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Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 11 — Jun. 2, 2014
  • pp: 13616–13624
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Modified E91 protocol demonstration with hybrid entanglement photon source

Mikio Fujiwara, Ken-ichiro Yoshino, Yoshihiro Nambu, Taro Yamashita, Shigehito Miki, Hirotaka Terai, Zhen Wang, Morio Toyoshima, Akihisa Tomita, and Masahide Sasaki  »View Author Affiliations


Optics Express, Vol. 22, Issue 11, pp. 13616-13624 (2014)
http://dx.doi.org/10.1364/OE.22.013616


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Abstract

We report on an experimental demonstration of the modified Ekert 91 protocol of quantum key distribution using a hybrid entanglement source with two different degrees of freedoms, a 1550 nm time-bin qubit and 810 nm polarization qubit. The violation of the Clauser-Horne-Shimony-Holt inequality could be demonstrated for the entanglement between the polarization qubit in free space and the time-bin qubit through 20 km fiber transmission. The secure key rate in our system is estimated 70-150 bps.

© 2014 Optical Society of America

1. Introduction

Data theft by directly tapping installed fibers is becoming a reality these years [1]. Quantum key distribution (QKD) [2

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

] provides a mean to detect such hacking on a physical channel, and allows two users to share random numbers with the unconditional security based on the fundamental laws of physics. Recently QKD systems have been deployed in the field environment [3

3. C. Elliott, A. Colvin, D. Pearson, O. Pikalo, J. Schlafer, and H. Yeh, “Current status of the DARPA Quantum Network,” Proc. SPIE 5815, 138–149 (2005). [CrossRef]

5

5. 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(11), 10387–10409 (2011). [CrossRef] [PubMed]

] in parallel with commercialization [6

6. I. D. Quantique, http://www.idquantique.com

,7

7. Q. Magi, Technologies, Inc., http://www.magiqtech.com

]. Moreover, some organizations have started practical use of QKD for their confidential communications [8,9]. Theoretical [10

10. C. C. W. Lim, M. Curty, N. Walenta, F. Xu, and H. Zbinden, “Concise security bounds for practical decoy-state quantum key distribution,” arXiv:quant-ph/1311.7129v1 (2013).

,11

11. K. Tamaki, M. Curty, G. Kato, H.-K. Lo, and K. Azuma, “Loss-tolerant quantum cryptography with imperfect source,” arXiv:quant-ph/1312.3514v2 (2013).

] and experimental [12

12. 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. 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]

14

14. K. Yoshino, T. Ochi, M. Fujiwara, M. Sasaki, and A. Tajima, “Maintenance-free operation of WDM quantum key distribution system through a field fiber over 30 days,” Opt. Express 21(25), 31395–31401 (2013). [CrossRef] [PubMed]

] efforts have been made continuously to enhance the performance and the reliability of QKD systems. Decoy-state methods [15

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

,16

16. X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A 72(1), 012326 (2005). [CrossRef]

] for the Bennett and Brassard scheme (BB84) [17

17. 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.

] and a derived protocol [18

18. M. Lucamarini, K. A. Patel, J. F. Dynes, B. Fröhlich, A. W. Sharpe, A. R. Dixon, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Efficient decoy-state quantum key distribution with quantified security,” Opt. Express 21(21), 24550–24565 (2013). [CrossRef] [PubMed]

] are widely used for long distance QKD through field installed fibers.

For fiber-based QKD, the time-bin format [22

22. W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84(20), 4737–4740 (2000). [CrossRef] [PubMed]

] is widely adopted because of its robustness against polarization mode disturbance. On the other hand, for free space transmission, the polarization format is mostly used. It also allows straightforward implementation of encoding and decoding with high precision and stability by using compact polarizing optical components.

2. Experimental setup of a modified E91 with a hybrid entanglement photon source

An 810 nm photon is input to a format-transformer, whose detailed structure and an equivalent optical setup are shown in Figs. 2(a)
Fig. 2 (a) Conceptual view and (b) equivalent optical setup of the format transformer with 800 ps time delay [28].
and 2(b). The format-transformer consists of a polarizer set at 45° and a polarization sensitive AMZI constructed of a Glan laser prism, polarization-maintained (PM) fiber, and a mirror [28

28. M. Fujiwara, M. Toyoshima, M. Sasaki, K. Yoshino, Y. Nambu, and A. Tomita, “Time-bin polarization format exchange technique for entanglement optical source,” US patent #8509446.

]. The path difference is set to provide the same delay (800 ps) in Bob’s PLC. The polarization qubit thus formed at the 810 nm photon is delivered in free space and coupled to a polarizing decoder circuit at Alice, as shown in Fig. 1(b).

The detectors at Alice side are Si based APDs [Perkin Elmer single photon counting modules (SPCMs)]. The detection efficiency and timing jitter of the SPCM are about 55% and 400 ps, respectively. The dark counts of SPCMs are a few kc/s. The detectors at Bob side are superconducting single photon detectors (SSPDs) [29

29. S. Miki, T. Yamashita, H. Terai, and Z. Wang, “High performance fiber-coupled NbTiN superconducting nanowire single photon detectors with Gifford-McMahon cryocooler,” Opt. Express 21(8), 10208–10214 (2013). [CrossRef] [PubMed]

,30

30. T. Yamashita, S. Miki, H. Terai, and Z. Wang, “Low-filling-factor superconducting single photon detector with high system detection efficiency,” Opt. Express 21(22), 27177–27184 (2013). [CrossRef] [PubMed]

]. The SSPDs have the detection efficiencies around 60-70% at the dark count rate of 100 c/s for 1550 nm photons. The coincidence counts are measured by the time interval analyzer (TIA [Hydra harp 400]). In order to compensate time delay of Bob side due to the fiber transmission, we add delay lines for the signals from Alice, as described in the following. Optical pulses synchronized with the SPCM signals are generated using laser diodes. The optical pulses are multiplexed with the trigger signals by dense wavelength division multiplexing (DWDM) filters and transmitted through 20 km single mode (SM) fibers. Those signals are detected by PIN photodiode, and sent to the TIA.

Through the format-transformer, the entanglement state is created in the following form;
|ϕ=12{|HA|0B+exp[iθ(τ)iθ(0)]|VA|1B},
(1)
where |H> and |V> represent horizontal and vertical polarization states, respectively. The indices A and B abbreviate Alice and Bob. The relative phase θ(t) is defined with respect to a reference path length difference τ between the short and the long arms.

3. Experimental results

Figure 3
Fig. 3 The degree of violation of a CHSH type Bell inequality as a function of the PLC operation temperature.
shows the degree of violation of the CHSH-type Bell inequality as a function of the PLC operation temperature. The phase of the PLC is almost linearly shifted in this region. Coincidence counts are accumulated for 10 s with the time window of 64 ps. The value of S is almost equal when we apply the time window with 128 ps, however, it changes drastically with longer time window. The error bar on the value of S is estimated to be less than 2% using three time measurements. The error bars are smaller than the size of the symbol. The influence of the accidental coincidence counts on both detectors is negligible small due to the narrow time window, so that we don’t correct the accidental coincidence counts. The violation of the CHSH inequality is obtained after 20 km fiber transmission with a modified E91 protocol type implementation.

The average information leakage (IEve) per raw key defined in [32

32. A. Acín, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani, “Device-independent security of quantum cryptography against collective attacks,” Phys. Rev. Lett. 98(23), 230501 (2007). [CrossRef] [PubMed]

] can be estimated using Eq. (4), and plotted in Fig. 4(c). The error bar in this figure is also smaller than the size of the symbol. The difference of the mutual information between Alice and Bob I(A, B) and the leakage information corresponds to the secure key rate. The mutual information between Alice and Bob I(A, B) estimated by the averaged bit error rate is 0.771 shown with red line in Fig. 4(c). The secure key rate (I(A,B)-IEve)is estimated 70-150 bps with our experimental setup.

4. Conclusion

We confirm the entanglement between the polarization qubit in free space and time-bin qubit transmitted through a 20 km fiber with the modified E91 protocol setup. The degree of the violation of the CHSH type Bell inequality and the bit error rate of the raw key indicate that the secure key can be generated with our setup. The key component of this system is the hybrid entanglement photon pair source with the format transformer. It enables us to implement various protocols such as bit commitment or oblivious transfer on the optical fiber. Those protocols provide features different from the QKD function, and proof of principle demonstrations have been carried out with polarization qubit [33

33. N. H. Y. Ng, S. K. Joshi, C. C. Ming, C. Kurtsiefer, and S. Wehner, “Experimental implementation of bit commitment in the noisy-storage model,” Nat. Commun. 3(1326), 1326 (2012). [CrossRef] [PubMed]

,34

34. C. Erven, N. Ng, N. Gigov, R. Laflamme, S. Wehner, and G. Weihs, “An experimental implementation of oblivious transfer in noisy storage model,” arXiv:quant-ph/1308.5098v3 (2014).

]. Our hybrid entanglement photon source can integrate the advantages of polarization and time-bin qubits and implement such protocols with one-to-many service system easily. The hybrid entanglement would thus play indispensable roles in secure photonic networks.

References and links

1.

http://www.thenewamerican.com/usnews/item/16086-nsa-taps-directly-into-undersea-fiber-optic-data-cables

2.

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

3.

C. Elliott, A. Colvin, D. Pearson, O. Pikalo, J. Schlafer, and H. Yeh, “Current status of the DARPA Quantum Network,” Proc. SPIE 5815, 138–149 (2005). [CrossRef]

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.

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(11), 10387–10409 (2011). [CrossRef] [PubMed]

6.

I. D. Quantique, http://www.idquantique.com

7.

Q. Magi, Technologies, Inc., http://www.magiqtech.com

8.

http://finance.yahoo.com/news/battelle-installs-first-commercial-quantum-130000271.html

9.

http://news.xinhuanet.com/english/china/2012-02/21/c_131423541.html

10.

C. C. W. Lim, M. Curty, N. Walenta, F. Xu, and H. Zbinden, “Concise security bounds for practical decoy-state quantum key distribution,” arXiv:quant-ph/1311.7129v1 (2013).

11.

K. Tamaki, M. Curty, G. Kato, H.-K. Lo, and K. Azuma, “Loss-tolerant quantum cryptography with imperfect source,” arXiv:quant-ph/1312.3514v2 (2013).

12.

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. 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]

13.

J. F. Dynes, I. Choi, A. W. Sharpe, A. R. Dixon, Z. L. Yuan, M. Fujiwara, M. Sasaki, and A. J. Shields, “Stability of high bit rate quantum key distribution on installed fiber,” Opt. Express 20(15), 16339–16347 (2012). [CrossRef]

14.

K. Yoshino, T. Ochi, M. Fujiwara, M. Sasaki, and A. Tajima, “Maintenance-free operation of WDM quantum key distribution system through a field fiber over 30 days,” Opt. Express 21(25), 31395–31401 (2013). [CrossRef] [PubMed]

15.

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

16.

X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A 72(1), 012326 (2005). [CrossRef]

17.

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.

18.

M. Lucamarini, K. A. Patel, J. F. Dynes, B. Fröhlich, A. W. Sharpe, A. R. Dixon, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Efficient decoy-state quantum key distribution with quantified security,” Opt. Express 21(21), 24550–24565 (2013). [CrossRef] [PubMed]

19.

K. De Greve, P. L. McMahon, L. Yu, J. S. Pelc, C. Jones, C. M. Natarajan, N. Y. Kim, E. Abe, S. Maier, C. Schneider, M. Kamp, S. Höfling, R. H. Hadfield, A. Forchel, M. M. Fejer, and Y. Yamamoto, “Complete tomography of a high-fidelity solid-state entangled spin-photon qubit pair,” Nat. Commun. 4(2228), 2228 (2013). [PubMed]

20.

T. Inagaki, N. Matsuda, O. Tadanaga, M. Asobe, and H. Takesue, “Entanglement distribution over 300 km of fiber,” Opt. Express 21(20), 23241–23249 (2013). [CrossRef] [PubMed]

21.

R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Ömer, M. Fürst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Entanglement-based quantum communication over 144 km,” Nat. Phys. 3(7), 481–486 (2007). [CrossRef]

22.

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84(20), 4737–4740 (2000). [CrossRef] [PubMed]

23.

M. Fujiwara, M. Toyoshima, M. Sasaki, K. Yoshino, Y. Nambu, and A. Tomita, “Performance of hybrid entanglement photon pair source for quantum key distribution,” Appl. Phys. Lett. 95(26), 261103 (2009). [CrossRef]

24.

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

25.

A. Acín, S. Massar, and S. Pironio, “Efficient quantum key distribution secure against no-signalling eavesdroppers,” New J. Phys. 8(126), 1–11 (2006).

26.

A. Ling, M. P. Peloso, I. Marcikic, V. Sacarani, A. Lamas-Linares, and C. Kurtsiefer, “Experimental quantum key distribution based on a Bell test,” Phys. Rev. A 78(2), 020301 (2008). [CrossRef]

27.

Y. Nambu, K. Yoshino, and A. Tomita, “Quantum encoder and decoder for practical quantum key distribution using a planar lightwave circuit,” J. Mod. Opt. 55(12), 1953–1970 (2008). [CrossRef]

28.

M. Fujiwara, M. Toyoshima, M. Sasaki, K. Yoshino, Y. Nambu, and A. Tomita, “Time-bin polarization format exchange technique for entanglement optical source,” US patent #8509446.

29.

S. Miki, T. Yamashita, H. Terai, and Z. Wang, “High performance fiber-coupled NbTiN superconducting nanowire single photon detectors with Gifford-McMahon cryocooler,” Opt. Express 21(8), 10208–10214 (2013). [CrossRef] [PubMed]

30.

T. Yamashita, S. Miki, H. Terai, and Z. Wang, “Low-filling-factor superconducting single photon detector with high system detection efficiency,” Opt. Express 21(22), 27177–27184 (2013). [CrossRef] [PubMed]

31.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden variable theories,” Phys. Rev. Lett. 23(15), 880–884 (1969). [CrossRef]

32.

A. Acín, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani, “Device-independent security of quantum cryptography against collective attacks,” Phys. Rev. Lett. 98(23), 230501 (2007). [CrossRef] [PubMed]

33.

N. H. Y. Ng, S. K. Joshi, C. C. Ming, C. Kurtsiefer, and S. Wehner, “Experimental implementation of bit commitment in the noisy-storage model,” Nat. Commun. 3(1326), 1326 (2012). [CrossRef] [PubMed]

34.

C. Erven, N. Ng, N. Gigov, R. Laflamme, S. Wehner, and G. Weihs, “An experimental implementation of oblivious transfer in noisy storage model,” arXiv:quant-ph/1308.5098v3 (2014).

OCIS Codes
(060.5565) Fiber optics and optical communications : Quantum communications
(270.5568) Quantum optics : Quantum cryptography

ToC Category:
Quantum Optics

History
Original Manuscript: April 9, 2014
Revised Manuscript: May 23, 2014
Manuscript Accepted: May 23, 2014
Published: May 29, 2014

Citation
Mikio Fujiwara, Ken-ichiro Yoshino, Yoshihiro Nambu, Taro Yamashita, Shigehito Miki, Hirotaka Terai, Zhen Wang, Morio Toyoshima, Akihisa Tomita, and Masahide Sasaki, "Modified E91 protocol demonstration with hybrid entanglement photon source," Opt. Express 22, 13616-13624 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-11-13616


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References

  1. http://www.thenewamerican.com/usnews/item/16086-nsa-taps-directly-into-undersea-fiber-optic-data-cables
  2. N. Gisin, G. Ribordy, W. Tittel, H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002). [CrossRef]
  3. C. Elliott, A. Colvin, D. Pearson, O. Pikalo, J. Schlafer, H. Yeh, “Current status of the DARPA Quantum Network,” Proc. SPIE 5815, 138–149 (2005). [CrossRef]
  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, A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys. 11(7), 075001 (2009). [CrossRef]
  5. 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, A. Zeilinger, “Field test of quantum key distribution in the Tokyo QKD Network,” Opt. Express 19(11), 10387–10409 (2011). [CrossRef] [PubMed]
  6. I. D. Quantique, http://www.idquantique.com
  7. Q. Magi, Technologies, Inc., http://www.magiqtech.com
  8. http://finance.yahoo.com/news/battelle-installs-first-commercial-quantum-130000271.html
  9. http://news.xinhuanet.com/english/china/2012-02/21/c_131423541.html
  10. C. C. W. Lim, M. Curty, N. Walenta, F. Xu, and H. Zbinden, “Concise security bounds for practical decoy-state quantum key distribution,” arXiv:quant-ph/1311.7129v1 (2013).
  11. K. Tamaki, M. Curty, G. Kato, H.-K. Lo, and K. Azuma, “Loss-tolerant quantum cryptography with imperfect source,” arXiv:quant-ph/1312.3514v2 (2013).
  12. 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. Voirol, N. Walenta, H. Zbinden, “Long-term performance of the SwissQuantum quantum key distribution network in a field environment,” New J. Phys. 13(12), 123001 (2011). [CrossRef]
  13. J. F. Dynes, I. Choi, A. W. Sharpe, A. R. Dixon, Z. L. Yuan, M. Fujiwara, M. Sasaki, A. J. Shields, “Stability of high bit rate quantum key distribution on installed fiber,” Opt. Express 20(15), 16339–16347 (2012). [CrossRef]
  14. K. Yoshino, T. Ochi, M. Fujiwara, M. Sasaki, A. Tajima, “Maintenance-free operation of WDM quantum key distribution system through a field fiber over 30 days,” Opt. Express 21(25), 31395–31401 (2013). [CrossRef] [PubMed]
  15. H.-K. Lo, X. Ma, K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94(23), 230504 (2005). [CrossRef] [PubMed]
  16. X. Ma, B. Qi, Y. Zhao, H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A 72(1), 012326 (2005). [CrossRef]
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