## Quantum key distribution at 1550 nm using a pulse heralded single photon source

Optics Express, Vol. 15, Issue 2, pp. 726-734 (2007)

http://dx.doi.org/10.1364/OE.15.000726

Acrobat PDF (154 KB)

### Abstract

Quantum key distribution with pulsed heralded single photon source was performed over 40 km of fiber for the first time to our knowledge. QBER was measured to be 4.23% suggesting security against unconditional attack.

© 2007 Optical Society of America

## 1. Introduction

2. C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” J. Cryptology **5**,3–28 (1992). [CrossRef]

3. P. Townsend, J. G. Rarity, and P. R. Tapster, “Single photon interference in a 10 km long optical fiber interferometer,” Electron. Lett. **29**,634–639 (1993a). [CrossRef]

*P*(2) cannot be decreased without sacrificing

*P*(1), the probability to have one photon in one pulse [4

4. G. Brassard, N. Lütkenhaus, T. Mor, and B. C. Sanders, “Limitations on practical quantum cryptography,” Phys. Rev. Lett. **85**,1330–1333 (2000). [CrossRef] [PubMed]

5. V. Scarani, A. Acín, G. Ribordy, and N. Gisin, “Quantum cryptography protocols robust against photon number splitting attacks for weak laser pulse implementations,” Phys. Rev. Lett. **92**,0579014 (2004). [CrossRef]

6. K. Inoue and T. Honjo, “Robustness of differential-phase-shift quantum key distribution against photon-numbersplitting attack,” Phys. Rev. A **71**,042305(2005). [CrossRef]

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

8. Y. Zhao, B. Qi, X. Ma, H.-K. Lo, and L. Qian,“Experimental quantum key distribution with decoy states,” Phys. Rev. Lett. **96**,070502 (2006). [CrossRef] [PubMed]

4. G. Brassard, N. Lütkenhaus, T. Mor, and B. C. Sanders, “Limitations on practical quantum cryptography,” Phys. Rev. Lett. **85**,1330–1333 (2000). [CrossRef] [PubMed]

9. S. Fasel, O. Alibart, A. Beveratos, S. Tanzilli, H. Zbinden, P. Baldi, and N. Gisin,“High-quality asynchronous heralded single-photon source at telecom wavelength,” New J. of Phys. **6**,163 (2004). [CrossRef]

10. Shigeki Takeuchi, Ryo Okamoto, and Keiji Sasaki,“High-yield single-photon source using gated spontaneous parametric downconversion,” Appl. Opt. **43** ,5708–5711 (2004). [CrossRef] [PubMed]

11. Ryo Okamoto, Shigeki Takeuchi, and Keiji Sasaki, “Detailed analysis of a single-photon source using gated spontaneous parametric downconversion,” J. Opt. Soc. Am. B **22**,2393–2401 (2005). [CrossRef]

12. A. Trifonov and A. Zavriyev,“Secure communication with a heralded single-photon source,” J. Opt. B **7**,S772–S777 (2005). [CrossRef]

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

14. 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]

15. H. Briegel, W. Dür, J. I. Cirac, and P. Zoller,“Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. **81**,5932–5935 (1998). [CrossRef]

*P*(2)=1.48×10

^{-5}) achieved after the sender station, we achieved QKD experiment with the quantum bit error rate (QBER) 4.23 % suggesting unconditional security [17]. Since we adopted pulsed HSPS, the system clocks (82 MHz) at the sender and the receiver were well synchronized, and is suitable for the future quantum-relays and quantum repeaters.

## 2. Heralded Single Photon Source

### 2.1. Principle

### 2.2. HSPS statistics

*n*=3 can be neglected [19

19. Using a model presented in reference [10, 11, 16], we estimated the average number of photon pairs *μ* at the crystal output to be 0.168 at the maximum pump power (195 mW), and 3 pairs event probability at the crystal ouput to be a fraction equal to 0.056 of the two pairs generation probability for this pump power.

*P*(1) and

*P*(2), the probability to have one or two photons at our HSPS output when a trigger signal was recorded in the signal path. Coincidences were recorded using a photon counter (Stanford Research SR400) for different pump powers. Accidental coincidence counts caused mostly by the simultaneous detection of a dark count and a single photon in the HBT setup were subtracted from the measured coincidences [9

9. S. Fasel, O. Alibart, A. Beveratos, S. Tanzilli, H. Zbinden, P. Baldi, and N. Gisin,“High-quality asynchronous heralded single-photon source at telecom wavelength,” New J. of Phys. **6**,163 (2004). [CrossRef]

*P*(1) is unity. In experiment

*P*(1) is limited by coupling efficiency of idler photons into single mode fiber (0.351) and also by optical losses (transmission coefficient of 0.842). The increase of

*P*(1) (from 0.18 to 0.296) compared to our previous experiment [16] can be explained by the new lens inserted in the setup and also a better aligment procedure.

*P*(1) decreases when decreasing pump power, due to a technical reason: When inserting optical attenuators in the pump beam to control pump power, the pump beam propagation axis was sligthly deviated, which caused a decrease of coupling efficiency for idler photons. The effect was compensated by realigning carefully the fiber coupler in the idler path when we performed QKD experiments.

*P*(2) for different pump power. In table 1 we give

*P*(2) with standard deviation calculated from experimental data. To find the true dependance of

*P*(2) to the pump power and avoid artifact due to the degradation of coupling losses caused by the optical attenuators, we applied a correction to

*P*(2),

*P*(2)=

_{c}*P*(2)×(0.296)

^{2}/

*P*(1)

^{2}which is plotted in Fig. 2. The linear regression for

*P*(2) gives a coefficient of 8.65×10

^{c}^{-5}pairs of photons per mW at our HSPS output. As our set up to measure

*P*(2) is limited by accidental coincidences, we cannot measure

*P*(2) below 1.24×10

^{-4}. For further QKD experiments with lower value of

*P*(2), we calculated our source

*P*(2) using the linear law governing

*P*(2) derived above.

### 2.3. HSPS spectrum

12. A. Trifonov and A. Zavriyev,“Secure communication with a heralded single-photon source,” J. Opt. B **7**,S772–S777 (2005). [CrossRef]

## 3. QKD system

20. C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett. **68**,3121–3124
(1992). [CrossRef] [PubMed]

*π*,

*π*/2 and 3

*π*/2) on one of the two optical signals (separated by the interferometer path delay) at the output of her interferometer. Bob applies one of two phase shifts (0,

*π*/2) on one of the two optical signals before his interferometer to choose the measurement basis. Bob could also use a beam splitter and two interferometers (passive choice of the base) instead of a phase modulator and a Mach-Zehnder. The main drawback of this system is that half of the photons are lost at the first Mach-Zehnder due to the unused interferometer output at Alice, and an other half are lost at Bob’s interferometer due to non interfering events.

*μs*and the second one is used to adjust delay between Alice and Bob. The second channel carries the 82 MHz clock signal from the femtosecond pump laser using a special optical emitter (Gravitron WSM-2) and receiver (Gravitron WRM-2) with very low jitter. This clock is used as a time reference for our QKD system. Phase modulation signals at Alice and Bob as well as detector gating signal at Bob are synchronized to the 82 MHz clock signal and applied only when a heralding signal is also present. With such a system, we are freed from the jitter (500 ps) of the gate signal due to SPCM (intrinsic jitter). The three optical channels could be multiplexed for transmission over only one fiber using standard wavelength division multiplexing technique. Time division multiplexing should also be used, to avoid propagation at the same time of the quantum signal and synchronization signals in order to reduce optical crosstalk at Bob’s receiver.

*d*per gate and quantum efficiency

_{B}*η*of detector are 2.05×10

_{B}^{-6}and 9.62% for detector 1, and 2.05×10

^{-6}and 8.64% for detector 2.

## 4. QKD results analysis

*P*(2) low enough to ensure security for QKD over 40 km. After inserting optical attenuators, we realigned the HSPS and then measured

*P*(1). HSPS rate was 12.4 kHz,

*P*(1) and

_{A}*P*(2), the probability to have one or two photons at Alice PMA output were estimated respectively to be 0.0423 and 1.48×10

_{A}^{-5}taking the losses in Alice set up into account. For the pump power used, three pairs event probability at the crystal output represent a fraction equal to 0.0028 of the two pairs probability. Bob receiver’s optical losses were 7.3 dB, and average visibility was 97% for interference fringes.

*Q*is the QBER,

*p*is the probability for Bob to have a detection in a time slot,

_{exp}*p*is the probability to have two photons at Alice output (equals to

_{m}*P*(2)). H is the entropy function. This gain was calculated in an asymptotic case, valid for on/off detectors with balanced quantum efficiencies [21]. QKD with security against coherent attack was confirmed for our experiment, with a positive

_{A}*G*of 1.35×10

^{-5}, equivalent to 44 bits in the final key (secret key creation rate is 0.16 secure bit/s). We estimated statistical fluctuation in our experiment. For our system, the expected QBER calculated from measured system parameters (detectors noise and quantum efficiency, losses, visibility and

*P*(1)) is 4.18±1.77%. This is consistent with our experiment result. We also checked the reliability of the measured QBER using hypothesis testing, and found that with a confidence of 90 % QBER is ≤ 7% , which is below the threshold QBER (8.61 %) for secure QKD.

_{A}*P*(1) similar to our HSPS (and

*P*(2)=0), secure communication is achievable over 76 km.With a further decrease of the

*P*(2) of our source, we can approach this limit.

## 5. Conclusion

22. M. Hayashi, “Practical evaluation of security for quantum key distribution,” Phys. Rev. A **74**,022307 (2006). [CrossRef]

## Acknowledgement

## References and links

1. | C.H. Bennett and G. Brassard, in |

2. | C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” J. Cryptology |

3. | P. Townsend, J. G. Rarity, and P. R. Tapster, “Single photon interference in a 10 km long optical fiber interferometer,” Electron. Lett. |

4. | G. Brassard, N. Lütkenhaus, T. Mor, and B. C. Sanders, “Limitations on practical quantum cryptography,” Phys. Rev. Lett. |

5. | V. Scarani, A. Acín, G. Ribordy, and N. Gisin, “Quantum cryptography protocols robust against photon number splitting attacks for weak laser pulse implementations,” Phys. Rev. Lett. |

6. | K. Inoue and T. Honjo, “Robustness of differential-phase-shift quantum key distribution against photon-numbersplitting attack,” Phys. Rev. A |

7. | H.-K. Lo, X. Ma, and K. Chen,“Decoy state quantum key distribution,” Phys. Rev. Lett. |

8. | Y. Zhao, B. Qi, X. Ma, H.-K. Lo, and L. Qian,“Experimental quantum key distribution with decoy states,” Phys. Rev. Lett. |

9. | S. Fasel, O. Alibart, A. Beveratos, S. Tanzilli, H. Zbinden, P. Baldi, and N. Gisin,“High-quality asynchronous heralded single-photon source at telecom wavelength,” New J. of Phys. |

10. | Shigeki Takeuchi, Ryo Okamoto, and Keiji Sasaki,“High-yield single-photon source using gated spontaneous parametric downconversion,” Appl. Opt. |

11. | Ryo Okamoto, Shigeki Takeuchi, and Keiji Sasaki, “Detailed analysis of a single-photon source using gated spontaneous parametric downconversion,” J. Opt. Soc. Am. B |

12. | A. Trifonov and A. Zavriyev,“Secure communication with a heralded single-photon source,” J. Opt. B |

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

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

15. | H. Briegel, W. Dür, J. I. Cirac, and P. Zoller,“Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. |

16. | A. Soujaeff, S. Takeuchi, K. Sasaki, T. Hasegawa, and M. Matsui, “Heralded single photon source at 1550 nm from pulsed parametric downconversion,” quant-ph/0611112, (2006). |

17. | D. Gottesman, H.-K. Lo, N. Lütkenhaus, and J. Preskill, “Security of quantum key distribution with imperfect devices,Quantum inf. comput. |

18. | H. K. Hong and L. Mandel, “Experimental realization of a localized one-photon state,” Phys. Rev. Lett. |

19. | Using a model presented in reference [10, 11, 16], we estimated the average number of photon pairs |

20. | C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett. |

21. | M. Koashi, “Efficient quantum key distribution with practical sources and detectors,” quant-ph/0609180, (2006). |

22. | M. Hayashi, “Practical evaluation of security for quantum key distribution,” Phys. Rev. A |

23. | Y. Adachi, T. Yamamoto, M. Koashi, and N. Imoto, “Simple and efficient quantum key distribution with parametric down-conversion,” quant-ph/0610118, (2006). |

**OCIS Codes**

(060.0060) Fiber optics and optical communications : Fiber optics and optical communications

(270.5290) Quantum optics : Photon statistics

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: August 18, 2006

Revised Manuscript: November 28, 2006

Manuscript Accepted: December 29, 2006

Published: January 22, 2007

**Citation**

Alexandre Soujaeff, Tsuyoshi Nishioka, Toshio Hasegawa, Shigeki Takeuchi, Toyohiro Tsurumaru, Keiji Sasaki, and Mitsuru Matsui, "Quantum key distribution at 1550 nm using a pulse heralded
single photon source," Opt. Express **15**, 726-734 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-2-726

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### References

- C.H. Bennett and G. Brassard, in proceedings of the IEEE International Conference on Computers, Systems and Signals Processing, (Institute of Electrical and Electronics Engineers, New York 1984), pp. 175-179.
- C. H. Bennett, F. Bessette, G. Brassard, L. Salvail and J. Smolin, "Experimental quantum cryptography," J. Cryptology 5, 3-28 (1992). [CrossRef]
- P. Townsend, J. G. Rarity and P. R. Tapster, "Single photon interference in a 10 km long optical fiber interferometer," Electron. Lett. 29, 634-639 (1993). [CrossRef]
- G. Brassard, N. Lütkenhaus, T. Mor and B. C. Sanders, "Limitations on practical quantum cryptography," Phys. Rev. Lett. 85, 1330-1333 (2000). [CrossRef] [PubMed]
- V. Scarani, A. Acín, G. Ribordy and N. Gisin, "Quantum cryptography protocols robust against photon number splitting attacks for weak laser pulse implementations," Phys. Rev. Lett. 92, 0579014 (2004). [CrossRef]
- K. Inoue and T. Honjo, "Robustness of differential-phase-shift quantum key distribution against photon-numbersplitting attack," Phys. Rev. A 71, 042305 (2005). [CrossRef]
- H.-K. Lo and X. Ma and K. Chen,"Decoy state quantum key distribution," Phys. Rev. Lett. 94, 230504 (2005). [CrossRef] [PubMed]
- Y. Zhao, B. Qi, X. Ma, H.-K. Lo and L. Qian,"Experimental quantum key distribution with decoy states," Phys. Rev. Lett. 96, 070502 (2006). [CrossRef] [PubMed]
- S. Fasel, O. Alibart, A. Beveratos, S. Tanzilli, H. Zbinden, P. Baldi and N. Gisin,"High-quality asynchronous heralded single-photon source at telecom wavelength," New J. of Phys. 6, 163 (2004). [CrossRef]
- Shigeki Takeuchi, Ryo Okamoto, and Keiji Sasaki,"High-yield single-photon source using gated spontaneous parametric downconversion," Appl. Opt. 43, 5708-5711 (2004). [CrossRef] [PubMed]
- Ryo Okamoto, Shigeki Takeuchi, and Keiji Sasaki, "Detailed analysis of a single-photon source using gated spontaneous parametric downconversion," J. Opt. Soc. Am. B 22, 2393-2401 (2005). [CrossRef]
- A. Trifonov and A. Zavriyev,"Secure communication with a heralded single-photon source," J. Opt. B 7, S772-S777 (2005). [CrossRef]
- N. Gisin, G. Ribordy, W. Tittel and H. Zbinden, "Quantum cryptography," Rev. Mod. Phys. 74, 145-195 (2002). [CrossRef]
- 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]
- H. Briegel, W. Dür, J. I. Cirac and P. Zoller,"Quantum repeaters: the role of imperfect local operations in quantum communication," Phys. Rev. Lett. 81, 5932-5935 (1998). [CrossRef]
- A. Soujaeff, S. Takeuchi, K. Sasaki, T. Hasegawa and M. Matsui, "Heralded single photon source at 1550 nm from pulsed parametric downconversion," quant-ph/0611112, (2006).
- D. Gottesman, H.-K. Lo, N. Lütkenhaus and J. Preskill, "Security of quantum key distribution with imperfect devices," Quantum Inf. Comput. 4, 325-360 (2004).
- H. K. Hong and L. Mandel, "Experimental realization of a localized one-photon state," Phys. Rev. Lett. 56, 58-60 (1986). [CrossRef] [PubMed]
- Using a model presented in reference [10, 11, 16], we estimated the average number of photon pairs μ at the crystal output to be 0.168 at the maximum pump power (195 mW), and 3 pairs event probability at the crystal ouput to be a fraction equal to 0.056 of the two pairs generation probability for this pump power.
- C. H. Bennett, "Quantum cryptography using any two nonorthogonal states," Phys. Rev. Lett. 68, 3121-3124 (1992). [CrossRef] [PubMed]
- M. Koashi, "Efficient quantum key distribution with practical sources and detectors," quant-ph/0609180, (2006).
- M. Hayashi, "Practical evaluation of security for quantum key distribution," Phys. Rev. A 74, 022307 (2006). [CrossRef]
- Y. Adachi, T. Yamamoto, M. Koashi, N. Imoto," Simple and efficient quantum key distribution with parametric down-conversion," quant-ph/0610118, (2006).

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