## 100 km differential phase shift quantum key distribution experiment with low jitter up-conversion detectors

Optics Express, Vol. 14, Issue 26, pp. 13073-13082 (2006)

http://dx.doi.org/10.1364/OE.14.013073

Acrobat PDF (277 KB)

### Abstract

We present a quantum key distribution experiment in which keys that were secure against all individual eavesdropping attacks allowed by quantum mechanics were distributed over 100 km of optical fiber. We implemented the differential phase shift quantum key distribution protocol and used low timing jitter 1.55 *µ*m single-photon detectors based on frequency up-conversion in periodically poled lithium niobate waveguides and silicon avalanche photodiodes. Based on the security analysis of the protocol against general individual attacks, we generated secure keys at a practical rate of 166 bit/s over 100 km of fiber. The use of the low jitter detectors also increased the sifted key generation rate to 2 Mbit/s over 10 km of fiber.

© 2006 Optical Society of America

## 1. Introduction

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

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

3. T. Honjo, K. Inoue, and H. Takahashi, “Differential-phase-shift quanum key distribution experiment with a planar light-wave circuit Mach-Zehnder interferometer,” Opt. Lett. **29**, 2797–2799 (2004). [CrossRef] [PubMed]

4. 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]

4. 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]

5. 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. N. Lütkenhaus, “Security against individual attacks for realistic quantum key distribution,” Phys. Rev. A **61**, 052304 (2000). [CrossRef]

9. G. Brassard, N. Lütkenhaus, T. Mor, and B. C. Sanders, “Limitations on Practical Quantum Cryptography,” Phys. Rev. Lett. **85**, 1330–1333 (2000). [CrossRef] [PubMed]

10. C. Gobby, Z. L. Yuan, and A. J. Shields, “Unconditionally secure quantum key distribution over 50 km of standard telecom fibre,” Electron. Lett. **40**, 1603–1605 (2004). [CrossRef]

12. H.-K. Lo, X. Ma, and K. Chen, “Decoy State Quantum Key Distribution,” Phys. Rev. Lett. **94**, 230504 (2005). [CrossRef] [PubMed]

13. X.-B. Wang, “Beating the Photon-Number-Splitting Attack in Practical Quantum Cryptography,” Phys. Rev. Lett. **94**, 230503 (2005). [CrossRef] [PubMed]

4. 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]

14. K. Inoue, E. Waks, and Y. Yamamoto, “Differential Phase Shift Quanum Key Distribution,” Phys. Rev. Lett. **89**, 037902 (2002). [CrossRef] [PubMed]

15. K. Inoue, E. Waks, and Y. Yamamoto, “Differential-phase-shift quanum key distribution using coherent light,” Phys. Rev. A **68**, 022317 (2003). [CrossRef]

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

16. 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]

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

18. 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]

18. 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]

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

19. 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**, 1725–1727 (2005). [CrossRef] [PubMed]

20. 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 GHz QKD,” New J. Phys. **8**, 32 (2006). [CrossRef]

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

## 2. Security of the differential phase shift quantum key distribution protocol

*π*, and sent over an optical fiber to Bob. Each photon coherently spreads over many pulses with a fixed phase modulation pattern. In the receiver side, Bob divides the incoming pulses into two paths and recombines them using 50/50 beamsplitters. The time delay introduced by his interferometer is equal to the inverse of the clock frequency, or else equal to the time separation between sequential pulses. Single-photon detectors are placed at the output ports of the second beamsplitter. After passing through Bob’s interferometer, the pulses interfere at the output beamsplitter and the phase difference between two consecutive pulses determines which detector records a detection event. Detector 1 in Fig. 1 records an event when the phase difference is 0 and detector 2 records an event when the phase difference is

*π*. Because the average photon number per pulse is less than one, Bob observes detection events only occasionally and at random time instances. Bob announces publicly the time instances at which a photon was detected, but he does not reveal which detector detected it. From her modulation data, Alice knows which detector in Bob’s site recorded the event. Thus, by assigning bit values 0 and 1 to detection events recorded by detector 1 and 2, respectively, they form a secret key.

*n*, then each of Alice’s photons is in a superposition of all the states that correspond to the

_{p}*n*time instances with the appropriate phase applied to each one of them. The overall wavefunction is a product state of these individual photon states. At Bob’s site, a detection event at a certain time instance tn reveals the phase difference between the pulses in time instances

_{p}*t*and

_{n}*t*

_{n+1}, which corresponds to one bit of information. However, these detection events occur completely randomly, so an eavesdropper cannot deterministically collapse the wavefunction in the same time instance and obtain the same bit of information as Bob.

18. 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]

*n*-slot wave-function using a quantum non-demolition (QND) measurement. Then, she sends to Bob

_{p}*n*photons, where

_{p}µT*µ*is the average photon number per pulse and

*T*is the total transmission efficiency of the quantum channel and Bob’s detection setup, and she stores

*n*(1-

_{p}µ*T*) photons coherently to be measured after Alice and Bob have revealed all classical information. This is the photon number splitting attack in the case of the DPS-QKD protocol. In the case that Eve is assumed to store and measure her photons individually it was shown in [18

**73**, 012344 (2006). [CrossRef]

*µ*(1-

*T*) of the sifted key. When

*T*≪1 and

*µ*is small this attack is relatively ineffective for the DPS-QKD protocol. However, in the presence of system errors, Eve can also apply an optimal measurement attack on a fraction of the photons transmitted to Bob. Assuming that Eve attaches an individual probe state to each single photon, and then measures the probes independently after all classical information has been revealed, it was shown that the collision probability for each bit

**73**, 012344 (2006). [CrossRef]

*e*is the innocent system error rate.

*n*-bit sifted key, which is a measure of Eve’s mutual information with Alice and Bob, is given by the expression:

8. N. Lütkenhaus, “Security against individual attacks for realistic quantum key distribution,” Phys. Rev. A **61**, 052304 (2000). [CrossRef]

*R*

_{sifted}is given by Eq. (5) below for the up-conversion single-photon detectors and

*f*(

*e*) characterizes the performance of the error correction algorithm. The QKD experiments presented in Sec. 4 are based on the results of the security analysis described here, and in particular Eq. (4).

## 3. The low jitter up-conversion detector

*µ*m up-conversion single-photon detector [19

19. 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**, 1725–1727 (2005). [CrossRef] [PubMed]

*µ*m is combined with a strong pump at 1.32

*µ*m in a wavelength division multiplexing coupler, and subsequently the two beams interact in a PPLN waveguide, designed for sum frequency generation at these wavelengths. This device allows for an internal conversion efficiency exceeding 99% of the signal to the 713 nm sum frequency output. After a long-pass filter, a dichroic beamsplitter and a prism that serve the purpose of eliminating the residual pump and its second harmonic, the converted photon is detected by a Si APD. The up-conversion detector presents more favorable characteristics for fiber-based quantum cryptography than the commonly used InGaAs/InP APD [16

16. 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]

*t*is the detector dead time,

_{d}*ν*the system clock frequency, and the factor 1/2 in the exponent appears because the average number of photons per second that reach each detector in Bob’s setup is

*νµT*/2. For commercial Si APDs with a dead time on the order of 50–80 ns, the exponential term becomes appreciable for low fiber losses and high count rates. The nongated mode operation, however, does not impose any severe limitation on the QKD system clock frequency, which is only determined by the speed of the electronic equipment and the Si APD timing jitter. In the experiments described in this paper a clock frequency of 1 GHz was used, while a 10 GHz system is also possible with these detectors [21

21. H. Takesue, E. Diamanti, C. Langrock, M. M. Fejer, and Y. Yamamoto, “10-GHz clock differential phase shift quantum key distribution experiment,” Opt. Express **14**, 9522–9530 (2006). [CrossRef] [PubMed]

19. 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**, 1725–1727 (2005). [CrossRef] [PubMed]

^{5}counts/s. As we observe in Fig. 3, the FWHM is 75 ps, which is significantly smaller than the 500 ps jitter obtained in experiments with high jitter up-conversion detectors. Nevertheless, the detection signal is clearly not Gaussian; there is a tail that can potentially cause errors in the adjacent 1 ns time slot in a DPS-QKD experiment with a clock frequency of 1 GHz. Fig. 3 shows, however, that 1 ns away from the peak the tail is sufficiently small to prevent intersymbol interference. It is clear that the improvement in timing jitter achieved with the low jitter Si APDs is significant, and so the error rate should be considerably lower in QKD systems employing these detectors.

## 4. DPS-QKD experimental setup and results

_{3}intensity modulator. The modulator was driven by a 15 GHz pulse pattern generator, so the pulse width was 66 ps. Subsequently, following the DPS-QKD protocol that is illustrated in Fig. 1, the phase of each pulse was modulated by 0 or

*π*with a LiNbO

_{3}phase modulator. The phase modulation signal was a 1 Gbit/s pseudorandom bit sequence with a length of 2

^{7}-1 bits, which was generated by a data generator. The pulses were appropriately attenuated and sent to Bob’s site through an optical fiber, where a 1-bit delay Mach-Zehnder interferometer based on planar lightwave circuit (PLC) technology was installed. The insertion loss of the interferometer was 2 dB, and the extinction ratio was greater than 20 dB. One 1.55

*µ*m up-conversion single-photon detector was connected to each of the output ports of the interferometer. The events detected by the two Si APDs were recorded using a time interval analyzer.

*µ*at its optimal value. In particular, based on the experimental parameters of the system, we maximized the secure key generation rate with respect to

*µ*using Eq. (4) which corresponds to the general individual attacks security analysis. The optimal value was 0.2, and was practically independent of the channel transmission efficiency. Subsequently, we performed QKD experiments, that is we measured the generation rate of the sifted keys that Alice and Bob exchanged, and by directly comparing the yielded keys we also measured the bit error rate of the transmission. For each fiber length, we measured the sifted key generation rate and error rate five times and took the average values. We then calculated the secure key generation rate from Eq. (4) using the experimental results for the sifted key generation rates and bit error rates. Alice and Bob were located in the same room and we performed fiber transmission experiments using fiber spools, while some additional data were taken with an optical attenuator simulating fiber loss. Fig. 5 shows the theoretical curves and experimental results for the sifted and secure key generation rate as a function of fiber length that we obtained with the described setup and procedure for two different experimental conditions.

*d*=1.95×10

^{-5}. The use of the 200 ps time window also decreased the effective quantum efficiency by 40%. Under these operating conditions, we performedQKD experiments for 10 km of optical fiber. We used dispersion-shifted fiber and so chromatic dispersion induced pulse broadening was negligible compared to the one caused by the detector timing jitter. The curves (a) of Fig. 5 correspond to the theoretical prediction for the sifted and secure key generation rate under these experimental conditions, when

*µ*is optimized to maximize the secure key generation rate using the general individual attacks security analysis. A baseline system bit error rate of 1.5% was assumed in these calculations. The clear square represents the fiber transmission experimental result for the secure key generation rate, while the sifted key generation rate at the corresponding fiber length is represented by the clear diamond. The clear circles and stars show the experimental results when we simulated additional fiber loss with an optical attenuator. As we observe in Fig. 5, the theoretical curves fit very well with the experimental results. At the fiber length of 10 km we achieved a sifted key generation rate of 2 Mbit/s with a bit error rate of 2.2%, thus the secure key generation rate at this fiber length was 0.468 Mbit/s. The use of the low jitter detectors resulted in a double sifted rate at small fiber loss compared to previous experiments with high jitter up-conversion detectors [4

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

*d*=3.5×10

^{-8}, and also reduced the effective quantum efficiency of the detector by 54%. Under these operating conditions, we performed QKD experiments for 25, 75 and 100 km of optical fiber. The 75 km fiber was dispersion-shifted fiber while the 25 km fiber was a standard single-mode fiber. Again, pulse broadening caused by chromatic dispersion was negligible compared with the one caused by detector timing jitter. The curves (b) of Fig. 5 correspond to the theoretical prediction for the sifted and secure key generation rate when the above experimental conditions are assumed. The filled squares and diamonds represent the fiber transmission experimental results, while the filled circles and stars correspond to data taken using the attenuator to simulate additional fiber loss. As in the previous case, we observe that the theoretical curves fit very well with the experimental data. By using these operating conditions, keys that were secure against general individual eavesdropping attacks appropriately defined for the DPS-QKD protocol were distributed at a rate of 166 bits/s over 100 km of fiber. The bit error rate for the 100 km experiment was 3.4%, of which 1% is attributed to imperfect interferometry, 1.7% to detector dark counts, and the remaining 0.7% to the timing jitter. This result shows that the key distribution distance for which security against all individual attacks allowed by quantum mechanics is guaranteed for the DPS-QKD protocol was considerably extended because of the improved timing jitter characteristics of the up-conversion detectors employed in the system. These characteristics led to small pulse broadening, which allowed the use of a short measurement time window to substantially reduce the effective dark counts, thus improving the signal to noise ratio and decreasing the bit error rate.

## 5. Conclusion

## Acknowledgements

## References and links

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

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

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

4. | 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. |

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

6. | D. Rosenberg, J. W. Harrington, P. R. Rice, P. A. Hiskett, C. G. Peterson, R. J. Hughes, J. E. Nordholt, A. E. Lita, and S. W. Nam, “Long distance decoy state quantum key distribution in optical fiber,” quant-ph/0607186 (2006). |

7. | 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, Bangalore, India, (IEEE, New York, 1984), 175–179. |

8. | N. Lütkenhaus, “Security against individual attacks for realistic quantum key distribution,” Phys. Rev. A |

9. | G. Brassard, N. Lütkenhaus, T. Mor, and B. C. Sanders, “Limitations on Practical Quantum Cryptography,” Phys. Rev. Lett. |

10. | C. Gobby, Z. L. Yuan, and A. J. Shields, “Unconditionally secure quantum key distribution over 50 km of standard telecom fibre,” Electron. Lett. |

11. | Y. Zhao, B. Qi, X. Ma, H.-K. Lo, and L. Qian, “Simulation and implementation of decoy state quantum key distribution over 60 km telecom fiber,” Proc. IEEE Int. Symp. Inf. Theor.2006, 2094–2098. |

12. | H.-K. Lo, X. Ma, and K. Chen, “Decoy State Quantum Key Distribution,” Phys. Rev. Lett. |

13. | X.-B. Wang, “Beating the Photon-Number-Splitting Attack in Practical Quantum Cryptography,” Phys. Rev. Lett. |

14. | K. Inoue, E. Waks, and Y. Yamamoto, “Differential Phase Shift Quanum Key Distribution,” Phys. Rev. Lett. |

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

16. | 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 |

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

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

19. | 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. |

20. | 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 GHz QKD,” New J. Phys. |

21. | H. Takesue, E. Diamanti, C. Langrock, M. M. Fejer, and Y. Yamamoto, “10-GHz clock differential phase shift quantum key distribution experiment,” Opt. Express |

**OCIS Codes**

(270.0270) Quantum optics : Quantum optics

(270.5570) Quantum optics : Quantum detectors

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: August 14, 2006

Revised Manuscript: November 8, 2006

Manuscript Accepted: November 8, 2006

Published: December 22, 2006

**Citation**

Eleni Diamanti, Hiroki Takesue, Carsten Langrock, M. M. Fejer, and Yoshihisa Yamamoto, "100 km differential phase shift quantum key distribution experiment with low jitter up-conversion detectors," Opt. Express **14**, 13073-13082 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-26-13073

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### References

- C. H. Bennett, F. Bessette, G. Brassard, L. Salvail and J. Smolin, "Experimental quantum cryptography," J. Cryptology 5,3-28 (1992). [CrossRef]
- N. Gisin, G. Ribordy, W. Tittel and H. Zbinden, "Quantum cryptography," Rev. Mod. Phys. 74,145-195 (2002). [CrossRef]
- T. Honjo, K. Inoue and H. Takahashi, "Differential-phase-shift quanum key distribution experiment with a planar light-wave circuit Mach-Zehnder interferometer," Opt. Lett. 29,2797-2799 (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. 84,3762-3764 (2004). [CrossRef]
- D. Rosenberg, J. W. Harrington, P. R. Rice, P. A. Hiskett, C. G. Peterson, R. J. Hughes, J. E. Nordholt, A. E. Lita and S. W. Nam, "Long distance decoy state quantum key distribution in optical fiber," quant-ph/0607186 (2006).
- 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, Bangalore, India, (IEEE, New York, 1984), 175-179.
- N. Lütkenhaus, "Security against individual attacks for realistic quantum key distribution," Phys. Rev. A 61,052304 (2000). [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]
- C. Gobby, Z. L. Yuan and A. J. Shields, "Unconditionally secure quantum key distribution over 50 km of standard telecom fibre," Electron. Lett. 40,1603-1605 (2004). [CrossRef]
- Y. Zhao, B. Qi, X. Ma, H.-K. Lo and L. Qian, "Simulation and implementation of decoy state quantum key distribution over 60 km telecom fiber," Proc. IEEE Int. Symp. Inf. Theor. 2006, 2094-2098.
- H.-K. Lo, X. Ma and K. Chen, "Decoy State Quantum Key Distribution," Phys. Rev. Lett. 94,230504 (2005). [CrossRef] [PubMed]
- X.-B. Wang, "Beating the Photon-number-splitting attack in practical Quantum Cryptography," Phys. Rev. Lett. 94,230503 (2005). [CrossRef] [PubMed]
- K. Inoue, E. Waks and Y. Yamamoto, "Differential phase shift quanum key distribution," Phys. Rev. Lett. 89,037902 (2002). [CrossRef] [PubMed]
- K. Inoue, E. Waks and Y. Yamamoto, "Differential-phase-shift quanum key distribution using coherent light," Phys. Rev. A 68,022317 (2003). [CrossRef]
- E. Diamanti, H. Takesue, T. Honjo, K. Inoue and Y. Yamamoto, "Performance of various quantum-key distribution systems using 1.55-m up-conversion single-photon detectors," Phys. Rev. A 72,052311 (2005). [CrossRef]
- K. Inoue and T. Honjo, "Robustness of differential-phase-shift quanum key distribution against photon-number splitting attack," Phys. Rev. A 71,042305 (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. 30,1725-1727 (2005). [CrossRef] [PubMed]
- 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 GHz QKD," New J. Phys. 8,32 (2006). [CrossRef]
- H. Takesue, E. Diamanti, C. Langrock, M. M. Fejer and Y. Yamamoto, "10-GHz clock differential phase shift quantum key distribution experiment," Opt. Express 14,9522-9530 (2006). [CrossRef] [PubMed]

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