We derive the time-dependent photo-detection probability equation of a superconducting single photon detector (SSPD) to study the responsive property for a pulse train at high repetition rate. Using this equation, we analyze the characteristics of SSPDs when illuminated by bright pulses in blinding attack on a quantum key distribution (QKD). We obtain good agreement between expected values based on our equation and actual experimental values. Such a time-dependent probability analysis contributes to security analysis.

© 2013 OSA

1. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys.74(1), 145–195 (2002). [CrossRef]
2. C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in International Conference on Computers Systems and Signal Processing (IEEE, 1984), pp.175–179. [CrossRef]
3. 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]
4. M. Peev, C. Pacher, R. Alleaume, C. Barreiro, W. Boxleitner, J. Bouda, R. Tualle-Brouri, E. Diamanti, M. Dianati, T. Debuisschert, J. F. Dynes, S. Fasel, S. Fossier, M. Fuerst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentchel, H. Hübel, G. Humer, T. Länger, M. Legre, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, E. Querasser, G. Ribordy, A. Poppe, L. Salvail, S. Robyr, M. Suda, A. W. Sharpe, A. J. Shields, D. Stucki, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, 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]
5. D. Stucki, M. Legre, F. Buntschu, B. Clausen, N. Felber, G. 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. Voirol, N. Walenta, and H. Zbinden, “Long-term performance of the SwissQuantum quantum key distribution network in a field environment,” New J. Phys.13(12), 123001 (2011). [CrossRef]
6. K. Inoue, E. Waks, and Y. Yamamoto, “Differential-phase-shift quantum key distribution using coherent light,” Phys. Rev. A68(2), 022317 (2003). [CrossRef]
7. T. Honjo, A. Uchida, K. Amano, K. Hirano, H. Someya, H. Okumura, K. Yoshimura, P. Davis, and Y. Tokura, “Differential-phase-shift quantum key distribution experiment using fast physical random bit generator with chaotic semiconductor lasers,” Opt. Express17(11), 9053–9061 (2009). [CrossRef] [PubMed]
8. G. Gol'tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, “Picosecond superconducting single-photon detector,” Appl. Phys. Lett.79(6), 705–707 (2001). [CrossRef]
9. A. Korneev, P. Kouminov, V. Matvienko, G. Chulkova, K. Smirnov, B. Voronov, G. N. Gol’tsman, M. Currie, W. Lo, K. Wilsher, J. Zhang, W. Słysz, A. Pearlman, A. Verevkin, and R. Sobolewski, “Sensitivity and gigahertz counting performance of NbN superconducting singlephoton detectors,” Appl. Phys. Lett.84(26), 5338–5340 (2004). [CrossRef]
10. S. Miki, M. Takeda, M. Fujiwara, M. Sasaki, and Z. Wang, “Compactly packaged superconducting nanowire single-photon detector with an optical cavity for multichannel system,” Opt. Express17(26), 23557–23564 (2009). [CrossRef] [PubMed]
11. S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, and Z. Wang, “Multi-channel SNSPD system with high detection efficiency at telecommunication wavelength,” Opt. Lett.35(13), 2133–2135 (2010). [CrossRef] [PubMed]
12. L. Lydersen, C. Wiechers, C. Wittmann, D. Elser, J. Skaar, and V. Makarov, “Hacking commercial quantum cryptography systems by tailored bright illumination,” Nat. Photonics4(10), 686–689 (2010). [CrossRef]
13. L. Lydersen, V. Makarov, and J. Skaar, “Secure gated detection scheme for quantum cryptography,” Phys. Rev. A83(3), 032306 (2011). [CrossRef]
14. M. Curty and N. Lütkenhaus, “Intercept-resend attacks in the Bennett-Brassard 1984 quantum-key-distribution protocol with weak coherent pulses,” Phys. Rev. A71(6), 062301 (2005). [CrossRef]
15. L. Lydersen, M. K. Akhlaghi, A. H. Majedi, J. Skaar, and V. Makarov, “Controlling a superconducting nanowire single-photon detector using tailored bright illumination,” New J. Phys.13(11), 113042 (2011). [CrossRef]
16. T. Honjo, M. Fujiwara, K. Shimizu, K. Tamaki, S. Miki, T. Yamashita, H. Terai, Z. Wang, and M. Sasaki, “Countermeasure against tailored bright illumination attack for DPS-QKD,” Opt. Express21(3), 2667–2673 (2013). [CrossRef]
17. M. Curty, L.-L. Zhang, H.-K. Lo, and N. Lutkenhaus, “Sequential attack against differential-phase-shift quantum key distribution with weak coherent states,” Quantum Inf. Comp.7, 665–688 (2007).
18. A. D. Semenov, G. N. Gol’tsman, and R. Sobolewski, “Hot-electron effect in superconductors and its applications for radiation sensors,” Supercond. Sci. Tech.15(4), R1–R16 (2002). [CrossRef]
19. A. J. Kerman, E. A. Dauler, W. E. Keicher, J. K. W. Yang, K. K. Berggren, G. Gol’tsman, and B. Voronov, “Kinetic-inductance-limited reset time of superconducting nanowire photon counters,” Appl. Phys. Lett.88(11), 111116 (2006). [CrossRef]
20. A. J. Kerman, W. Yang, R. J. Molnar, E. A. Dauler, and K. K. Berggren, “Electrothermal feedback in superconducting nanowire single-photon detectors,” Phys. Rev. B79(10), 100509 (2009). [CrossRef]
21. Z. L. Yuan, J. F. Dynes, and A. J. Shields, “Resilience of gated avalanche photodiodes against bright illumination attacks in quantum cryptography,” Appl. Phys. Lett.98(23), 231104 (2011). [CrossRef]
22. S. M. Barnett, L. S. Philips, and D. T. Pegg, “Imperfect photodetection as projection onto mixed states,” Opt. Commun.158(1–6), 45–49 (1998). [CrossRef]

Appl. Phys. Lett.

• G. Gol'tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, “Picosecond superconducting single-photon detector,” Appl. Phys. Lett.79(6), 705–707 (2001). [CrossRef]
• A. Korneev, P. Kouminov, V. Matvienko, G. Chulkova, K. Smirnov, B. Voronov, G. N. Gol’tsman, M. Currie, W. Lo, K. Wilsher, J. Zhang, W. Słysz, A. Pearlman, A. Verevkin, and R. Sobolewski, “Sensitivity and gigahertz counting performance of NbN superconducting singlephoton detectors,” Appl. Phys. Lett.84(26), 5338–5340 (2004). [CrossRef]
• A. J. Kerman, E. A. Dauler, W. E. Keicher, J. K. W. Yang, K. K. Berggren, G. Gol’tsman, and B. Voronov, “Kinetic-inductance-limited reset time of superconducting nanowire photon counters,” Appl. Phys. Lett.88(11), 111116 (2006). [CrossRef]
• Z. L. Yuan, J. F. Dynes, and A. J. Shields, “Resilience of gated avalanche photodiodes against bright illumination attacks in quantum cryptography,” Appl. Phys. Lett.98(23), 231104 (2011). [CrossRef]

Nat. Photonics

• L. Lydersen, C. Wiechers, C. Wittmann, D. Elser, J. Skaar, and V. Makarov, “Hacking commercial quantum cryptography systems by tailored bright illumination,” Nat. Photonics4(10), 686–689 (2010). [CrossRef]

New J. Phys.

• L. Lydersen, M. K. Akhlaghi, A. H. Majedi, J. Skaar, and V. Makarov, “Controlling a superconducting nanowire single-photon detector using tailored bright illumination,” New J. Phys.13(11), 113042 (2011). [CrossRef]
• M. Peev, C. Pacher, R. Alleaume, C. Barreiro, W. Boxleitner, J. Bouda, R. Tualle-Brouri, E. Diamanti, M. Dianati, T. Debuisschert, J. F. Dynes, S. Fasel, S. Fossier, M. Fuerst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentchel, H. Hübel, G. Humer, T. Länger, M. Legre, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, E. Querasser, G. Ribordy, A. Poppe, L. Salvail, S. Robyr, M. Suda, A. W. Sharpe, A. J. Shields, D. Stucki, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, 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]
• D. Stucki, M. Legre, F. Buntschu, B. Clausen, N. Felber, G. 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. Voirol, N. Walenta, and H. Zbinden, “Long-term performance of the SwissQuantum quantum key distribution network in a field environment,” New J. Phys.13(12), 123001 (2011). [CrossRef]

Opt. Commun.

• S. M. Barnett, L. S. Philips, and D. T. Pegg, “Imperfect photodetection as projection onto mixed states,” Opt. Commun.158(1–6), 45–49 (1998). [CrossRef]

Opt. Express

• S. Miki, M. Takeda, M. Fujiwara, M. Sasaki, and Z. Wang, “Compactly packaged superconducting nanowire single-photon detector with an optical cavity for multichannel system,” Opt. Express17(26), 23557–23564 (2009). [CrossRef] [PubMed]
• T. Honjo, M. Fujiwara, K. Shimizu, K. Tamaki, S. Miki, T. Yamashita, H. Terai, Z. Wang, and M. Sasaki, “Countermeasure against tailored bright illumination attack for DPS-QKD,” Opt. Express21(3), 2667–2673 (2013). [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]
• T. Honjo, A. Uchida, K. Amano, K. Hirano, H. Someya, H. Okumura, K. Yoshimura, P. Davis, and Y. Tokura, “Differential-phase-shift quantum key distribution experiment using fast physical random bit generator with chaotic semiconductor lasers,” Opt. Express17(11), 9053–9061 (2009). [CrossRef] [PubMed]

Opt. Lett.

• S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, and Z. Wang, “Multi-channel SNSPD system with high detection efficiency at telecommunication wavelength,” Opt. Lett.35(13), 2133–2135 (2010). [CrossRef] [PubMed]

Phys. Rev. A

• K. Inoue, E. Waks, and Y. Yamamoto, “Differential-phase-shift quantum key distribution using coherent light,” Phys. Rev. A68(2), 022317 (2003). [CrossRef]
• L. Lydersen, V. Makarov, and J. Skaar, “Secure gated detection scheme for quantum cryptography,” Phys. Rev. A83(3), 032306 (2011). [CrossRef]
• M. Curty and N. Lütkenhaus, “Intercept-resend attacks in the Bennett-Brassard 1984 quantum-key-distribution protocol with weak coherent pulses,” Phys. Rev. A71(6), 062301 (2005). [CrossRef]

Phys. Rev. B

• A. J. Kerman, W. Yang, R. J. Molnar, E. A. Dauler, and K. K. Berggren, “Electrothermal feedback in superconducting nanowire single-photon detectors,” Phys. Rev. B79(10), 100509 (2009). [CrossRef]

Quantum Inf. Comp.

• M. Curty, L.-L. Zhang, H.-K. Lo, and N. Lutkenhaus, “Sequential attack against differential-phase-shift quantum key distribution with weak coherent states,” Quantum Inf. Comp.7, 665–688 (2007).

Rev. Mod. Phys.

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

Supercond. Sci. Tech.

• A. D. Semenov, G. N. Gol’tsman, and R. Sobolewski, “Hot-electron effect in superconductors and its applications for radiation sensors,” Supercond. Sci. Tech.15(4), R1–R16 (2002). [CrossRef]

Other

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

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