## 10-GHz clock differential phase shift quantum key distribution experiment

Optics Express, Vol. 14, Issue 20, pp. 9522-9530 (2006)

http://dx.doi.org/10.1364/OE.14.009522

Acrobat PDF (329 KB)

### Abstract

This paper reports the first quantum key distribution experiment implemented with a 10-GHz clock frequency. We used a 10-GHz actively mode-locked fiber laser as a source of short coherent pulses and single photon detectors based on frequency up-conversion in periodically poled lithium niobate waveguides. The use of short pulses and low-jitter up-conversion detectors significantly reduced the bit errors caused by detector dark counts even after long-distance transmission of a weak coherent state pulse. We employed the differential phase shift quantum key distribution protocol, and generated sifted keys at a rate of 3.7 kbit/s over a 105 km fiber with a bit error rate of 9.7%.

© 2006 Optical Society of America

## 1. Introduction

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

2. P. D. Townsend, “Secure key distribution system based on quantum cryptography” Electron. Lett. **30**809 (1994). [CrossRef]

3. G. Ribordy, J. D. Gautier, N. Gisin, O. Guinnard, and H. Zbinden, “Automated ‘plug & play’ quantum key distribution,” Electron. Lett. **34**2116 (1998). [CrossRef]

4. M. Bourennane, F. Gibson, A. Karlsson, A. Hening, P. Jonsson, T. Tsegaye, D. Ljunggren, and E. Sundberg, “Experiments on long wavelength (1550 nm) “plug and play” quantum cryptography systems,” Opt. Express **4**383 (1999). [CrossRef] [PubMed]

5. D. Stucki, N. Gisin, O. Guinnard, G. Ribordy, and H. Zbinden, “Quantum key distribution over 67 km with a plug & play system,” New J. Phys. **4**41 (2002). [CrossRef]

7. 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**, 2797 (2004). [CrossRef] [PubMed]

8. H. Takesue, E. Diamanti, T. Honjo, C. Langrock, M. M. Fejer, K. Inoue, and Y. Yamamoto, “Differential phase shift quantum key distribution experiment over 105 km fibre,” New J. Phys. **7**, 232 (2005). [CrossRef]

8. H. Takesue, E. Diamanti, T. Honjo, C. Langrock, M. M. Fejer, K. Inoue, and Y. Yamamoto, “Differential phase shift quantum key distribution experiment over 105 km fibre,” New J. Phys. **7**, 232 (2005). [CrossRef]

9. C. Gobby, Z. L. Yuan, and A. J. Shields, “Quantum key distribution over 122 km of standard telecom fiber,” Appl. Phys. Lett. **84**3762–3764 (2004). [CrossRef]

8. H. Takesue, E. Diamanti, T. Honjo, C. Langrock, M. M. Fejer, K. Inoue, and Y. Yamamoto, “Differential phase shift quantum key distribution experiment over 105 km fibre,” New J. Phys. **7**, 232 (2005). [CrossRef]

10. R. T. Thew, S. Tanzilli, L. Krainer, S. C. Zeller, A. Rochas, I. Rech, S. Cova, H. Zbinden, and N. Gisin, “Low-jitter up-conversion detectors for telecom wavelength QKD,” New J. Phys. **8**32 (2006). [CrossRef]

## 2. Differential phase shift quantum key distribution protocol

*N, ϕ*and

_{k}*M*are the total number of time slots, the classical phase modulation at time slot

*k*(={0,

*π*}), and the number of photons in N time slots, respectively. The phase difference between adjacent time slots

*ϕ*

_{k+1}-

*ϕ*corresponds to bit “0” or “1”. Since the average number of photons per pulse is set at much smaller than 1, the number of photons

_{k}*M*is much smaller than the number of phase differences,

*N*-1. This means that it is impossible to reconstruct the whole wavefunction including

*N*-1 phase differences with

*M*(<

*N*-1) measurements. Thus, the security of DPS-QKD is based on the non-orthogonality of a wavefunction spanned by many time slots.

**7**, 232 (2005). [CrossRef]

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

14. E. Diamanti, H. Takesue, T. Honjo, K. Inoue, and Y. Yamamoto, “Performance of various quantum-key-distribution systems using 1.55-*µ*m up-conversion single-photon detectors,” Phys. Rev. A **72**, 052311 (2005). [CrossRef]

15. E. Waks, H. Takesue, and Y. Yamamoto, “Security of differential-phase-shift quantum key distribution against individual attacks,” Phys. Rev. A **73**, 012344 (2006). [CrossRef]

## 3. Experiments

### 3.1. Generation of coherent pulse train at 10-GHz clock frequency

*π*0

*π*0

*π*..), by which we switched the port where the majority of light was output. Here too, the ratio of the two output powers was ~20 dB. This implies that the error caused by imperfect interferometry in a QKD experiment is suppressed to ~1%. This value is similar to that observed in our previous QKD experiments with a 1-GHz clock frequency using coherent pulses generated by modulating CW semiconductor laser light with an external intensity modulator [7

7. 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**, 2797 (2004). [CrossRef] [PubMed]

**7**, 232 (2005). [CrossRef]

### 3.2. Up-conversion detectors

16. 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 LiNbO_{3} waveguides,” Opt. Lett. , **30**, 1725 (2005). [CrossRef] [PubMed]

*µ*m), and then reflected by a dichroic mirror to separate long-wavelength photons (1.3 and 1.5

*µ*m). The reflected light is then input into a prism to further suppress the pump and SHG components, and finally focused onto a low-jitter Si-APD (MPD photon counting detector module). When we input a ~100-mW pump light, we obtained a peak quantum efficiency of ~8 %. However, as reported in [16

16. 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 LiNbO_{3} waveguides,” Opt. Lett. , **30**, 1725 (2005). [CrossRef] [PubMed]

### 3.3. QKD experiments

*e*, is calculated with the following equation.

_{d}*f*, Δ

_{c}, d*t*, and

*R*denote the clock frequency, the dark count rate per second, the time window width and the sifted key rate, respectively.

_{si f ted}*e*is calculated by plugging the experimentally obtained sifted key rate shown in Fig. 5(a) in Eq. (2), whose result is shown in Fig. 5(b). This result shows that

_{d}*e*improves as Δ

_{d}*t*is reduced, but the improvement begins to saturate when Δ

*t*is smaller than 20 ps. When Δ

*t*is below 10 ps, the improvement could no longer be seen. This saturation of the error rate improvement results from the timing jitter of the up-conversion detectors discussed above. Therefore, we used a 10-ps time window in the following key generation experiments.

15. E. Waks, H. Takesue, and Y. Yamamoto, “Security of differential-phase-shift quantum key distribution against individual attacks,” Phys. Rev. A **73**, 012344 (2006). [CrossRef]

## 4. Summary

## Acknowledgments

## References and links

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

2. | P. D. Townsend, “Secure key distribution system based on quantum cryptography” Electron. Lett. |

3. | G. Ribordy, J. D. Gautier, N. Gisin, O. Guinnard, and H. Zbinden, “Automated ‘plug & play’ quantum key distribution,” Electron. Lett. |

4. | M. Bourennane, F. Gibson, A. Karlsson, A. Hening, P. Jonsson, T. Tsegaye, D. Ljunggren, and E. Sundberg, “Experiments on long wavelength (1550 nm) “plug and play” quantum cryptography systems,” Opt. Express |

5. | D. Stucki, N. Gisin, O. Guinnard, G. Ribordy, and H. Zbinden, “Quantum key distribution over 67 km with a plug & play system,” New J. Phys. |

6. | A. Yoshizawa, R. Kaji, and H. Tsuchida,“10.5 km fiber-optic quantum key distribution at 1550 nm with a key rate of 45 kHz,” Jpn. J. Appl. Phys. |

7. | 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. |

8. | H. Takesue, E. Diamanti, T. Honjo, C. Langrock, M. M. Fejer, K. Inoue, and Y. Yamamoto, “Differential phase shift quantum key distribution experiment over 105 km fibre,” New J. Phys. |

9. | C. Gobby, Z. L. Yuan, and A. J. Shields, “Quantum key distribution over 122 km of standard telecom fiber,” Appl. Phys. Lett. |

10. | R. T. Thew, S. Tanzilli, L. Krainer, S. C. Zeller, A. Rochas, I. Rech, S. Cova, H. Zbinden, and N. Gisin, “Low-jitter up-conversion detectors for telecom wavelength QKD,” New J. Phys. |

11. | K. Inoue, E. Waks, and Y. Yamamoto, “Differential phase shift quantum key distribution,” Phys. Rev. Lett. |

12. | K. Inoue, E. Waks, and Y. Yamamoto, “Differential-phase-shift quantum key distribution using coherent light,” Phys. Rev. A |

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

14. | E. Diamanti, H. Takesue, T. Honjo, K. Inoue, and Y. Yamamoto, “Performance of various quantum-key-distribution systems using 1.55- |

15. | E. Waks, H. Takesue, and Y. Yamamoto, “Security of differential-phase-shift quantum key distribution against individual attacks,” Phys. Rev. A |

16. | 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 LiNbO |

**OCIS Codes**

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

(270.0270) Quantum optics : Quantum optics

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: July 26, 2006

Revised Manuscript: September 12, 2006

Manuscript Accepted: September 13, 2006

Published: October 2, 2006

**Citation**

Hiroki Takesue, Eleni Diamanti, Carsten Langrock, M. M. Fejer, and Yoshihisa Yamamoto, "10-GHz clock differential phase shift quantum key distribution experiment," Opt. Express **14**, 9522-9530 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-20-9522

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### References

- N. Gisin, G. Ribordy, W. Tittel and H. Zbinden, "Quantum cryptography," Rev. Mod. Phys. 74, 145-195 (2002). [CrossRef]
- P. D. Townsend, "Secure key distribution system based on quantum cryptography," Electron. Lett. 30809 (1994). [CrossRef]
- G. Ribordy, J. D. Gautier, N. Gisin, O. Guinnard and H. Zbinden, "Automated ‘plug & play’ quantum key distribution," Electron. Lett. 342116 (1998). [CrossRef]
- M. Bourennane, F. Gibson, A. Karlsson, A. Hening, P. Jonsson, T. Tsegaye, D. Ljunggren and E. Sundberg, "Experiments on long wavelength (1550 nm) "plug and play" quantum cryptography systems," Opt. Express 4383 (1999). [CrossRef] [PubMed]
- D. Stucki, N. Gisin, O. Guinnard, G. Ribordy and H. Zbinden, "Quantum key distribution over 67 km with a plug & play system," New J. Phys. 441 (2002). [CrossRef]
- A. Yoshizawa, R. Kaji and H. Tsuchida,"10.5 km fiber-optic quantum key distribution at 1550 nm with a key rate of 45 kHz," Jpn. J. Appl. Phys. 43 (2004) L735.
- 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, 2797 (2004). [CrossRef] [PubMed]
- H. Takesue, E. Diamanti, T. Honjo, C. Langrock, M. M. Fejer, K. Inoue and Y. Yamamoto, "Differential phase shift quantum key distribution experiment over 105 km fibre," New J. Phys. 7, 232 (2005). [CrossRef]
- C. Gobby, Z. L. Yuan and A. J. Shields, "Quantum key distribution over 122 km of standard telecom fiber," Appl. Phys. Lett. 843762-3764 (2004). [CrossRef]
- R. T. Thew, S. Tanzilli, L. Krainer, S. C. Zeller, A. Rochas, I. Rech, S. Cova, H. Zbinden and N. Gisin, "Low-jitter up-conversion detectors for telecom wavelength QKD," New J. Phys. 832 (2006). [CrossRef]
- K. Inoue, E. Waks and Y. Yamamoto, "Differential phase shift quantum key distribution," Phys. Rev. Lett. 89, 037902 (2002). [CrossRef] [PubMed]
- K. Inoue, E. Waks and Y. Yamamoto, "Differential-phase-shift quantum key distribution using coherent light," Phys. Rev. A 68, 022317 (2003). [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]
- E. Diamanti, H. Takesue, T. Honjo, K. Inoue, and Y. Yamamoto, "Performance of various quantum-keydistribution systems using 1.55-μm up-conversion single-photon detectors," Phys. Rev. A 72, 052311 (2005). [CrossRef]
- E. Waks, H. Takesue and Y. Yamamoto, "Security of differential-phase-shift quantum key distribution against individual attacks," Phys. Rev. A 73, 012344 (2006). [CrossRef]
- C. Langrock, E. Diamanti, R. V. Roussev, Y. Yamamoto, M. M. Fejer, and H. Takesue, "Highly efficient singlephoton detection at communication wavelengths by use of upconversion in reverse-proton-exchanged periodically poled LiNbO3 waveguides," Opt. Lett., 30, 1725 (2005). [CrossRef] [PubMed]

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