Abstract

This paper reports experimental results for a long-term field trial of 1-GHz clock differential phase shift quantum key distribution that was incorporated in the test-bed optical fiber network installed in the Tokyo metropolitan area. A photon transmitter and a photon receiver were connected to a 90-km loop-back optical link with a 30-dB loss. Superconducting single photon detectors were employed to detect photons with a low dark count rate. Stable maintenance-free operation was achieved for 25 days, where the average sifted key generation rate and the quantum bit error rate were 11 kb/s and 2.6%, respectively. The average generation rate of a secure key after error correction and privacy amplification was 1.1 kb/s with a fluctuation of ± 0.5 kb/s. The achieved performance was examined using detailed bit error analysis. A comparison with meteorological data revealed the way in which the field environment influenced the key distribution performance.

© 2013 IEEE

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  1. C. H. Bennett, G. Brassard, "Quantum cryptography: Public key distribution and coin tossing," Proc. IEEE Int. Conf. Comput. Syst., Signal Process. (1984) pp. 175-179.
  2. M. A. Nielsen, I. L. Chuang, Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000, ch. 12.6).
  3. N. Gisin, G. Ribordy, W. Tittel, H. Zbinden, "Quantum cryptography," Rev. Mod. Phys. 74, 145-195 (2002).
  4. H.-K. Lo, H. F. Chau, "Unconditional security of quantum key distribution over arbitrarily long distance," Science 283, 2050-2056 (1999).
  5. P. W. Shor, J. Preskill, "Simple proof of security of the BB84 quantum key distribution protocol," Phys. Rev. Lett. 85, 441-444 (2000).
  6. V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dusek, N. Lutkenhaus, M. Peev, "The security of practical quantum key distribution," Rev. Mod. Phys. 81, 1301-1350 (2009).
  7. C. Elliott, A. Colvin, D. Pearson, O. Pikalo, J. Schlafer, H. Yeh, "Current status of the DARPA quantum network ," Proc. SPIE: Quantum Inf. Comput. III 5815, 138-149 (2005).
  8. 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, A. Zeilinger, "The SECOQC quantum key distribution network in Vienna," New J. Phys. 11, 075001-1 -075001-37 (2009).
  9. S. Wang, W. Chen, Z.-Q. Yin, Y. Zhang, T. Zhang, H.-W. Li, F.-X. Xu, Z. Zhou, Y. Yang, D.-J. Huang, L.-J. Zhang, F.-Y. Li, D. Liu, Y.-G. Wang, G.-C. Guo, Z.-F. Han, "Field test of wavelength-saving quantum key distribution network," Opt. Lett. 35 , 2454-2456 (2010 ).
  10. D. Stucki, M. Legre, F. Buntschu, B. Clausen, N. Felber, N. Gisin, L. Henzen, P. Junod, G. Litzistorf, P. Monbaron, L. Monat, J.-B. Page, D. Perroud, G. Ribordy, A. Rochas, S. Robyr, J. Tavares, R. Thew, P. Trinkler, S. Ventura, R. Voiroi, N. Walenta, H. Zbinden, "Long-term performance of the SwissQuantum quantum key distribution network in a field environment," New J. Phys. 13 , 123001-1-123001-18 (2011).
  11. M. Sasaki, M. Fujiwara, H. Ishizuka, W. Klaus, K. Wakui, M. Takeoka, 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, A. Zeilinger, "Field test of quantum key distribution in the Tokyo QKD Network," Opt. Exp. 19, 10387-10409 (2011).
  12. K. Inoue, E. Waks, Y. Yamamoto, "Differential-phase-shift quantum key distribution using coherent light," Phys. Rev. A 68, 022317-1-022317-4 (2003 ).
  13. H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, Y. Yamamoto, "Quantum key distribution over 40 dB channel loss using superconducting single photon detectors," Nat. Photon. 1, 343-348 (2007).
  14. K. Wen, K. Tamaki, Y. Yamamoto, "Unconditional security of single-photon differential phase shift quantum key distribution," Phys. Rev. Lett. 103, 170503-1-170503-4 (2009).
  15. K. Tamaki, M. Koashi, and G. Kato, “Unconditional security of coherent-state-based differential phase shift quantum key distribution protocol with block-wise phase randomization,” submitted for publication Phy. Rev. A..
  16. E. Waks, H. Takesue, Y. Yamamoto, "Security of differential-phase-shift quantum key distribution against individual attacks," Phys. Rev.A 73, 012344-1-012344-9 (2003).
  17. M. Hayashi, "Practical evaluation of security for quantum key distribution ," Phy. Rev.A 74, 022307-1-022307-19 (2006).
  18. M. Hayashi, T. Tsurumaru, "Concise and tight security analysis of the Bennett-Brassard 1984 protocol with finite key lengths ," New J. Phys. 14, 093014-1-093014-39 (2012).
  19. D. Elkouss, A. Leverrier, R. Alleaumé, and J. J. Boutrous, 2009, Jan.,. Efficient Reconciliation Protocol for Discrete-Variable Quantum Key Distribution. [Online]. Available: http://arxiv.org/PS_cache/arxiv/pdf/0901/0901.2140v1.pdf.
  20. S. Obana and A. Tanaka, “General purpose hash function family computer and shared key creating system,” Patent WO/2007/034685, Mar. 29, 2007..
  21. A. Tanaka, M. Fujiwara, K. Yoshino, S. Takahashi, Y. Nambu, A. Tomita, S. Miki, T. Yamashita, Z. Wang, M. Sasaki, A. Tajima, "High-speed quantum key distribution system for 1-Mbps real-time key generation," IEEE J. Quantum Electron. 48, 542-550 (2012).
  22. G. K. Batchelor, An Introduction to Fluid Dynamics (Cambridge Univ. Press, 1967).
  23. Y. Katsuyama, Y. Mitsunaga, Y. Ishida, "Vibration characteristics of an optical fiber cable installed on an aerial line," Trans. Inst. Electron., Inform. Commun. Eng. J64-B, 69-74 (1981) in Japanese.
  24. A. Yariv, Quantum Electronics (Wiley, 1989).
  25. N. Namekata, H. Takesue, T. Honjo, Y. Tokura, S. Inoue, "High-rate quantum key distribution over 100 km using ultra-low-noise, 2-GHz sinusoidally gated InGaAs/InP avalanche photodiodes," Opt. Exp. 19, 10632-10639 (2011).
  26. Y. Nambu, S. Takahashi, K. Yoshino, A. Tanaka, M. Fujiwara, M. Sasaki, A. Tajima, S. Yorozu, A. Tomita, "Efficient and low-noise single-photon avalanche photodiode for 1.244-GHz clocked quantum key distribution," Opt. Exp. 19 , 20532-20541 ( 2011).
  27. Y. Zhao, C.-H. F. Fung, B. Qi, C. Chen, H.-K. Lo, "Qunatum hacking: Experimental demonstration of time-shift attack against practical quantum-key-distribution systems ," Phys. Rev. A 78, 042333-1-042333-5 (2008).
  28. C.-H. F. Fung, K. Tamaki, B. Qi, H.-K. Lo, X.-F. Ma, "Security proof of quantum key distribution with detection efficiency mismatch," Quantum Info. Comp 9, 0131-0165 (2009).
  29. L. Lydersen, M. K. Akhlaghi, A. H. Majedi, J. Skaar, V. Makarov, "Controlling a superconducting nanowire single-photon detector using tailored bright illumination ," New J. Phys. 13, 113042-1-113042-14 (2011).
  30. T. Honjo, M. Fujiwara, K. Shimizu, K. Tamaki, S. Miki, T. Yamashita, H. Terai, Z. Wang, M. Sasaki, "Countermeasure against tailored bright illumination attack for DPS-QKD ," Opt. Exp. 21, 2667-2673 (2013).
  31. M. Fujiwara, T. Honjo, K. Shimizu, K. Tamaki, M. Sasaki, " Characteristics of superconducting single photon detector in DPS-QKD system under bright illumination blinding attack ," Opt. Exp. 21, 6304-6312 (2013).

2013

T. Honjo, M. Fujiwara, K. Shimizu, K. Tamaki, S. Miki, T. Yamashita, H. Terai, Z. Wang, M. Sasaki, "Countermeasure against tailored bright illumination attack for DPS-QKD ," Opt. Exp. 21, 2667-2673 (2013).

M. Fujiwara, T. Honjo, K. Shimizu, K. Tamaki, M. Sasaki, " Characteristics of superconducting single photon detector in DPS-QKD system under bright illumination blinding attack ," Opt. Exp. 21, 6304-6312 (2013).

2012

M. Hayashi, T. Tsurumaru, "Concise and tight security analysis of the Bennett-Brassard 1984 protocol with finite key lengths ," New J. Phys. 14, 093014-1-093014-39 (2012).

A. Tanaka, M. Fujiwara, K. Yoshino, S. Takahashi, Y. Nambu, A. Tomita, S. Miki, T. Yamashita, Z. Wang, M. Sasaki, A. Tajima, "High-speed quantum key distribution system for 1-Mbps real-time key generation," IEEE J. Quantum Electron. 48, 542-550 (2012).

2011

N. Namekata, H. Takesue, T. Honjo, Y. Tokura, S. Inoue, "High-rate quantum key distribution over 100 km using ultra-low-noise, 2-GHz sinusoidally gated InGaAs/InP avalanche photodiodes," Opt. Exp. 19, 10632-10639 (2011).

D. Stucki, M. Legre, F. Buntschu, B. Clausen, N. Felber, N. Gisin, L. Henzen, P. Junod, G. Litzistorf, P. Monbaron, L. Monat, J.-B. Page, D. Perroud, G. Ribordy, A. Rochas, S. Robyr, J. Tavares, R. Thew, P. Trinkler, S. Ventura, R. Voiroi, N. Walenta, H. Zbinden, "Long-term performance of the SwissQuantum quantum key distribution network in a field environment," New J. Phys. 13 , 123001-1-123001-18 (2011).

M. Sasaki, M. Fujiwara, H. Ishizuka, W. Klaus, K. Wakui, M. Takeoka, 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, A. Zeilinger, "Field test of quantum key distribution in the Tokyo QKD Network," Opt. Exp. 19, 10387-10409 (2011).

L. Lydersen, M. K. Akhlaghi, A. H. Majedi, J. Skaar, V. Makarov, "Controlling a superconducting nanowire single-photon detector using tailored bright illumination ," New J. Phys. 13, 113042-1-113042-14 (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, A. Zeilinger, "The SECOQC quantum key distribution network in Vienna," New J. Phys. 11, 075001-1 -075001-37 (2009).

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dusek, N. Lutkenhaus, M. Peev, "The security of practical quantum key distribution," Rev. Mod. Phys. 81, 1301-1350 (2009).

C.-H. F. Fung, K. Tamaki, B. Qi, H.-K. Lo, X.-F. Ma, "Security proof of quantum key distribution with detection efficiency mismatch," Quantum Info. Comp 9, 0131-0165 (2009).

K. Wen, K. Tamaki, Y. Yamamoto, "Unconditional security of single-photon differential phase shift quantum key distribution," Phys. Rev. Lett. 103, 170503-1-170503-4 (2009).

2008

Y. Zhao, C.-H. F. Fung, B. Qi, C. Chen, H.-K. Lo, "Qunatum hacking: Experimental demonstration of time-shift attack against practical quantum-key-distribution systems ," Phys. Rev. A 78, 042333-1-042333-5 (2008).

2007

H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, Y. Yamamoto, "Quantum key distribution over 40 dB channel loss using superconducting single photon detectors," Nat. Photon. 1, 343-348 (2007).

2006

M. Hayashi, "Practical evaluation of security for quantum key distribution ," Phy. Rev.A 74, 022307-1-022307-19 (2006).

2005

C. Elliott, A. Colvin, D. Pearson, O. Pikalo, J. Schlafer, H. Yeh, "Current status of the DARPA quantum network ," Proc. SPIE: Quantum Inf. Comput. III 5815, 138-149 (2005).

2003

E. Waks, H. Takesue, Y. Yamamoto, "Security of differential-phase-shift quantum key distribution against individual attacks," Phys. Rev.A 73, 012344-1-012344-9 (2003).

2002

N. Gisin, G. Ribordy, W. Tittel, H. Zbinden, "Quantum cryptography," Rev. Mod. Phys. 74, 145-195 (2002).

2000

P. W. Shor, J. Preskill, "Simple proof of security of the BB84 quantum key distribution protocol," Phys. Rev. Lett. 85, 441-444 (2000).

1999

H.-K. Lo, H. F. Chau, "Unconditional security of quantum key distribution over arbitrarily long distance," Science 283, 2050-2056 (1999).

1981

Y. Katsuyama, Y. Mitsunaga, Y. Ishida, "Vibration characteristics of an optical fiber cable installed on an aerial line," Trans. Inst. Electron., Inform. Commun. Eng. J64-B, 69-74 (1981) in Japanese.

IEEE J. Quantum Electron.

A. Tanaka, M. Fujiwara, K. Yoshino, S. Takahashi, Y. Nambu, A. Tomita, S. Miki, T. Yamashita, Z. Wang, M. Sasaki, A. Tajima, "High-speed quantum key distribution system for 1-Mbps real-time key generation," IEEE J. Quantum Electron. 48, 542-550 (2012).

Nat. Photon.

H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, Y. Yamamoto, "Quantum key distribution over 40 dB channel loss using superconducting single photon detectors," Nat. Photon. 1, 343-348 (2007).

New J. Phys.

D. Stucki, M. Legre, F. Buntschu, B. Clausen, N. Felber, N. Gisin, L. Henzen, P. Junod, G. Litzistorf, P. Monbaron, L. Monat, J.-B. Page, D. Perroud, G. Ribordy, A. Rochas, S. Robyr, J. Tavares, R. Thew, P. Trinkler, S. Ventura, R. Voiroi, N. Walenta, H. Zbinden, "Long-term performance of the SwissQuantum quantum key distribution network in a field environment," New J. Phys. 13 , 123001-1-123001-18 (2011).

M. Hayashi, T. Tsurumaru, "Concise and tight security analysis of the Bennett-Brassard 1984 protocol with finite key lengths ," New J. Phys. 14, 093014-1-093014-39 (2012).

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, A. Zeilinger, "The SECOQC quantum key distribution network in Vienna," New J. Phys. 11, 075001-1 -075001-37 (2009).

L. Lydersen, M. K. Akhlaghi, A. H. Majedi, J. Skaar, V. Makarov, "Controlling a superconducting nanowire single-photon detector using tailored bright illumination ," New J. Phys. 13, 113042-1-113042-14 (2011).

Opt. Exp.

T. Honjo, M. Fujiwara, K. Shimizu, K. Tamaki, S. Miki, T. Yamashita, H. Terai, Z. Wang, M. Sasaki, "Countermeasure against tailored bright illumination attack for DPS-QKD ," Opt. Exp. 21, 2667-2673 (2013).

M. Fujiwara, T. Honjo, K. Shimizu, K. Tamaki, M. Sasaki, " Characteristics of superconducting single photon detector in DPS-QKD system under bright illumination blinding attack ," Opt. Exp. 21, 6304-6312 (2013).

N. Namekata, H. Takesue, T. Honjo, Y. Tokura, S. Inoue, "High-rate quantum key distribution over 100 km using ultra-low-noise, 2-GHz sinusoidally gated InGaAs/InP avalanche photodiodes," Opt. Exp. 19, 10632-10639 (2011).

Y. Nambu, S. Takahashi, K. Yoshino, A. Tanaka, M. Fujiwara, M. Sasaki, A. Tajima, S. Yorozu, A. Tomita, "Efficient and low-noise single-photon avalanche photodiode for 1.244-GHz clocked quantum key distribution," Opt. Exp. 19 , 20532-20541 ( 2011).

M. Sasaki, M. Fujiwara, H. Ishizuka, W. Klaus, K. Wakui, M. Takeoka, 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, A. Zeilinger, "Field test of quantum key distribution in the Tokyo QKD Network," Opt. Exp. 19, 10387-10409 (2011).

Opt. Lett.

S. Wang, W. Chen, Z.-Q. Yin, Y. Zhang, T. Zhang, H.-W. Li, F.-X. Xu, Z. Zhou, Y. Yang, D.-J. Huang, L.-J. Zhang, F.-Y. Li, D. Liu, Y.-G. Wang, G.-C. Guo, Z.-F. Han, "Field test of wavelength-saving quantum key distribution network," Opt. Lett. 35 , 2454-2456 (2010 ).

Phy. Rev.A

M. Hayashi, "Practical evaluation of security for quantum key distribution ," Phy. Rev.A 74, 022307-1-022307-19 (2006).

Phys. Rev. A

Y. Zhao, C.-H. F. Fung, B. Qi, C. Chen, H.-K. Lo, "Qunatum hacking: Experimental demonstration of time-shift attack against practical quantum-key-distribution systems ," Phys. Rev. A 78, 042333-1-042333-5 (2008).

K. Inoue, E. Waks, Y. Yamamoto, "Differential-phase-shift quantum key distribution using coherent light," Phys. Rev. A 68, 022317-1-022317-4 (2003 ).

Phys. Rev. Lett.

K. Wen, K. Tamaki, Y. Yamamoto, "Unconditional security of single-photon differential phase shift quantum key distribution," Phys. Rev. Lett. 103, 170503-1-170503-4 (2009).

Phys. Rev. Lett.

P. W. Shor, J. Preskill, "Simple proof of security of the BB84 quantum key distribution protocol," Phys. Rev. Lett. 85, 441-444 (2000).

Phys. Rev.A

E. Waks, H. Takesue, Y. Yamamoto, "Security of differential-phase-shift quantum key distribution against individual attacks," Phys. Rev.A 73, 012344-1-012344-9 (2003).

Proc. SPIE: Quantum Inf. Comput. III

C. Elliott, A. Colvin, D. Pearson, O. Pikalo, J. Schlafer, H. Yeh, "Current status of the DARPA quantum network ," Proc. SPIE: Quantum Inf. Comput. III 5815, 138-149 (2005).

Quantum Info. Comp

C.-H. F. Fung, K. Tamaki, B. Qi, H.-K. Lo, X.-F. Ma, "Security proof of quantum key distribution with detection efficiency mismatch," Quantum Info. Comp 9, 0131-0165 (2009).

Rev. Mod. Phys.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dusek, N. Lutkenhaus, M. Peev, "The security of practical quantum key distribution," Rev. Mod. Phys. 81, 1301-1350 (2009).

N. Gisin, G. Ribordy, W. Tittel, H. Zbinden, "Quantum cryptography," Rev. Mod. Phys. 74, 145-195 (2002).

Science

H.-K. Lo, H. F. Chau, "Unconditional security of quantum key distribution over arbitrarily long distance," Science 283, 2050-2056 (1999).

Trans. Inst. Electron., Inform. Commun. Eng.

Y. Katsuyama, Y. Mitsunaga, Y. Ishida, "Vibration characteristics of an optical fiber cable installed on an aerial line," Trans. Inst. Electron., Inform. Commun. Eng. J64-B, 69-74 (1981) in Japanese.

Other

A. Yariv, Quantum Electronics (Wiley, 1989).

G. K. Batchelor, An Introduction to Fluid Dynamics (Cambridge Univ. Press, 1967).

C. H. Bennett, G. Brassard, "Quantum cryptography: Public key distribution and coin tossing," Proc. IEEE Int. Conf. Comput. Syst., Signal Process. (1984) pp. 175-179.

M. A. Nielsen, I. L. Chuang, Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000, ch. 12.6).

D. Elkouss, A. Leverrier, R. Alleaumé, and J. J. Boutrous, 2009, Jan.,. Efficient Reconciliation Protocol for Discrete-Variable Quantum Key Distribution. [Online]. Available: http://arxiv.org/PS_cache/arxiv/pdf/0901/0901.2140v1.pdf.

S. Obana and A. Tanaka, “General purpose hash function family computer and shared key creating system,” Patent WO/2007/034685, Mar. 29, 2007..

K. Tamaki, M. Koashi, and G. Kato, “Unconditional security of coherent-state-based differential phase shift quantum key distribution protocol with block-wise phase randomization,” submitted for publication Phy. Rev. A..

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