Abstract

Security certification of quantum key distribution (QKD) systems under practical conditions is necessary for social deployment. This article focused on the transmitter, and, in particular, investigated the intensity fluctuation of the optical pulses emitted by a gain-switched semiconductor laser used in QKD systems implementing decoy-BB84 protocol. A large intensity fluctuation was observed for low excitation, showing strong negative correlation between the adjacent pulses, which would affect the final key rate. The fluctuation decreased and the correlation disappeared as excitation increased. Simulation with rate equations successfully reproduced the experimental results and revealed that the large fluctuation originates from an intrinsic instability of gain-switched lasers driven periodically at a rate comparable to the inverse of carrier lifetime, as in GHz-clock QKD systems. Methods for further reduction of the intensity fluctuation were also discussed.

© 2017 Optical Society of America

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Corrections

31 January 2017: Corrections were made to Eqs. (1), (2), (4), and (10); and the body text.


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References

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2016 (1)

Y. Nagamatsu, A. Mizutani, R. Ikuta, T. Yamamoto, N. Imoto, and K. Tamaki, “Security of quantum key distribution with light sources that are not independently and identically distributed,” Phys. Rev. A 93, 042325 (2016).
[Crossref]

2015 (1)

A. Mizutani, M. Curty, C. C. W. Lim, N. Imoto, and K. Tamaki, “Finite-key security analysis of quantum key distribution with imperfect light sources,” New J. Phys. 17, 093011 (2015).
[Crossref]

2014 (2)

M. Hayashi and R. Nakayama, “Security analysis of the decoy method with the bennett–brassard 1984 protocol for finite key lengths,” New J. Phys. 16, 063009 (2014).
[Crossref]

T. Kobayashi, A. Tomita, and A. Okamoto, “Evaluation of the phase randomness of a light source in quantum-key-distribution systems with an attenuated laser,” Phys. Rev. A 90, 032320 (2014).
[Crossref]

2013 (1)

B. Frohlich, J. F. Dynes, M. Lucamarini, A. W. Sharpe, Z. Yuan, and A. J. Shields, “A quantum access network,” Nature 501, 69–72 (2013).
[Crossref] [PubMed]

2012 (1)

S.-H. Sun, M. Gao, M.-S. Jiang, C.-Y. Li, and L.-M. Liang, “Partially random phase attack to the practical two-way quantum-key-distribution system,” Phys. Rev. A 85, 032304 (2012).
[Crossref]

2011 (2)

2010 (1)

2009 (5)

X.-B. Wang, L. Yang, C.-Z. Peng, and J.-W. Pan, “Decoy-state quantum key distribution with both source errors and statistical fluctuations,” New. J. Phys. 11, 075006 (2009).
[Crossref]

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dusek, and M. P. Norbert Lütkenhaus, “The Security of Practical Quantum Key Distribution,” Rev. Mod. Phys. 81, 1301–1353 (2009).
[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, 075001 (2009).
[Crossref]

T. E. Chapuran, P. Toliver, N. A. Peters, J. Jackel, M. S. Goodman, R. J. Runser, S. R. McNown, N. Dallmann, R. J. Hughes, K. P. McCabe, J. E. Nordholt, C. G. Peterson, K. T. Tyagi, L. Mercer, and H. Dardy, “Optical networking for quantum key distribution and quantum communications,” New J. Phys. 11, 105001 (2009).
[Crossref]

W. Chen, Z.-F. Han, T. Zhang, H. Wen, Z.-Q. Yin, F.-X. Xu, Q.-L. Wu, Y. Liu, Y. Zhang, X.-F Mo, Y.-Z. Gui, G. Wei, and G.-C. Guo, “Field experiment on a “star type” metropolitan quantum key distribution network,” IEEE Photonics Technol. Lett. 21, 575–577 (2009).
[Crossref]

2008 (1)

X.-B. Wang, C.-Z. Peng, J. Zhang, L. Yang, and J.-W. Pan, “General theory of decoy-state quantum cryptography with source errors,” Phys. Rev. A 77, 042311 (2008).
[Crossref]

2007 (1)

H.-K. Lo and J. Preskill, “Security of quantum key distribution using weak coherent states with nonrandom phases,” Quantum Info. Comput. 7, 431–458 (2007).

2005 (2)

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

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

2004 (1)

D. Gottesman, H.-K. Lo, N. Lütkenhaus, and J. Preskill, “Security of quantum key distribution with imperfect devices,” Quantum Info. Comput. 5, 325 (2004).

2003 (1)

W.-Y. Hwang, “Quantum Key Distribution with High Loss: Toward Global Secure Communication,” Phys. Rev. Lett. 91, 057901 (2003).
[Crossref] [PubMed]

2002 (1)

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

2000 (1)

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

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, 075001 (2009).
[Crossref]

Asai, T.

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, 075001 (2009).
[Crossref]

Bechmann-Pasquinucci, H.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dusek, and M. P. Norbert Lütkenhaus, “The Security of Practical Quantum Key Distribution,” Rev. Mod. Phys. 81, 1301–1353 (2009).
[Crossref]

Bennett, C. H.

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

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, 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, 075001 (2009).
[Crossref]

Brassard, G.

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

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

Cai, W.-Q.

Cerf, N. J.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dusek, and M. P. Norbert Lütkenhaus, “The Security of Practical Quantum Key Distribution,” Rev. Mod. Phys. 81, 1301–1353 (2009).
[Crossref]

Chapuran, T. E.

T. E. Chapuran, P. Toliver, N. A. Peters, J. Jackel, M. S. Goodman, R. J. Runser, S. R. McNown, N. Dallmann, R. J. Hughes, K. P. McCabe, J. E. Nordholt, C. G. Peterson, K. T. Tyagi, L. Mercer, and H. Dardy, “Optical networking for quantum key distribution and quantum communications,” New J. Phys. 11, 105001 (2009).
[Crossref]

Chen, K.

Chen, L.-K.

Chen, T.-Y.

Chen, W.

W. Chen, Z.-F. Han, T. Zhang, H. Wen, Z.-Q. Yin, F.-X. Xu, Q.-L. Wu, Y. Liu, Y. Zhang, X.-F Mo, Y.-Z. Gui, G. Wei, and G.-C. Guo, “Field experiment on a “star type” metropolitan quantum key distribution network,” IEEE Photonics Technol. Lett. 21, 575–577 (2009).
[Crossref]

Chen, Z.-B.

Curty, M.

A. Mizutani, M. Curty, C. C. W. Lim, N. Imoto, and K. Tamaki, “Finite-key security analysis of quantum key distribution with imperfect light sources,” New J. Phys. 17, 093011 (2015).
[Crossref]

Dallmann, N.

T. E. Chapuran, P. Toliver, N. A. Peters, J. Jackel, M. S. Goodman, R. J. Runser, S. R. McNown, N. Dallmann, R. J. Hughes, K. P. McCabe, J. E. Nordholt, C. G. Peterson, K. T. Tyagi, L. Mercer, and H. Dardy, “Optical networking for quantum key distribution and quantum communications,” New J. Phys. 11, 105001 (2009).
[Crossref]

Dardy, H.

T. E. Chapuran, P. Toliver, N. A. Peters, J. Jackel, M. S. Goodman, R. J. Runser, S. R. McNown, N. Dallmann, R. J. Hughes, K. P. McCabe, J. E. Nordholt, C. G. Peterson, K. T. Tyagi, L. Mercer, and H. Dardy, “Optical networking for quantum key distribution and quantum communications,” New J. Phys. 11, 105001 (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, 075001 (2009).
[Crossref]

Diamanti, 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, 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, 075001 (2009).
[Crossref]

Dixon, A. R.

Domeki, T.

Dusek, M.

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H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94, 230504 (2005).
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A. Mizutani, M. Curty, C. C. W. Lim, N. Imoto, and K. Tamaki, “Finite-key security analysis of quantum key distribution with imperfect light sources,” New J. Phys. 17, 093011 (2015).
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G. Brassard, N. Lütkenhaus, T. Mor, and B. C. Sanders, “Limitations on practical quantum cryptography,” Phys. Rev. Lett. 85, 1330 (2000).
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Y. Nagamatsu, A. Mizutani, R. Ikuta, T. Yamamoto, N. Imoto, and K. Tamaki, “Security of quantum key distribution with light sources that are not independently and identically distributed,” Phys. Rev. A 93, 042325 (2016).
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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. Express 19, 10387–10409 (2011).
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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. Express 19, 10387–10409 (2011).
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Stucki, D.

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Suda, M.

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Tajima, A.

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Takesue, H.

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Tanaka, A.

Themel, T.

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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, 075001 (2009).
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Treiber, A.

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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. Express 19, 10387–10409 (2011).
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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, 075001 (2009).
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T. E. Chapuran, P. Toliver, N. A. Peters, J. Jackel, M. S. Goodman, R. J. Runser, S. R. McNown, N. Dallmann, R. J. Hughes, K. P. McCabe, J. E. Nordholt, C. G. Peterson, K. T. Tyagi, L. Mercer, and H. Dardy, “Optical networking for quantum key distribution and quantum communications,” New J. Phys. 11, 105001 (2009).
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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, 075001 (2009).
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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, 075001 (2009).
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Wan, X.

Wang, J.

Wang, L.-J.

Wang, X.-B.

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Wei, G.

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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, 075001 (2009).
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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, 075001 (2009).
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Wen, H.

W. Chen, Z.-F. Han, T. Zhang, H. Wen, Z.-Q. Yin, F.-X. Xu, Q.-L. Wu, Y. Liu, Y. Zhang, X.-F Mo, Y.-Z. Gui, G. Wei, and G.-C. Guo, “Field experiment on a “star type” metropolitan quantum key distribution network,” IEEE Photonics Technol. Lett. 21, 575–577 (2009).
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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, 075001 (2009).
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Wu, Q.-L.

W. Chen, Z.-F. Han, T. Zhang, H. Wen, Z.-Q. Yin, F.-X. Xu, Q.-L. Wu, Y. Liu, Y. Zhang, X.-F Mo, Y.-Z. Gui, G. Wei, and G.-C. Guo, “Field experiment on a “star type” metropolitan quantum key distribution network,” IEEE Photonics Technol. Lett. 21, 575–577 (2009).
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Xu, F.-X.

W. Chen, Z.-F. Han, T. Zhang, H. Wen, Z.-Q. Yin, F.-X. Xu, Q.-L. Wu, Y. Liu, Y. Zhang, X.-F Mo, Y.-Z. Gui, G. Wei, and G.-C. Guo, “Field experiment on a “star type” metropolitan quantum key distribution network,” IEEE Photonics Technol. Lett. 21, 575–577 (2009).
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Yamamoto, T.

Y. Nagamatsu, A. Mizutani, R. Ikuta, T. Yamamoto, N. Imoto, and K. Tamaki, “Security of quantum key distribution with light sources that are not independently and identically distributed,” Phys. Rev. A 93, 042325 (2016).
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Yang, L.

X.-B. Wang, L. Yang, C.-Z. Peng, and J.-W. Pan, “Decoy-state quantum key distribution with both source errors and statistical fluctuations,” New. J. Phys. 11, 075006 (2009).
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X.-B. Wang, C.-Z. Peng, J. Zhang, L. Yang, and J.-W. Pan, “General theory of decoy-state quantum cryptography with source errors,” Phys. Rev. A 77, 042311 (2008).
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Yin, Z.-Q.

W. Chen, Z.-F. Han, T. Zhang, H. Wen, Z.-Q. Yin, F.-X. Xu, Q.-L. Wu, Y. Liu, Y. Zhang, X.-F Mo, Y.-Z. Gui, G. Wei, and G.-C. Guo, “Field experiment on a “star type” metropolitan quantum key distribution network,” IEEE Photonics Technol. Lett. 21, 575–577 (2009).
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Yoshino, K.

Yuan, Z.

B. Frohlich, J. F. Dynes, M. Lucamarini, A. W. Sharpe, Z. Yuan, and A. J. Shields, “A quantum access network,” Nature 501, 69–72 (2013).
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Yuan, Z. L.

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, O. Thomas, and A. J. Shields, “Probing higher order correlations of the photon field with photon number resolving avalanche photodiodes,” Opt. Express 19, (14), 13268–13276 (2011).
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Yuan, Z.-L.

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, 075001 (2009).
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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. Express 19, 10387–10409 (2011).
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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, 075001 (2009).
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X.-B. Wang, C.-Z. Peng, J. Zhang, L. Yang, and J.-W. Pan, “General theory of decoy-state quantum cryptography with source errors,” Phys. Rev. A 77, 042311 (2008).
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W. Chen, Z.-F. Han, T. Zhang, H. Wen, Z.-Q. Yin, F.-X. Xu, Q.-L. Wu, Y. Liu, Y. Zhang, X.-F Mo, Y.-Z. Gui, G. Wei, and G.-C. Guo, “Field experiment on a “star type” metropolitan quantum key distribution network,” IEEE Photonics Technol. Lett. 21, 575–577 (2009).
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W. Chen, Z.-F. Han, T. Zhang, H. Wen, Z.-Q. Yin, F.-X. Xu, Q.-L. Wu, Y. Liu, Y. Zhang, X.-F Mo, Y.-Z. Gui, G. Wei, and G.-C. Guo, “Field experiment on a “star type” metropolitan quantum key distribution network,” IEEE Photonics Technol. Lett. 21, 575–577 (2009).
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IEEE Photonics Technol. Lett. (1)

W. Chen, Z.-F. Han, T. Zhang, H. Wen, Z.-Q. Yin, F.-X. Xu, Q.-L. Wu, Y. Liu, Y. Zhang, X.-F Mo, Y.-Z. Gui, G. Wei, and G.-C. Guo, “Field experiment on a “star type” metropolitan quantum key distribution network,” IEEE Photonics Technol. Lett. 21, 575–577 (2009).
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Nature (1)

B. Frohlich, J. F. Dynes, M. Lucamarini, A. W. Sharpe, Z. Yuan, and A. J. Shields, “A quantum access network,” Nature 501, 69–72 (2013).
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T. E. Chapuran, P. Toliver, N. A. Peters, J. Jackel, M. S. Goodman, R. J. Runser, S. R. McNown, N. Dallmann, R. J. Hughes, K. P. McCabe, J. E. Nordholt, C. G. Peterson, K. T. Tyagi, L. Mercer, and H. Dardy, “Optical networking for quantum key distribution and quantum communications,” New J. Phys. 11, 105001 (2009).
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Opt. Express (3)

Phys. Rev. A (4)

Y. Nagamatsu, A. Mizutani, R. Ikuta, T. Yamamoto, N. Imoto, and K. Tamaki, “Security of quantum key distribution with light sources that are not independently and identically distributed,” Phys. Rev. A 93, 042325 (2016).
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X.-B. Wang, C.-Z. Peng, J. Zhang, L. Yang, and J.-W. Pan, “General theory of decoy-state quantum cryptography with source errors,” Phys. Rev. A 77, 042311 (2008).
[Crossref]

T. Kobayashi, A. Tomita, and A. Okamoto, “Evaluation of the phase randomness of a light source in quantum-key-distribution systems with an attenuated laser,” Phys. Rev. A 90, 032320 (2014).
[Crossref]

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[Crossref] [PubMed]

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[Crossref] [PubMed]

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[Crossref] [PubMed]

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[Crossref]

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Figures (8)

Fig. 1
Fig. 1

Experimental set up for the intensity measurement. A distributed feedback (DFB) laser diode was driven by a DC bias current and electric pulses from a pulse pattern generator (PPG) to operate in the gain-switching mode. The output was coupled to a single mode optical fiber and detected by a high speed pin-photodiode (PD) and collected by a oscilloscope (OSC). Input optical power to the photodiode was controlled by an attenuator (ATT).

Fig. 2
Fig. 2

The temporal profiles of the laser pulses for three DC excitation values. The left panels represent experimantally obtained waveforms, where DC bias current JDC was set to (a) 0.65 Jth, (b) 0.7 Jth, and (c) 0.9 Jth with a fixed pulse current JAC = 3Jth. The right panels represent the ones simulated including electrical noise, where the normalized DC excitation Λ DC was set to (d) 0.6, (e) 0.63, and (f) 0.8 with a fixed pulse current Λ AC = 3. Pulse intensity was defined as the pulse area for one period depicted by an arrow shown in panel (a).

Fig. 3
Fig. 3

Measured (a–c), simulated with electrical noise (d–f), and simulated without electrical noise (g–i) distributions of pulse intensity fluctuation of a GSSL. DC bias current JDC was set to (a) 0.65 Jth, (b) 0.7 Jth, and (c) 0.9 Jth with a fixed pulse current JAC = 3Jth for measured distributions. Normalized DC pumping Λ DC was set to (d) 0.6, (e) 0.63, and (f) 0.8 with a fixed pulse current Λ AC = 3 for simulated distributions. The fluctuation of the laser intensity x is presented by the normalized deviation from the mean value μ = 〈x〉 as (xμ)/μ.

Fig. 4
Fig. 4

Intensity fluctuation of a GSSL depicted as a function of the DC bias current for the pulse currents JAC = 2Jth, JAC = 3Jth, and JAC = 4Jth. The intensity fluctuation is measured by the triplication of the standard deviation of intensity distribution normalized by the mean value: 3σ/μ.

Fig. 5
Fig. 5

Autocorrelation function of the intensity between adjacent pulses (leg=1). Negative correlation was observed for weak excitations. The pulse current was set to JAC = 3Jth

Fig. 6
Fig. 6

Calculated temporal behavior of the light intensity from a GSSL. (a) ΛDC = 0.58 (b) ΛDC = 0.6, and (c) ΛDC = 0.8 with pulse pumping ΛAC = 3.

Fig. 7
Fig. 7

Calculated intensity fluctuation of a GSSL. (a) normalized fluctuation 3σ/μ, and (b) the autocorrelation function, as a function of DC pumping with a fixed pulse pumping Λ AC = 3.

Fig. 8
Fig. 8

Calculated temporal behavior of normalized carrier density and photon density of the periodically driven GSSL operation. The laser was driven by pumping pulses of 100-ps duration during the period between the broken lines (0–0.1 ns, 0.8–0.9 ns, . . .). The threshold carrier density is depicted as a horizontal dash-dot line. The operating conditions are Λ DC = 0.58 and Λ AC = 3.

Tables (1)

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Table 1 Parameters for a typical semiconductor laser

Equations (10)

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η k = n = 0 Y n p k | n ,
p k | n = p n | k p k l p n | l p l ,
d I d t = Γ g ( N N g ) I I τ p + Γ β sp N τ N
d N d t = Λ g ( N N g ) I N τ N
( Δ I n + 1 Δ N n + 1 ) = ( I n + 1 I n I n + 1 N n N n + 1 I n N n + 1 N n ) ( Δ I n Δ N n ) .
Λ ( t ) = Λ DC + Λ AC ( t ) + F ( t ) ,
g ( 2 ) ( 0 ) = a 2 a 2 a a 2 ,
ρ = d n ¯ f ( n ¯ ) n = 0 e n ¯ n ¯ n n ! | n n | ,
g ( 2 ) ( 0 ) = 1 + s 2 n ¯ 2 ,
τ eff = 1 1 Λ DC τ p .

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