practical long-distance quantum key distribution system using decoy levels,” New J. Phys.11(4), 045009 (2009).
[CrossRef]

Hasani, Y.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Hasegawa, T.

Hayashi, M.

M. Hayashi, “Upper bounds of eavesdropper’s performances in finite-length code with the decoy method,” Phys. Rev. A76(1), 012329 (2007).
[CrossRef]

M. Hayashi, “Practical evaluation of security for quantum key distribution,” Phys. Rev. A74(2), 022307 (2006).
[CrossRef]

Hentschel, M.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Honjo, T.

Hübel, H.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Hughes, R. J.

D. Rosenberg, C. G. Peterson, J. W. Harrington, P. R. Rice, N. Dallmann, K. T. Tyagi, K. P. McCabe, S. Nam, B. Baek, R. H. Hadfield, R. J. Hughes, and J. E. Nordholt, “Practical long-distance quantum key distribution system using decoy levels,” New J. Phys.11(4), 045009 (2009).
[CrossRef]

Humer, G.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Hwang, W.-Y.

W.-Y. Hwang, “Quantum key distribution with high loss: toward global secure communication,” Phys. Rev. Lett.91(5), 057901 (2003).
[CrossRef] [PubMed]

Inamori, H.

H. Inamori, N. Lütkenhaus, and D. Mayers, “Unconditional security of practical quantum key distribution,” Eur. Phys. J. D41(3), 599–627 (2007).
[CrossRef]

Ishizuka, H.

Jouguet, P.

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics7(5), 378–381 (2013).
[CrossRef]

Kardynal, B. E.

Z. L. Yuan, B. E. Kardynal, A. W. Sharpe, and A. J. Shields, “High speed single photon detection in the near infrared,” Appl. Phys. Lett.91(4), 041114 (2007).
[CrossRef]

Klaus, W.

Koashi, M.

M. Koashi and J. Preskill, “Secure quantum key distribution with an uncharacterized source,” Phys. Rev. Lett.90(5), 057902 (2003).
[CrossRef] [PubMed]

Kobayashi, H.

Kraus, B.

R. Renner, N. Gisin, and B. Kraus, “Information-theoretic security proof for quantum-key-distribution protocols,” Phys. Rev. A72(1), 012332 (2005).
[CrossRef]

B. Kraus, N. Gisin, and R. Renner, “Lower and upper bounds on the secret-key rate for quantum key distribution protocols using one-way classical communication,” Phys. Rev. Lett.95(8), 080501 (2005).
[CrossRef] [PubMed]

Kunz-Jacques, S.

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics7(5), 378–381 (2013).
[CrossRef]

La?amme, R.

C. Erven, X. Ma, R. Laflamme, and G. Weihs, “Entangled quantum key distribution with a biased basis choice,” New J. Phys.11(4), 045025 (2009).
[CrossRef]

Länger, T.

M. Sasaki, M. Fujiwara, H. Ishizuka, W. Klaus, K. Wakui, M. Takeoka, S. Miki, T. Yamashita, Z. Wang, A. Tanaka, K. Yoshino, Y. Nambu, S. Takahashi, A. Tajima, A. Tomita, T. Domeki, T. Hasegawa, Y. Sakai, H. Kobayashi, T. Asai, K. Shimizu, T. Tokura, T. Tsurumaru, M. Matsui, T. Honjo, K. Tamaki, H. Takesue, Y. Tokura, J. F. Dynes, A. R. Dixon, A. W. Sharpe, Z. L. Yuan, A. J. Shields, S. Uchikoga, M. Legré, S. Robyr, P. Trinkler, L. Monat, J. B. Page, G. Ribordy, A. Poppe, A. Allacher, O. Maurhart, T. Länger, M. Peev, and A. Zeilinger, “Field test of quantum key distribution in the Tokyo QKD Network,” Opt. Express19(11), 10387–10409 (2011).
[CrossRef] [PubMed]

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Legré, M.

M. Sasaki, M. Fujiwara, H. Ishizuka, W. Klaus, K. Wakui, M. Takeoka, S. Miki, T. Yamashita, Z. Wang, A. Tanaka, K. Yoshino, Y. Nambu, S. Takahashi, A. Tajima, A. Tomita, T. Domeki, T. Hasegawa, Y. Sakai, H. Kobayashi, T. Asai, K. Shimizu, T. Tokura, T. Tsurumaru, M. Matsui, T. Honjo, K. Tamaki, H. Takesue, Y. Tokura, J. F. Dynes, A. R. Dixon, A. W. Sharpe, Z. L. Yuan, A. J. Shields, S. Uchikoga, M. Legré, S. Robyr, P. Trinkler, L. Monat, J. B. Page, G. Ribordy, A. Poppe, A. Allacher, O. Maurhart, T. Länger, M. Peev, and A. Zeilinger, “Field test of quantum key distribution in the Tokyo QKD Network,” Opt. Express19(11), 10387–10409 (2011).
[CrossRef] [PubMed]

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Leverrier, A.

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics7(5), 378–381 (2013).
[CrossRef]

Lieger, R.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Lim, C. C. W.

M. Tomamichel, C. C. W. Lim, N. Gisin, and R. Renner, “Tight finite-key analysis for quantum cryptography,” Nat Commun3, 634 (2012).
[CrossRef] [PubMed]

Lo, H. K.

H. K. Lo and J. Preskill, “Security of quantum key distribution using weak coherent states with nonrandom phases,” Quantum Inf. Comput.7, 431 (2007).

Lo, H.-K.

X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A72(1), 012326 (2005).
[CrossRef]

H.-K. Lo, H. F. Chau, and M. Ardehali, “Efficient quantum key distribution scheme and proof of its unconditional security,” J. of Crypt.18(2), 133–165 (2005).
[CrossRef]

H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett.94(23), 230504 (2005).
[CrossRef] [PubMed]

Lodewyck, J.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Lorünser, T.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Lucamarini, M.

B. Fröhlich, J. F. Dynes, M. Lucamarini, A. W. Sharpe, Z. Yuan, and A. J. Shields, “A quantum access network,” Nature501(7465), 69–72 (2013).
[CrossRef] [PubMed]

M. Lucamarini, J. F. Dynes, Z. L. Yuan, and A. J. Shields, “Practical treatment of quantum bugs,” Proc. SPIE8542, Electro-Optical Remote Sensing, Photonic Technologies, and Applications VI (2012).

Lütkenhaus, N.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys.81(3), 1301–1350 (2009).
[CrossRef]

N. J. Beaudry, T. Moroder, and N. Lütkenhaus, “Squashing models for optical measurements in quantum communication,” Phys. Rev. Lett.101(9), 093601 (2008).
[CrossRef] [PubMed]

H. Inamori, N. Lütkenhaus, and D. Mayers, “Unconditional security of practical quantum key distribution,” Eur. Phys. J. D41(3), 599–627 (2007).
[CrossRef]

Ma, X.

Z. Wei, W. Wang, Z. Zhang, M. Gao, Z. Ma, and X. Ma, “Decoy-state quantum key distribution with biased basis choice,” Sci Rep3, 2453 (2013).
[CrossRef] [PubMed]

C. Erven, X. Ma, R. Laflamme, and G. Weihs, “Entangled quantum key distribution with a biased basis choice,” New J. Phys.11(4), 045025 (2009).
[CrossRef]

H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett.94(23), 230504 (2005).
[CrossRef] [PubMed]

X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A72(1), 012326 (2005).
[CrossRef]

Ma, Z.

Z. Wei, W. Wang, Z. Zhang, M. Gao, Z. Ma, and X. Ma, “Decoy-state quantum key distribution with biased basis choice,” Sci Rep3, 2453 (2013).
[CrossRef] [PubMed]

Marhold, A.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Matsui, M.

Matsumoto, R.

S. Watanabe, R. Matsumoto, and T. Uyematsu, “Noise tolerance of the BB84 protocol with random privacy amplification,” Int. J. Quantum Inf.4(6), 935–946 (2006).
[CrossRef]

Matyus, T.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Maurhart, O.

M. Sasaki, M. Fujiwara, H. Ishizuka, W. Klaus, K. Wakui, M. Takeoka, S. Miki, T. Yamashita, Z. Wang, A. Tanaka, K. Yoshino, Y. Nambu, S. Takahashi, A. Tajima, A. Tomita, T. Domeki, T. Hasegawa, Y. Sakai, H. Kobayashi, T. Asai, K. Shimizu, T. Tokura, T. Tsurumaru, M. Matsui, T. Honjo, K. Tamaki, H. Takesue, Y. Tokura, J. F. Dynes, A. R. Dixon, A. W. Sharpe, Z. L. Yuan, A. J. Shields, S. Uchikoga, M. Legré, S. Robyr, P. Trinkler, L. Monat, J. B. Page, G. Ribordy, A. Poppe, A. Allacher, O. Maurhart, T. Länger, M. Peev, and A. Zeilinger, “Field test of quantum key distribution in the Tokyo QKD Network,” Opt. Express19(11), 10387–10409 (2011).
[CrossRef] [PubMed]

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Mayers, D.

H. Inamori, N. Lütkenhaus, and D. Mayers, “Unconditional security of practical quantum key distribution,” Eur. Phys. J. D41(3), 599–627 (2007).
[CrossRef]

McCabe, K. P.

D. Rosenberg, C. G. Peterson, J. W. Harrington, P. R. Rice, N. Dallmann, K. T. Tyagi, K. P. McCabe, S. Nam, B. Baek, R. H. Hadfield, R. J. Hughes, and J. E. Nordholt, “Practical long-distance quantum key distribution system using decoy levels,” New J. Phys.11(4), 045009 (2009).
[CrossRef]

Miki, S.

Monat, L.

M. Sasaki, M. Fujiwara, H. Ishizuka, W. Klaus, K. Wakui, M. Takeoka, S. Miki, T. Yamashita, Z. Wang, A. Tanaka, K. Yoshino, Y. Nambu, S. Takahashi, A. Tajima, A. Tomita, T. Domeki, T. Hasegawa, Y. Sakai, H. Kobayashi, T. Asai, K. Shimizu, T. Tokura, T. Tsurumaru, M. Matsui, T. Honjo, K. Tamaki, H. Takesue, Y. Tokura, J. F. Dynes, A. R. Dixon, A. W. Sharpe, Z. L. Yuan, A. J. Shields, S. Uchikoga, M. Legré, S. Robyr, P. Trinkler, L. Monat, J. B. Page, G. Ribordy, A. Poppe, A. Allacher, O. Maurhart, T. Länger, M. Peev, and A. Zeilinger, “Field test of quantum key distribution in the Tokyo QKD Network,” Opt. Express19(11), 10387–10409 (2011).
[CrossRef] [PubMed]

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Moroder, T.

N. J. Beaudry, T. Moroder, and N. Lütkenhaus, “Squashing models for optical measurements in quantum communication,” Phys. Rev. Lett.101(9), 093601 (2008).
[CrossRef] [PubMed]

Nam, S.

D. Rosenberg, C. G. Peterson, J. W. Harrington, P. R. Rice, N. Dallmann, K. T. Tyagi, K. P. McCabe, S. Nam, B. Baek, R. H. Hadfield, R. J. Hughes, and J. E. Nordholt, “Practical long-distance quantum key distribution system using decoy levels,” New J. Phys.11(4), 045009 (2009).
[CrossRef]

Nambu, Y.

Nauerth, S.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Nordholt, J. E.

D. Rosenberg, C. G. Peterson, J. W. Harrington, P. R. Rice, N. Dallmann, K. T. Tyagi, K. P. McCabe, S. Nam, B. Baek, R. H. Hadfield, R. J. Hughes, and J. E. Nordholt, “Practical long-distance quantum key distribution system using decoy levels,” New J. Phys.11(4), 045009 (2009).
[CrossRef]

Pacher, C.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Page, J. B.

Page, J.-B.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Patel, K.

K. Patel, J. F. Dynes, I. Choi, A. W. Sharpe, A. R. Dixon, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Coexistence of high-bit-rate quantum key distribution and data on optical fiber,” Phys. Rev. X2(4), 041010 (2012).
[CrossRef]

Pearson, E. S.

C. Clopper and E. S. Pearson, “The use of confidence or fiducial limits illustrated in the case of the binomial,” Biometrika26(4), 404–413 (1934).
[CrossRef]

Peev, M.

M. Sasaki, M. Fujiwara, H. Ishizuka, W. Klaus, K. Wakui, M. Takeoka, S. Miki, T. Yamashita, Z. Wang, A. Tanaka, K. Yoshino, Y. Nambu, S. Takahashi, A. Tajima, A. Tomita, T. Domeki, T. Hasegawa, Y. Sakai, H. Kobayashi, T. Asai, K. Shimizu, T. Tokura, T. Tsurumaru, M. Matsui, T. Honjo, K. Tamaki, H. Takesue, Y. Tokura, J. F. Dynes, A. R. Dixon, A. W. Sharpe, Z. L. Yuan, A. J. Shields, S. Uchikoga, M. Legré, S. Robyr, P. Trinkler, L. Monat, J. B. Page, G. Ribordy, A. Poppe, A. Allacher, O. Maurhart, T. Länger, M. Peev, and A. Zeilinger, “Field test of quantum key distribution in the Tokyo QKD Network,” Opt. Express19(11), 10387–10409 (2011).
[CrossRef] [PubMed]

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys.81(3), 1301–1350 (2009).
[CrossRef]

Penty, R. V.

K. Patel, J. F. Dynes, I. Choi, A. W. Sharpe, A. R. Dixon, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Coexistence of high-bit-rate quantum key distribution and data on optical fiber,” Phys. Rev. X2(4), 041010 (2012).
[CrossRef]

Peterson, C. G.

D. Rosenberg, C. G. Peterson, J. W. Harrington, P. R. Rice, N. Dallmann, K. T. Tyagi, K. P. McCabe, S. Nam, B. Baek, R. H. Hadfield, R. J. Hughes, and J. E. Nordholt, “Practical long-distance quantum key distribution system using decoy levels,” New J. Phys.11(4), 045009 (2009).
[CrossRef]

Poppe, A.

M. Sasaki, M. Fujiwara, H. Ishizuka, W. Klaus, K. Wakui, M. Takeoka, S. Miki, T. Yamashita, Z. Wang, A. Tanaka, K. Yoshino, Y. Nambu, S. Takahashi, A. Tajima, A. Tomita, T. Domeki, T. Hasegawa, Y. Sakai, H. Kobayashi, T. Asai, K. Shimizu, T. Tokura, T. Tsurumaru, M. Matsui, T. Honjo, K. Tamaki, H. Takesue, Y. Tokura, J. F. Dynes, A. R. Dixon, A. W. Sharpe, Z. L. Yuan, A. J. Shields, S. Uchikoga, M. Legré, S. Robyr, P. Trinkler, L. Monat, J. B. Page, G. Ribordy, A. Poppe, A. Allacher, O. Maurhart, T. Länger, M. Peev, and A. Zeilinger, “Field test of quantum key distribution in the Tokyo QKD Network,” Opt. Express19(11), 10387–10409 (2011).
[CrossRef] [PubMed]

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Preskill, J.

H. K. Lo and J. Preskill, “Security of quantum key distribution using weak coherent states with nonrandom phases,” Quantum Inf. Comput.7, 431 (2007).

M. Koashi and J. Preskill, “Secure quantum key distribution with an uncharacterized source,” Phys. Rev. Lett.90(5), 057902 (2003).
[CrossRef] [PubMed]

Qi, B.

X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A72(1), 012326 (2005).
[CrossRef]

Querasser, E.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Rarity, J. G.

P. D. Townsend, J. G. Rarity, and P. R. Tapster, “Enhanced single-photon fringe visibility in a 10 km-long prototype quantum cryptography,” Electron. Lett.29(14), 1291 (1993).
[CrossRef]

Renner, R.

M. Tomamichel, C. C. W. Lim, N. Gisin, and R. Renner, “Tight finite-key analysis for quantum cryptography,” Nat Commun3, 634 (2012).
[CrossRef] [PubMed]

V. Scarani and R. Renner, “Quantum cryptography with finite resources: unconditional security bound for discrete-variable protocols with one-way postprocessing,” Phys. Rev. Lett.100(20), 200501 (2008).
[CrossRef] [PubMed]

R. Renner, “Symmetry of large physical systems implies independence of subsystems,” Nat. Phys.3(9), 645–649 (2007).
[CrossRef]

R. Renner, N. Gisin, and B. Kraus, “Information-theoretic security proof for quantum-key-distribution protocols,” Phys. Rev. A72(1), 012332 (2005).
[CrossRef]

B. Kraus, N. Gisin, and R. Renner, “Lower and upper bounds on the secret-key rate for quantum key distribution protocols using one-way classical communication,” Phys. Rev. Lett.95(8), 080501 (2005).
[CrossRef] [PubMed]

Ribordy, G.

M. Sasaki, M. Fujiwara, H. Ishizuka, W. Klaus, K. Wakui, M. Takeoka, S. Miki, T. Yamashita, Z. Wang, A. Tanaka, K. Yoshino, Y. Nambu, S. Takahashi, A. Tajima, A. Tomita, T. Domeki, T. Hasegawa, Y. Sakai, H. Kobayashi, T. Asai, K. Shimizu, T. Tokura, T. Tsurumaru, M. Matsui, T. Honjo, K. Tamaki, H. Takesue, Y. Tokura, J. F. Dynes, A. R. Dixon, A. W. Sharpe, Z. L. Yuan, A. J. Shields, S. Uchikoga, M. Legré, S. Robyr, P. Trinkler, L. Monat, J. B. Page, G. Ribordy, A. Poppe, A. Allacher, O. Maurhart, T. Länger, M. Peev, and A. Zeilinger, “Field test of quantum key distribution in the Tokyo QKD Network,” Opt. Express19(11), 10387–10409 (2011).
[CrossRef] [PubMed]

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys.74(1), 145–195 (2002).
[CrossRef]

Rice, P. R.

D. Rosenberg, C. G. Peterson, J. W. Harrington, P. R. Rice, N. Dallmann, K. T. Tyagi, K. P. McCabe, S. Nam, B. Baek, R. H. Hadfield, R. J. Hughes, and J. E. Nordholt, “Practical long-distance quantum key distribution system using decoy levels,” New J. Phys.11(4), 045009 (2009).
[CrossRef]

Robyr, S.

M. Sasaki, M. Fujiwara, H. Ishizuka, W. Klaus, K. Wakui, M. Takeoka, S. Miki, T. Yamashita, Z. Wang, A. Tanaka, K. Yoshino, Y. Nambu, S. Takahashi, A. Tajima, A. Tomita, T. Domeki, T. Hasegawa, Y. Sakai, H. Kobayashi, T. Asai, K. Shimizu, T. Tokura, T. Tsurumaru, M. Matsui, T. Honjo, K. Tamaki, H. Takesue, Y. Tokura, J. F. Dynes, A. R. Dixon, A. W. Sharpe, Z. L. Yuan, A. J. Shields, S. Uchikoga, M. Legré, S. Robyr, P. Trinkler, L. Monat, J. B. Page, G. Ribordy, A. Poppe, A. Allacher, O. Maurhart, T. Länger, M. Peev, and A. Zeilinger, “Field test of quantum key distribution in the Tokyo QKD Network,” Opt. Express19(11), 10387–10409 (2011).
[CrossRef] [PubMed]

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Rosenberg, D.

D. Rosenberg, C. G. Peterson, J. W. Harrington, P. R. Rice, N. Dallmann, K. T. Tyagi, K. P. McCabe, S. Nam, B. Baek, R. H. Hadfield, R. J. Hughes, and J. E. Nordholt, “Practical long-distance quantum key distribution system using decoy levels,” New J. Phys.11(4), 045009 (2009).
[CrossRef]

Sakai, Y.

Salvail, L.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Sasaki, M.

Scarani, V.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys.81(3), 1301–1350 (2009).
[CrossRef]

R. Y. Q. Cai and V. Scarani, “Finite-key analysis for practical implementations of quantum key distribution,” New J. Phys.11(4), 045024 (2009).
[CrossRef]

V. Scarani and R. Renner, “Quantum cryptography with finite resources: unconditional security bound for discrete-variable protocols with one-way postprocessing,” Phys. Rev. Lett.100(20), 200501 (2008).
[CrossRef] [PubMed]

Sharpe, A. W.

B. Fröhlich, J. F. Dynes, M. Lucamarini, A. W. Sharpe, Z. Yuan, and A. J. Shields, “A quantum access network,” Nature501(7465), 69–72 (2013).
[CrossRef] [PubMed]

K. Patel, J. F. Dynes, I. Choi, A. W. Sharpe, A. R. Dixon, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Coexistence of high-bit-rate quantum key distribution and data on optical fiber,” Phys. Rev. X2(4), 041010 (2012).
[CrossRef]

M. Sasaki, M. Fujiwara, H. Ishizuka, W. Klaus, K. Wakui, M. Takeoka, S. Miki, T. Yamashita, Z. Wang, A. Tanaka, K. Yoshino, Y. Nambu, S. Takahashi, A. Tajima, A. Tomita, T. Domeki, T. Hasegawa, Y. Sakai, H. Kobayashi, T. Asai, K. Shimizu, T. Tokura, T. Tsurumaru, M. Matsui, T. Honjo, K. Tamaki, H. Takesue, Y. Tokura, J. F. Dynes, A. R. Dixon, A. W. Sharpe, Z. L. Yuan, A. J. Shields, S. Uchikoga, M. Legré, S. Robyr, P. Trinkler, L. Monat, J. B. Page, G. Ribordy, A. Poppe, A. Allacher, O. Maurhart, T. Länger, M. Peev, and A. Zeilinger, “Field test of quantum key distribution in the Tokyo QKD Network,” Opt. Express19(11), 10387–10409 (2011).
[CrossRef] [PubMed]

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Z. L. Yuan, B. E. Kardynal, A. W. Sharpe, and A. J. Shields, “High speed single photon detection in the near infrared,” Appl. Phys. Lett.91(4), 041114 (2007).
[CrossRef]

Shields, A. J.

B. Fröhlich, J. F. Dynes, M. Lucamarini, A. W. Sharpe, Z. Yuan, and A. J. Shields, “A quantum access network,” Nature501(7465), 69–72 (2013).
[CrossRef] [PubMed]

K. Patel, J. F. Dynes, I. Choi, A. W. Sharpe, A. R. Dixon, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Coexistence of high-bit-rate quantum key distribution and data on optical fiber,” Phys. Rev. X2(4), 041010 (2012).
[CrossRef]

M. Sasaki, M. Fujiwara, H. Ishizuka, W. Klaus, K. Wakui, M. Takeoka, S. Miki, T. Yamashita, Z. Wang, A. Tanaka, K. Yoshino, Y. Nambu, S. Takahashi, A. Tajima, A. Tomita, T. Domeki, T. Hasegawa, Y. Sakai, H. Kobayashi, T. Asai, K. Shimizu, T. Tokura, T. Tsurumaru, M. Matsui, T. Honjo, K. Tamaki, H. Takesue, Y. Tokura, J. F. Dynes, A. R. Dixon, A. W. Sharpe, Z. L. Yuan, A. J. Shields, S. Uchikoga, M. Legré, S. Robyr, P. Trinkler, L. Monat, J. B. Page, G. Ribordy, A. Poppe, A. Allacher, O. Maurhart, T. Länger, M. Peev, and A. Zeilinger, “Field test of quantum key distribution in the Tokyo QKD Network,” Opt. Express19(11), 10387–10409 (2011).
[CrossRef] [PubMed]

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Z. L. Yuan, B. E. Kardynal, A. W. Sharpe, and A. J. Shields, “High speed single photon detection in the near infrared,” Appl. Phys. Lett.91(4), 041114 (2007).
[CrossRef]

M. Lucamarini, J. F. Dynes, Z. L. Yuan, and A. J. Shields, “Practical treatment of quantum bugs,” Proc. SPIE8542, Electro-Optical Remote Sensing, Photonic Technologies, and Applications VI (2012).

Shimizu, K.

Stucki, D.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Suda, M.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Tajima, A.

Takahashi, S.

Takeoka, M.

Takesue, H.

Tamaki, K.

Tamas, C.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Tanaka, A.

Tapster, P. R.

P. D. Townsend, J. G. Rarity, and P. R. Tapster, “Enhanced single-photon fringe visibility in a 10 km-long prototype quantum cryptography,” Electron. Lett.29(14), 1291 (1993).
[CrossRef]

Themel, T.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Thew, R. T.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Thoma, Y.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Tittel, W.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys.74(1), 145–195 (2002).
[CrossRef]

Tokura, T.

Tokura, Y.

Tomamichel, M.

M. Tomamichel, C. C. W. Lim, N. Gisin, and R. Renner, “Tight finite-key analysis for quantum cryptography,” Nat Commun3, 634 (2012).
[CrossRef] [PubMed]

Tomita, A.

Townsend, P. D.

P. D. Townsend, J. G. Rarity, and P. R. Tapster, “Enhanced single-photon fringe visibility in a 10 km-long prototype quantum cryptography,” Electron. Lett.29(14), 1291 (1993).
[CrossRef]

Treiber, A.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Trinkler, P.

M. Sasaki, M. Fujiwara, H. Ishizuka, W. Klaus, K. Wakui, M. Takeoka, S. Miki, T. Yamashita, Z. Wang, A. Tanaka, K. Yoshino, Y. Nambu, S. Takahashi, A. Tajima, A. Tomita, T. Domeki, T. Hasegawa, Y. Sakai, H. Kobayashi, T. Asai, K. Shimizu, T. Tokura, T. Tsurumaru, M. Matsui, T. Honjo, K. Tamaki, H. Takesue, Y. Tokura, J. F. Dynes, A. R. Dixon, A. W. Sharpe, Z. L. Yuan, A. J. Shields, S. Uchikoga, M. Legré, S. Robyr, P. Trinkler, L. Monat, J. B. Page, G. Ribordy, A. Poppe, A. Allacher, O. Maurhart, T. Länger, M. Peev, and A. Zeilinger, “Field test of quantum key distribution in the Tokyo QKD Network,” Opt. Express19(11), 10387–10409 (2011).
[CrossRef] [PubMed]

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Tsurumaru, T.

Tualle-Brouri, R.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Tyagi, K. T.

D. Rosenberg, C. G. Peterson, J. W. Harrington, P. R. Rice, N. Dallmann, K. T. Tyagi, K. P. McCabe, S. Nam, B. Baek, R. H. Hadfield, R. J. Hughes, and J. E. Nordholt, “Practical long-distance quantum key distribution system using decoy levels,” New J. Phys.11(4), 045009 (2009).
[CrossRef]

Uchikoga, S.

Uyematsu, T.

S. Watanabe, R. Matsumoto, and T. Uyematsu, “Noise tolerance of the BB84 protocol with random privacy amplification,” Int. J. Quantum Inf.4(6), 935–946 (2006).
[CrossRef]

Vannel, F.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Wakui, K.

Walenta, N.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Wang, W.

Z. Wei, W. Wang, Z. Zhang, M. Gao, Z. Ma, and X. Ma, “Decoy-state quantum key distribution with biased basis choice,” Sci Rep3, 2453 (2013).
[CrossRef] [PubMed]

Wang, X.-B.

X.-B. Wang, “Beating the photon-number-splitting attack in practical quantum cryptography,” Phys. Rev. Lett.94(23), 230503 (2005).
[CrossRef] [PubMed]

Wang, Z.

Watanabe, S.

S. Watanabe, R. Matsumoto, and T. Uyematsu, “Noise tolerance of the BB84 protocol with random privacy amplification,” Int. J. Quantum Inf.4(6), 935–946 (2006).
[CrossRef]

Wei, Z.

Z. Wei, W. Wang, Z. Zhang, M. Gao, Z. Ma, and X. Ma, “Decoy-state quantum key distribution with biased basis choice,” Sci Rep3, 2453 (2013).
[CrossRef] [PubMed]

Weier, H.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Weihs, G.

C. Erven, X. Ma, R. Laflamme, and G. Weihs, “Entangled quantum key distribution with a biased basis choice,” New J. Phys.11(4), 045025 (2009).
[CrossRef]

Weinfurter, H.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Wiesner, S.

S. Wiesner, “Conjugate coding,” Sigact News15(1), 78–88 (1983).
[CrossRef]

Wimberger, I.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Yamashita, T.

Yoshino, K.

Yuan, Z.

B. Fröhlich, J. F. Dynes, M. Lucamarini, A. W. Sharpe, Z. Yuan, and A. J. Shields, “A quantum access network,” Nature501(7465), 69–72 (2013).
[CrossRef] [PubMed]

Yuan, Z. L.

K. Patel, J. F. Dynes, I. Choi, A. W. Sharpe, A. R. Dixon, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Coexistence of high-bit-rate quantum key distribution and data on optical fiber,” Phys. Rev. X2(4), 041010 (2012).
[CrossRef]

M. Sasaki, M. Fujiwara, H. Ishizuka, W. Klaus, K. Wakui, M. Takeoka, S. Miki, T. Yamashita, Z. Wang, A. Tanaka, K. Yoshino, Y. Nambu, S. Takahashi, A. Tajima, A. Tomita, T. Domeki, T. Hasegawa, Y. Sakai, H. Kobayashi, T. Asai, K. Shimizu, T. Tokura, T. Tsurumaru, M. Matsui, T. Honjo, K. Tamaki, H. Takesue, Y. Tokura, J. F. Dynes, A. R. Dixon, A. W. Sharpe, Z. L. Yuan, A. J. Shields, S. Uchikoga, M. Legré, S. Robyr, P. Trinkler, L. Monat, J. B. Page, G. Ribordy, A. Poppe, A. Allacher, O. Maurhart, T. Länger, M. Peev, and A. Zeilinger, “Field test of quantum key distribution in the Tokyo QKD Network,” Opt. Express19(11), 10387–10409 (2011).
[CrossRef] [PubMed]

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Z. L. Yuan, B. E. Kardynal, A. W. Sharpe, and A. J. Shields, “High speed single photon detection in the near infrared,” Appl. Phys. Lett.91(4), 041114 (2007).
[CrossRef]

M. Lucamarini, J. F. Dynes, Z. L. Yuan, and A. J. Shields, “Practical treatment of quantum bugs,” Proc. SPIE8542, Electro-Optical Remote Sensing, Photonic Technologies, and Applications VI (2012).

Zbinden, H.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys.74(1), 145–195 (2002).
[CrossRef]

Zeilinger, A.

M. Sasaki, M. Fujiwara, H. Ishizuka, W. Klaus, K. Wakui, M. Takeoka, S. Miki, T. Yamashita, Z. Wang, A. Tanaka, K. Yoshino, Y. Nambu, S. Takahashi, A. Tajima, A. Tomita, T. Domeki, T. Hasegawa, Y. Sakai, H. Kobayashi, T. Asai, K. Shimizu, T. Tokura, T. Tsurumaru, M. Matsui, T. Honjo, K. Tamaki, H. Takesue, Y. Tokura, J. F. Dynes, A. R. Dixon, A. W. Sharpe, Z. L. Yuan, A. J. Shields, S. Uchikoga, M. Legré, S. Robyr, P. Trinkler, L. Monat, J. B. Page, G. Ribordy, A. Poppe, A. Allacher, O. Maurhart, T. Länger, M. Peev, and A. Zeilinger, “Field test of quantum key distribution in the Tokyo QKD Network,” Opt. Express19(11), 10387–10409 (2011).
[CrossRef] [PubMed]

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

Zhang, Z.

Z. Wei, W. Wang, Z. Zhang, M. Gao, Z. Ma, and X. Ma, “Decoy-state quantum key distribution with biased basis choice,” Sci Rep3, 2453 (2013).
[CrossRef] [PubMed]

Zhao, Y.

X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A72(1), 012326 (2005).
[CrossRef]

Am. Stat.

A. Agresti and B. A. Coull, “Approximate is better than ‘exact’ for interval estimation of binomial proportions,” Am. Stat.52, 119 (1998).

Appl. Phys. Lett.

Z. L. Yuan, B. E. Kardynal, A. W. Sharpe, and A. J. Shields, “High speed single photon detection in the near infrared,” Appl. Phys. Lett.91(4), 041114 (2007).
[CrossRef]

Biometrika

C. Clopper and E. S. Pearson, “The use of confidence or fiducial limits illustrated in the case of the binomial,” Biometrika26(4), 404–413 (1934).
[CrossRef]

Electron. Lett.

P. D. Townsend, J. G. Rarity, and P. R. Tapster, “Enhanced single-photon fringe visibility in a 10 km-long prototype quantum cryptography,” Electron. Lett.29(14), 1291 (1993).
[CrossRef]

Eur. Phys. J. D

H. Inamori, N. Lütkenhaus, and D. Mayers, “Unconditional security of practical quantum key distribution,” Eur. Phys. J. D41(3), 599–627 (2007).
[CrossRef]

Int. J. Quantum Inf.

S. Watanabe, R. Matsumoto, and T. Uyematsu, “Noise tolerance of the BB84 protocol with random privacy amplification,” Int. J. Quantum Inf.4(6), 935–946 (2006).
[CrossRef]

J. of Crypt.

H.-K. Lo, H. F. Chau, and M. Ardehali, “Efficient quantum key distribution scheme and proof of its unconditional security,” J. of Crypt.18(2), 133–165 (2005).
[CrossRef]

Nat Commun

M. Tomamichel, C. C. W. Lim, N. Gisin, and R. Renner, “Tight finite-key analysis for quantum cryptography,” Nat Commun3, 634 (2012).
[CrossRef] [PubMed]

Nat. Photonics

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics7(5), 378–381 (2013).
[CrossRef]

Nat. Phys.

R. Renner, “Symmetry of large physical systems implies independence of subsystems,” Nat. Phys.3(9), 645–649 (2007).
[CrossRef]

Nature

B. Fröhlich, J. F. Dynes, M. Lucamarini, A. W. Sharpe, Z. Yuan, and A. J. Shields, “A quantum access network,” Nature501(7465), 69–72 (2013).
[CrossRef] [PubMed]

New J. Phys.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11(7), 075001 (2009).
[CrossRef]

R. Y. Q. Cai and V. Scarani, “Finite-key analysis for practical implementations of quantum key distribution,” New J. Phys.11(4), 045024 (2009).
[CrossRef]

C. Erven, X. Ma, R. Laflamme, and G. Weihs, “Entangled quantum key distribution with a biased basis choice,” New J. Phys.11(4), 045025 (2009).
[CrossRef]

D. Rosenberg, C. G. Peterson, J. W. Harrington, P. R. Rice, N. Dallmann, K. T. Tyagi, K. P. McCabe, S. Nam, B. Baek, R. H. Hadfield, R. J. Hughes, and J. E. Nordholt, “Practical long-distance quantum key distribution system using decoy levels,” New J. Phys.11(4), 045009 (2009).
[CrossRef]

Opt. Express

Phys. Rev. A

R. Renner, N. Gisin, and B. Kraus, “Information-theoretic security proof for quantum-key-distribution protocols,” Phys. Rev. A72(1), 012332 (2005).
[CrossRef]

M. Hayashi, “Practical evaluation of security for quantum key distribution,” Phys. Rev. A74(2), 022307 (2006).
[CrossRef]

M. Hayashi, “Upper bounds of eavesdropper’s performances in finite-length code with the decoy method,” Phys. Rev. A76(1), 012329 (2007).
[CrossRef]

X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A72(1), 012326 (2005).
[CrossRef]

T. Tsurumaru and K. Tamaki, “Security proof for QKD systems with threshold detectors,” Phys. Rev. A78, 032302 (2008).
[CrossRef]

Phys. Rev. Lett.

M. Koashi and J. Preskill, “Secure quantum key distribution with an uncharacterized source,” Phys. Rev. Lett.90(5), 057902 (2003).
[CrossRef] [PubMed]

W.-Y. Hwang, “Quantum key distribution with high loss: toward global secure communication,” Phys. Rev. Lett.91(5), 057901 (2003).
[CrossRef] [PubMed]

X.-B. Wang, “Beating the photon-number-splitting attack in practical quantum cryptography,” Phys. Rev. Lett.94(23), 230503 (2005).
[CrossRef] [PubMed]

H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett.94(23), 230504 (2005).
[CrossRef] [PubMed]

V. Scarani and R. Renner, “Quantum cryptography with finite resources: unconditional security bound for discrete-variable protocols with one-way postprocessing,” Phys. Rev. Lett.100(20), 200501 (2008).
[CrossRef] [PubMed]

B. Kraus, N. Gisin, and R. Renner, “Lower and upper bounds on the secret-key rate for quantum key distribution protocols using one-way classical communication,” Phys. Rev. Lett.95(8), 080501 (2005).
[CrossRef] [PubMed]

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett.67(6), 661–663 (1991).
[CrossRef] [PubMed]

N. J. Beaudry, T. Moroder, and N. Lütkenhaus, “Squashing models for optical measurements in quantum communication,” Phys. Rev. Lett.101(9), 093601 (2008).
[CrossRef] [PubMed]

Phys. Rev. X

K. Patel, J. F. Dynes, I. Choi, A. W. Sharpe, A. R. Dixon, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Coexistence of high-bit-rate quantum key distribution and data on optical fiber,” Phys. Rev. X2(4), 041010 (2012).
[CrossRef]

Quantum Inf. Comput.

H. K. Lo and J. Preskill, “Security of quantum key distribution using weak coherent states with nonrandom phases,” Quantum Inf. Comput.7, 431 (2007).

Rev. Mod. Phys.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys.74(1), 145–195 (2002).
[CrossRef]

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys.81(3), 1301–1350 (2009).
[CrossRef]

Sci Rep

Z. Wei, W. Wang, Z. Zhang, M. Gao, Z. Ma, and X. Ma, “Decoy-state quantum key distribution with biased basis choice,” Sci Rep3, 2453 (2013).
[CrossRef] [PubMed]

Sigact News

S. Wiesner, “Conjugate coding,” Sigact News15(1), 78–88 (1983).
[CrossRef]

Other

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 (Institute of Electrical and Electronics Engineers, New York, 1984), pp. 175–179.

D. Mayers, D. Coppersmith, ed., in Advances in Cryptology:Proceedings of CRYPTO '95, vol. 963 of Lecture Notes in Computer Science, D. Coppersmith, Ed. (Springer-Verlag, 1995), pp. 124–135; in Advances in Cryptology: Proceedings of CRYPTO '96, vol. 1109 of Lecture Notes in Computer Science, N. Koblitz, Ed. (Springer-Verlag, 1996), pp. 343–357.

V. Scarani and R. Renner, “Security bounds for quantum cryptography with finite resources,” in Theory of Quantum Computation, Communication, and Cryptography, vol. 5106 of Lecture Notes in Computer Science, (Berlin Springer, 2008), pp 83–95.

M. Lucamarini, J. F. Dynes, Z. L. Yuan, and A. J. Shields, “Practical treatment of quantum bugs,” Proc. SPIE8542, Electro-Optical Remote Sensing, Photonic Technologies, and Applications VI (2012).

M. Hayashi and R. Nakayama, “Security analysis of the decoy method with the Bennett-Brassard 1984 protocol for finite key lengths,” arXiv:1302.4139 (2013).

M. Koashi, “Efficient quantum key distribution with practical sources and detectors,” arXiv:quant-ph/0609180 (2006).

A. Wald, “Tests of statistical hypotheses concerning several parameters when the number of observations is large,” in Transactions of the American Mathematical Society, vol. 54 (1943), pp. 426–482.

J. Hasegawa, M. Hayashi, T. Hiroshima, and A. Tomita, “Security analysis of decoy state quantum key distribution incorporating finite statistics,” arXiv:0707.3541 (2007).

J. W. Harrington, J. M. Ettinger, R. J. Hughes, and J. E. Nordholt, “Enhancing practical security of quantum key distribution with a few decoy states,” arXiv:quant-ph/0503002 (2005).

P. Rice and J. W. Harrington, “Numerical analysis of decoy state quantum key distribution protocols,” arXiv:0901.0013 (2009).

J. Hasegawa, M. Hayashi, T. Hiroshima, A. Tanaka, and A. Tomita, “Experimental decoy state quantum key distribution with unconditional security incorporating finite statistics,” arXiv:0705.3081 (2007).

S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge University Press, 2004).

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 (5)

Fig. 1
Fig. 1

Experimental setup for the T12 protocol. In Alice’s layout, light pulses are emitted by a 1550 nm laser diode (LD), pulsed at 1 GHz, and transmitted through an intensity modulator (IM) and an unbalanced Mach-Zehnder interferometer. This is composed by a fibre-integrated beam-splitter (BS), a phase modulator (PM) and a final polarising BS (PBS). A variable attenuator (VA) is used to set the intensity of the pulses at the desired level. An optical power meter (OPM) measures the total flux in the fibre and adjust the VA in real-time in order to keep it constant. After a fibre spool of different lengths, the light passes through a polarization control (PC) and a second interferometer that matches Alice’s. In one arm, a fibre-stretcher (FS) is used to match the arm’s length between the two distant interferometers, thus generating interference at the final BS. Pulses are eventually measured by a detection unit (DU).

Fig. 2
Fig. 2

Secure key rate of the T12 protocol versus the size of the detected data sample, for ε= 10 10 . Parameters are obtained with the setup of Fig. 1 from an experimental QKD run over a 50 Km optical fibre. The key rate, depicted with a red line, is measured in percentage from the asymptotic value. Pie-charts with the breakdown of the counts leading to the final secure bits are given for sample sizes of 1011 counts and 1.4×105 counts. The latter value is the smallest sample size providing a positive rate and can be acquired in less than 60 ms with our system. For a typical acquisition time of 20 minutes, the block size is ~5×109 counts and the corresponding secure key rate is indicated by a violet circle on the red line. In addition, the minority basis probability has been optimised so to obtain the highest secure key rate at all distances. It goes from pX = 0.0065 for a sample of 1011 counts to pX = 0.2290 for a sample of 1.4×105 counts.

Fig. 3
Fig. 3

Advanced data analysis for the T12 protocol. Displayed are the basis-dependent and intensity-dependent counts and QBERs acquired by the system. The quantum channel is a 50.km optical fibre and the key session time is 20 minutes.

Fig. 4
Fig. 4

Experimental total and basis-dependent secure key rates. For the T12 protocol (pX = 1/16) data are in red colours. For the standard BB84 protocol (pX = 1/2) data are in blue colours. Experimental data are obtained over a 50 km optical fibre link and a typical acquisition time of 20 minutes. Each of the total key rates is given by the sum of the respective basis-dependent key rates.

Fig. 5
Fig. 5

, Experimental secure key rates as a function of fibre distance. The fibre distances experimentally tested are 35, 50, 65 and 80 km, respectively. For the T12 protocol (pX = 1/16, filled circles) the values of the secure key rate at these distances are 2.20, 1.09, 0.40 and 0.12 Mbps. For the standard BB84 protocol (pX = 1/2, empty circles) they are 1.18, 0.63, 0.26 and 0.06 Mbps. The solid and dashed lines are theoretical curves for T12 and BB84 protocol, respectively. The inset shows the real-time secure key rate provided by the T12 protocol at 50 km, over more than 3 hours of continuous operation. All the samples at this distance feature secure key rates exceeding 1 Mbps.

Tables (2)

Tables Icon

Table 1 Quantities for the advanced data analysis of the T12 protocol

Tables Icon

Table 2 Relations among experimental, statistical and estimated quantities.

Equations (23)

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

r= H ξ PE (A|E)(lea k EC +Δ)/n,
H ξ PE (A|E)= min σ AE Γ ξ PE H( A|E )
Δ=7 n log 2 ( 2 ε s ε PE ) +2 log 2 [ 1 2(ε ε s ε EC ) ]
H( A|E )= g ˜ uZ (0) + g ˜ uZ (1) [1h( q ˜ X (1) )]
g ˜ uZ (k) = y ˜ Z (k) ( e u u k /k!) ( C uZZ / N uZZ )
R Z =( C uZZ / N uZZ )r =min{ e u y ˜ Z (0) +u e u y ˜ Z (1) [1h( q ˜ X (1) )] } C uZZ N uZZ f EC h( Q Z ) Δ N uZZ
={ e u y ¯ Z (0) +u e u y ¯ Z (1) [1h( q ¯ X (1) )] } C uZZ N uZZ f EC h( Q Z ) Δ N uZZ
Γ ξ PE ={ σ AE : λ m λ ξ PE }.
Y μZ = k e μ μ k k! y Z (k) ,
B μX = k e μ μ k k! y X (k) q X (k) .
Y μ j Z k e μ j ( μ j ) k k! y ˜ Z (k) Y μ j Z + , j={0,1,2},
B μ j X k e μ j ( μ j ) k k! y ˜ X (k) q ˜ X (k) B μ j X + , j={0,1,2}
Y μ j Z =β( ε P E Y 2 ; C μ j ZZ , N μ j ZZ C μ j ZZ +1 ), j={0,1,2},
Y μ j Z + =β( 1 ε P E Y 2 ; C μ j ZZ +1, N μ j ZZ C μ j ZZ ), j={0,1,2}.
minimise: y ˜ Z (0)
subject to: 0 y ˜ Z (0) , y ˜ Z (1) ,..., y ˜ Z (k) 1,
Y μ j Z k e μ j ( μ j ) k k! y ˜ Z (k) Y μ j Z + , j={0,1,2}.
maximise: q ˜ X (1)
subject to: 0 y ˜ X (0) , y ˜ X (1) ,..., y ˜ X (k) 1,
0 q ˜ X (0) , q ˜ X (2) ,..., q ˜ X (k) 1, 0 q ˜ X (1) 1/2,
Y μ j X k e μ j ( μ j ) k k! y ˜ X (k) Y μ j X + , j={0,1,2},
B μ j X k e μ j ( μ j ) k k! y ˜ X (k) q ˜ X (k) B μ j X + , j={0,1,2}.
q ˜ X (1) q ¯ X (1) = B uX + 1 2 y ¯ X (0) e u u y ¯ X (1)

Metrics