## Long-distance entanglement-based quantum key distribution over optical fiber

Optics Express, Vol. 16, Issue 23, pp. 19118-19126 (2008)

http://dx.doi.org/10.1364/OE.16.019118

Acrobat PDF (207 KB)

### Abstract

We report the first entanglement-based quantum key distribution (QKD) experiment over a 100-km optical fiber. We used superconducting single photon detectors based on NbN nanowires that provide high-speed single photon detection for the 1.5-µm telecom band, an efficient entangled photon pair source that consists of a fiber coupled periodically poled lithium niobate waveguide and ultra low loss filters, and planar lightwave circuit Mach-Zehnder interferometers (MZIs) with ultra stable operation. These characteristics enabled us to perform an entanglement-based QKD experiment over a 100-km optical fiber. In the experiment, which lasted approximately 8 hours, we successfully generated a 16 kbit sifted key with a quantum bit error rate of 6.9 % at a rate of 0.59 bits per second, from which we were able to distill a 3.9 kbit secure key.

© 2008 Optical Society of America

## 1. Introduction

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

2. H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, “Quantum key distribution over 40 dB channel loss using superconducting single-photon detectors,” Nat. Photonics **1**, 343 (2007). [CrossRef]

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

4. C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bell’s theorem,” Phys. Rev. Lett. **68**, 557–559 (1992). [CrossRef] [PubMed]

5. T. Jennewein, C Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett. **84**, 4729–4732 (2000). [CrossRef] [PubMed]

10. T. Honjo, H. Takesue, and K. Inoue, “Differential-phase quantum key distribution experiment using a series of quantum entangled photon pairs,” Opt. Lett. **32**, 1165 (2007). [CrossRef] [PubMed]

8. S. Fasel, N. Gisin, G. Ribordy, and H. Zbinden, “Quantum key distribution over 30 km of standard fiber using energy-time entangled photon pairs: a comparison of two chromatic dispersion reduction methods,” Eur. Phys. J. D **30**, 2013148 (2004). [CrossRef]

10. T. Honjo, H. Takesue, and K. Inoue, “Differential-phase quantum key distribution experiment using a series of quantum entangled photon pairs,” Opt. Lett. **32**, 1165 (2007). [CrossRef] [PubMed]

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

11. A. Yoshizawa, R. Kaji, and H. Tsuchida, “Gated-mode single-photon detection at 1550 nm by discharge pulse counting,” Appl. Phys. Lett. **84**, 3606 (2004). [CrossRef]

12. M. A. Albota and F. N. C. Wong, , “Efficient single-photon counting at 1.55 µm by means of frequency upconversion,” Opt. Lett. **29**, 1449–1451 (2004). [CrossRef] [PubMed]

13. C. Langrock, E. Diamanti, R. V. Roussev, Y. Yamamoto, M. M. Fejer, and H. Takesue, “Highly efficient single-photon detection at communication wavelengths by use of upconversion in reverse-protonexchanged periodically poled LiNbO3 waveguides,” Opt. Lett. **30**, 1725–1727 (2005). [CrossRef] [PubMed]

14. N. Namekata, S. Sasamori, and S. Inoue, “800 MHz single-photon detection at 1550-nm using an InGaAs/InP avalanche photodiode operated with a sine wave gating,” Opt. Express **14**, 10043–10049 (2006). [CrossRef] [PubMed]

15. G. N. 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 optical detector,” Appl. Phys. Lett. **79**, 705 (2001). [CrossRef]

17. A. Yoshizawa, R. Kaji, and H. Tsuchida, “Generation of polarization-entangled. photon pairs at 1550 nm using two PPLN waveguides,” Electron. Lett. **39**, 621–622 (2003). [CrossRef]

18. X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, “Optical-fiber source of polarization-entangled photons in the 1550 nm telecom band,” Phys. Rev. Lett. **94**, 053601 (2005). [CrossRef] [PubMed]

20. H. Takesue, Y. Tokura, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, and S. Itabashi, “Entanglement generation using silicon wire waveguide,” Appl. Phys. Lett. **91**, 201108 (2007). [CrossRef]

21. T. Honjo, K. Inoue, and H. Takahashi, “Differential-phase-shift quantum key distribution experiment with a planar light-wave circuit Mach-Zehnder interferometer,” Opt. Lett. **29**, 23, 2797, (2004). [CrossRef]

## 2. BBM92 QKD with time-bin entangled photon pairs

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

22. J. Brendel, W. Tittel, H. Zbinden, and N. Gisin, “Pulsed energy-time entangled twin-photon source for quantum Communication,” Phys. Rev. Lett. **82**, 2594 (1999). [CrossRef]

24. H. Takesue and K. Inoue, “Generation of 1.5-um band time-bin entanglement using spontaneous fiber four-wave mixing and planar lightwave circuit interferometers,” Phys. Rev. A **72**, 041804(R) (2005). [CrossRef]

*k*>

*represents a state in which there is a photon in the*

_{x}*k*th time slot in mode

*x*, signal (

*s*) or idler (

*i*). The signal and idler photons are separated by an optical filter, and then transmitted to Alice and Bob, respectively. At each site, each photon is passed through a 1-bit delay MZI, which splits the photon into three time slots, t1, t2 and t3. In the 2

^{nd}time slot, a state in which the photon passed through the long path of the MZI and another state in which the photon passed through the short path of the MZI interfere with each other. The final state is described by

*tn*>

*represents a state in which a photon is detected at time slot*

_{x}*tn*on side

*x*, |

*Dn*,

*tn*>

*represents a state in which a photon is detected at time slot*

_{x}*tn*and detector

*d*on side

*x*, and θ

*represents the phase difference of the MZI on side*

_{x}*x*, Alice (a) or Bob (b). In Eq. (2), the states in which Alice and Bob detect photons at different time slots are omitted. A pair consisting of the 1

^{st}and 3

^{rd}time slots is called time-basis and the 2

^{nd}time slot is called energy-basis. To obtain a perfect correlation, we set the sum of the phase differences, θ

_{a}+θ

_{b}, of these MZIs at 0. When we post-select a case where both Alice and Bob detect photons in the t2 time slot (energy-basis), the final state is described by Eq. (3).

*d*>

*represents a state in which a photon is detected at detector*

_{x}*d*on side

*x*, Alice (a) or Bob (b). In this case, a correlation appears between detectors. On the other hand, when we post-select the case where both Alice and Bob detect a photon in time slot t1 or t3 (timebasis), the final state is described by Eq. (4).

*t*>

*represents a state in which a photon is detected at time slot*

_{x}*t*on side

*x*, Alice (a) or Bob (b). In this case, a correlation appears between the detection times. Selection on the above basis is made spontaneously with no active selection procedure.

## 3. Experimental setup

25. T. Honjo, H. Takesue, H. Kamada, Y. Nishida, O. Tadanaga, M. Asobe, and K. Inoue, “Long-distance distribution of time-bin entangled photon pairs over 100 km using frequency up-conversion detectors,” Opt. Express , **15**, 13957–13964 (2007). [CrossRef] [PubMed]

_{3}intensity modulator. The pulse width and repetition frequency were 100 ps and 1 GHz, respectively. A series of double pulses was generated by extinguishing one of three sequential pulses with another intensity modulator. The coherence time of the laser output was ~10 µs, which is far longer than the temporal interval between the double pulses. The pulses were amplified with an erbium-doped fiber amplifier (EDFA) and filtered through a fiber Bragg grating filter that suppresses the amplified spontaneous emission noise from the EDFA. After passing through a polarization controller, the pulses were launched into PPLN (1), where a series of 775.5-nm double pulses was generated by the second harmonic generation process. The output light from PPLN (1) was input into filters that transmitted the 775.5-nm pulses while eliminating the remaining 1551-nm light. The series of 775.5-nm double pulses was polarization-controlled and then input into PPLN (2). A series of time-bin entangled photon pairs was generated in PPLN (2) by the parametric down conversion process [26]. The pump, signal and idler frequencies are denoted by

*f*

*p*,,

*f*

*and*

_{s}*f*

*, respectively. These three frequencies have a relationship of*

_{i}*f*

*,=*

_{p}*f*

*+*

_{s}*f*

*,.*

_{i}21. T. Honjo, K. Inoue, and H. Takahashi, “Differential-phase-shift quantum key distribution experiment with a planar light-wave circuit Mach-Zehnder interferometer,” Opt. Lett. **29**, 23, 2797, (2004). [CrossRef]

27. R. H. Hadfield, M. J. Stevens, S. S. Gruber, A. J. Miller, R. E. Schwall, R. P. Mirin, and S. W. Nam, “Single photon source characterization with a superconducting single photon detector,” Opt. Express **13**, 10846–10853 (2005). [CrossRef] [PubMed]

28. S. Miki, M. Fujiwara, M. Sasaki, A. J. Miller, R. H. Hadfield, S. W. Nam, and Z. Wang, “Large sensitive-area NbN nanowire superconducting single-photon detectors fabricated on single-crystal MgO substrates,” Appl. Phys. Lett. **92**, 061116 (2008). [CrossRef]

## 4. Experimental results

*n*pairs in a given pulse had a Poisson distribution [29

29. P. R. Tapster and J. G. Rarity, “Photon statistics of pulsed parametric light,” J. Mod. Optics **45**, 595–604 (1998). [CrossRef]

*c*

*and*

_{s}*c*

*, respectively, as [30*

_{i}30. H. Takesue, “Long-distance distribution of time-bin entanglement generated in a cooled fiber,” Opt. Express **14**, 3453 (2006). [CrossRef] [PubMed]

*R*

*and*

_{cc}*R*

*, respectively, as follows.*

_{acc}*V*, is then given by

*R*

*, is expressed as follows.*

_{sift}*µ*

*is the average number of photon pairs per time-bin entanglement slot, and*

_{t}*f*is the repetition frequency of the distribution of the time-bin entanglement slots, and the other parameters are the same as in Eqs. (5) and (6). Half of the accidental coincidences contribute to the error and so QBER is expressed as follows.

*µ*

*is*

_{c}*µ*

*/*

_{t}*2*in this evaluation. Substituting the estimated average number of photon pairs per time-bin entanglement slot of 0.04 and the other experimental conditions, we theoretically estimated the sifted key generation rate to be 30.0 bps and the QBER to be 1.9 %, which shows that our experimental results are reasonable. In addition, we estimated the secure key generation rate from the above experimental results. The secure key distribution rate against any individual attack for the BBM92 QKD protocol is given by the following expression [31

31. E. Waks, A. Zeevi, Y. Zeevi, and Yamamoto, “Security of quantum key distribution with entangled photons against individual attacks,” Phys. Rev. A **65**, 052310 (2002). [CrossRef]

*e*and

*f*(

*e*) represent the bit error rate in a sifted key and the performance of the error correction algorithm, respectively. With the above equation, an 86,248-bit secure key will be distilled from our sifted keys with a key generation rate of 20.2 bps.

## 5. Summary

## References and links

1. | N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. |

2. | H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, “Quantum key distribution over 40 dB channel loss using superconducting single-photon detectors,” Nat. Photonics |

3. | A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. |

4. | C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bell’s theorem,” Phys. Rev. Lett. |

5. | T. Jennewein, C Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett. |

6. | D. S. Naik, C. G. Peterson, A. G. White, A. J. Berglund, and P. G. Kwiat, “Entangled state quantum cryptography: eavesdropping on the Ekert protocol,” Phys. Rev. Lett. |

7. | W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Quantum Cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. |

8. | S. Fasel, N. Gisin, G. Ribordy, and H. Zbinden, “Quantum key distribution over 30 km of standard fiber using energy-time entangled photon pairs: a comparison of two chromatic dispersion reduction methods,” Eur. Phys. J. D |

9. | A. Poppe, A. Fedrizzi, R. Ursin, H. Bohm, T. Lorunser, O. Maurhardt, M. Peev, M. Suda, C. Kurtsiefer, H. Weinfurter, T. Jennewein, and A. Zeilinger, “Practical quantum key distribution with polarization entangled photons,” Opt. Express , |

10. | T. Honjo, H. Takesue, and K. Inoue, “Differential-phase quantum key distribution experiment using a series of quantum entangled photon pairs,” Opt. Lett. |

11. | A. Yoshizawa, R. Kaji, and H. Tsuchida, “Gated-mode single-photon detection at 1550 nm by discharge pulse counting,” Appl. Phys. Lett. |

12. | M. A. Albota and F. N. C. Wong, , “Efficient single-photon counting at 1.55 µm by means of frequency upconversion,” Opt. Lett. |

13. | C. Langrock, E. Diamanti, R. V. Roussev, Y. Yamamoto, M. M. Fejer, and H. Takesue, “Highly efficient single-photon detection at communication wavelengths by use of upconversion in reverse-protonexchanged periodically poled LiNbO3 waveguides,” Opt. Lett. |

14. | N. Namekata, S. Sasamori, and S. Inoue, “800 MHz single-photon detection at 1550-nm using an InGaAs/InP avalanche photodiode operated with a sine wave gating,” Opt. Express |

15. | G. N. 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 optical detector,” Appl. Phys. Lett. |

16. | S. Tanzilli, W. Tittel, H. De Riedmatten, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Euro Phys. J. |

17. | A. Yoshizawa, R. Kaji, and H. Tsuchida, “Generation of polarization-entangled. photon pairs at 1550 nm using two PPLN waveguides,” Electron. Lett. |

18. | X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, “Optical-fiber source of polarization-entangled photons in the 1550 nm telecom band,” Phys. Rev. Lett. |

19. | H. Takesue and K. Inoue, “Generation of polarization entangled photon pairs and violation of Bell’s inequality using spontaneous four-wave mixing in a fiber loop,” Phys. Rev. A |

20. | H. Takesue, Y. Tokura, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, and S. Itabashi, “Entanglement generation using silicon wire waveguide,” Appl. Phys. Lett. |

21. | T. Honjo, K. Inoue, and H. Takahashi, “Differential-phase-shift quantum key distribution experiment with a planar light-wave circuit Mach-Zehnder interferometer,” Opt. Lett. |

22. | J. Brendel, W. Tittel, H. Zbinden, and N. Gisin, “Pulsed energy-time entangled twin-photon source for quantum Communication,” Phys. Rev. Lett. |

23. | I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, “Time-bin entangled qubits for quantum communication created by femtosecond pulses,” Phys. Rev. A |

24. | H. Takesue and K. Inoue, “Generation of 1.5-um band time-bin entanglement using spontaneous fiber four-wave mixing and planar lightwave circuit interferometers,” Phys. Rev. A |

25. | T. Honjo, H. Takesue, H. Kamada, Y. Nishida, O. Tadanaga, M. Asobe, and K. Inoue, “Long-distance distribution of time-bin entangled photon pairs over 100 km using frequency up-conversion detectors,” Opt. Express , |

26. | M. Asobe, H. Miyazawa, O. Tadanaga, Y. Nishida, and H. Suzuki, “Wavelength conversion using quasi-phase matched LiNbO |

27. | R. H. Hadfield, M. J. Stevens, S. S. Gruber, A. J. Miller, R. E. Schwall, R. P. Mirin, and S. W. Nam, “Single photon source characterization with a superconducting single photon detector,” Opt. Express |

28. | S. Miki, M. Fujiwara, M. Sasaki, A. J. Miller, R. H. Hadfield, S. W. Nam, and Z. Wang, “Large sensitive-area NbN nanowire superconducting single-photon detectors fabricated on single-crystal MgO substrates,” Appl. Phys. Lett. |

29. | P. R. Tapster and J. G. Rarity, “Photon statistics of pulsed parametric light,” J. Mod. Optics |

30. | H. Takesue, “Long-distance distribution of time-bin entanglement generated in a cooled fiber,” Opt. Express |

31. | E. Waks, A. Zeevi, Y. Zeevi, and Yamamoto, “Security of quantum key distribution with entangled photons against individual attacks,” Phys. Rev. A |

**OCIS Codes**

(190.4370) Nonlinear optics : Nonlinear optics, fibers

(270.0270) Quantum optics : Quantum optics

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: September 22, 2008

Revised Manuscript: October 28, 2008

Manuscript Accepted: October 28, 2008

Published: November 4, 2008

**Citation**

T. Honjo, S. W. Nam, H. Takesue, Q. Zhang, H. Kamada, Y. Nishida, O. Tadanaga, M. Asobe, B. Baek, R Hadfield, S. Miki, M. Fujiwara, M. Sasaki, Z. Wang, K. Inoue, and Y. Yamamoto, "Long-distance entanglement-based quantum key distribution over optical fiber," Opt. Express **16**, 19118-19126 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-23-19118

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### References

- N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, "Quantum cryptography," Rev. Mod. Phys. 74, 145 (2002). [CrossRef]
- H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, "Quantum key distribution over 40 dB channel loss using superconducting single-photon detectors," Nat. Photonics 1, 343 (2007). [CrossRef]
- A. K. Ekert, "Quantum cryptography based on Bell's theorem," Phys. Rev. Lett. 67, 661-663 (1991). [CrossRef] [PubMed]
- C. H. Bennett, G. Brassard and N. D. Mermin, "Quantum cryptography without Bell's theorem," Phys. Rev. Lett. 68, 557-559 (1992). [CrossRef] [PubMed]
- T. Jennewein, C Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, "Quantum cryptography with entangled photons," Phys. Rev. Lett. 84, 4729-4732 (2000). [CrossRef] [PubMed]
- D. S. Naik, C. G. Peterson, A. G. White, A. J. Berglund, and P. G. Kwiat, "Entangled state quantum cryptography: eavesdropping on the Ekert protocol," Phys. Rev. Lett. 84, 4733-4736 (2000). [CrossRef] [PubMed]
- W. Tittel, J. Brendel, H. Zbinden and N. Gisin, "Quantum Cryptography using entangled photons in energy-time Bell states," Phys. Rev. Lett. 84, 4737-4740 (2000). [CrossRef] [PubMed]
- S. Fasel, N. Gisin, G. Ribordy, and H. Zbinden, "Quantum key distribution over 30 km of standard fiber using energy-time entangled photon pairs: a comparison of two chromatic dispersion reduction methods," Eur. Phys. J. D 30, 2013148 (2004). [CrossRef]
- A. Poppe A. Fedrizzi, R. Ursin, H. Bohm, T. Lorunser, O. Maurhardt, M. Peev, M. Suda, C. Kurtsiefer, H. Weinfurter, T. Jennewein, A. Zeilinger, "Practical quantum key distribution with polarization entangled photons," Opt. Express 12, 3865-3871 (2004). [CrossRef] [PubMed]
- T. Honjo, H. Takesue and K. Inoue, "Differential-phase quantum key distribution experiment using a series of quantum entangled photon pairs," Opt. Lett. 32, 1165 (2007). [CrossRef] [PubMed]
- A. Yoshizawa, R. Kaji and H. Tsuchida, "Gated-mode single-photon detection at 1550 nm by discharge pulse counting," Appl. Phys. Lett. 84, 3606 (2004). [CrossRef]
- M. A. Albota and F. N. C. Wong, "Efficient single-photon counting at 1.55 ?m by means of frequency upconversion," Opt. Lett. 29, 1449-1451 (2004). [CrossRef] [PubMed]
- C. Langrock, E. Diamanti, R. V. Roussev, Y. Yamamoto, M. M. Fejer, and H. Takesue, "Highly efficient single-photon detection at communication wavelengths by use of upconversion in reverse-proton-exchanged periodically poled LiNbO3 waveguides," Opt. Lett. 30, 1725-1727 (2005). [CrossRef] [PubMed]
- N. Namekata, S. Sasamori, and S. Inoue, "800 MHz single-photon detection at 1550-nm using an InGaAs/InP avalanche photodiode operated with a sine wave gating," Opt. Express 14, 10043-10049 (2006). [CrossRef] [PubMed]
- G. N. 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 optical detector," Appl. Phys. Lett. 79, 705 (2001). [CrossRef]
- S. Tanzilli, W. Tittel, H. De Riedmatten, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, "PPLN waveguide for quantum communication," Euro Phys. J. 18, 155-160 (2002).
- A. Yoshizawa, R. Kaji, and H. Tsuchida, "Generation of polarization-entangled. photon pairs at 1550 nm using two PPLN waveguides," Electron. Lett. 39, 621-622 (2003). [CrossRef]
- X. Li, P. L. Voss, J. E. Sharping and P. Kumar, "Optical-fiber source of polarization-entangled photons in the 1550 nm telecom band," Phys. Rev. Lett. 94, 053601 (2005). [CrossRef] [PubMed]
- H. Takesue and K. Inoue, "Generation of polarization entangled photon pairs and violation of Bell's inequality using spontaneous four-wave mixing in a fiber loop," Phys. Rev. A 70, 031802(R) (2004). [CrossRef]
- H. Takesue, Y. Tokura, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, and S. Itabashi, "Entanglement generation using silicon wire waveguide," Appl. Phys. Lett. 91, 201108 (2007). [CrossRef]
- T. Honjo, K. Inoue and H. Takahashi, "Differential-phase-shift quantum key distribution experiment with a planar light-wave circuit Mach-Zehnder interferometer," Opt. Lett. 29, 23, 2797, (2004). [CrossRef]
- J. Brendel, W. Tittel, H. Zbinden and N. Gisin, "Pulsed energy-time entangled twin-photon source for quantum Communication," Phys. Rev. Lett. 82, 2594 (1999). [CrossRef]
- I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, "Time-bin entangled qubits for quantum communication created by femtosecond pulses," Phys. Rev. A 66, 062308 (2002). [CrossRef]
- H. Takesue and K. Inoue, "Generation of 1.5-um band time-bin entanglement using spontaneous fiber four-wave mixing and planar lightwave circuit interferometers," Phys. Rev. A 72, 041804(R) (2005). [CrossRef]
- T. Honjo, H. Takesue, H. Kamada, Y. Nishida, O. Tadanaga, M. Asobe and K. Inoue, "Long-distance distribution of time-bin entangled photon pairs over 100 km using frequency up-conversion detectors," Opt. Express 15, 13957-13964 (2007). [CrossRef] [PubMed]
- M. Asobe, H. Miyazawa, O. Tadanaga, Y. Nishida, and H. Suzuki, "Wavelength conversion using quasi-phase matched LiNbO3 waveguides," The Optical Electronics and Communications Conference, Yokohama, Japan, July 8-12 2002, paper PD2-8.
- R. H. Hadfield, M. J. Stevens, S. S. Gruber, A. J. Miller, R. E. Schwall, R. P. Mirin, and S. W. Nam, "Single photon source characterization with a superconducting single photon detector," Opt. Express 13, 10846-10853 (2005). [CrossRef] [PubMed]
- S. Miki, M. Fujiwara, M. Sasaki, A. J. Miller, R. H. Hadfield, S. W. Nam and Z. Wang, "Large sensitive-area NbN nanowire superconducting single-photon detectors fabricated on single-crystal MgO substrates," Appl. Phys. Lett. 92, 061116 (2008). [CrossRef]
- P. R. Tapster and J. G. Rarity, "Photon statistics of pulsed parametric light," J. Mod. Optics 45, 595-604 (1998). [CrossRef]
- H. Takesue, "Long-distance distribution of time-bin entanglement generated in a cooled fiber," Opt. Express 14, 3453 (2006). [CrossRef] [PubMed]
- E. Waks, A. Zeevi, and Y. Yamamoto, "Security of quantum key distribution with entangled photons against individual attacks," Phys. Rev. A 65, 052310 (2002). [CrossRef]

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