## Practical quantum key distribution over 60 hours at an optical fiber distance of 20km using weak and vacuum decoy pulses for enhanced security

Optics Express, Vol. 15, Issue 13, pp. 8465-8471 (2007)

http://dx.doi.org/10.1364/OE.15.008465

Acrobat PDF (645 KB)

### Abstract

Experimental one-way decoy pulse quantum key distribution running continuously for 60 hours is demonstrated over a fiber distance of 20km. We employ a decoy protocol which involves one weak decoy pulse and a vacuum pulse. The obtained secret key rate is on average over 10kbps. This is the highest rate reported using this decoy protocol over this fiber distance and duration.

© 2007 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]

4. D. Stucki, N. Gisin, O. Guinnard, G. Ribordy, and H. Zbinden, “Quantum key distribution over 67km with a plug & play system,” New J. Phys. **4**41.1–41.8 (2002). [CrossRef]

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

6. X.-B. Wang, “Beating the photon pulse-number-splitting attack in practical quantum cryptography,” Phys. Rev. Lett. **94**, 230503-1–4 (2005) and
H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. **94**, 230504-1–4 (2005). [CrossRef] [PubMed]

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

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

8. W.-Y. Hwang, “Quantum key distribution with high loss: toward global secure communication,” Phys. Rev. Lett. **91**, 057901-1–4 (2003). [CrossRef] [PubMed]

10. Y. Zhao, B. Qi, X. Ma, H.-K. Lo, and L. Qian, “Experimental quantum key distribution with decoy states,” Phys. Rev. Lett. **96**, 070502-1–4 (2006). [CrossRef] [PubMed]

10. Y. Zhao, B. Qi, X. Ma, H.-K. Lo, and L. Qian, “Experimental quantum key distribution with decoy states,” Phys. Rev. Lett. **96**, 070502-1–4 (2006). [CrossRef] [PubMed]

11. Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “Unconditionally secure one-way quantum key distribution using decoy pulses,” Appl. Phys. Lett. **90**, 011118-1–3 (2007). [CrossRef]

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

6. X.-B. Wang, “Beating the photon pulse-number-splitting attack in practical quantum cryptography,” Phys. Rev. Lett. **94**, 230503-1–4 (2005) and
H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. **94**, 230504-1–4 (2005). [CrossRef] [PubMed]

*ν*than the signal pulse

*μ*and another which has an intensity close to zero or “vacuum-like” [13

13. X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A **72**, 012306-1–15 (2005). [CrossRef]

*Q*

^{L}_{1}is then given by three transmittances, signal, decoy and vacuum respectively:

*Q*,

_{μ}*Q*and

_{ν}*Y*

_{0}[13

13. X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A **72**, 012306-1–15 (2005). [CrossRef]

10. Y. Zhao, B. Qi, X. Ma, H.-K. Lo, and L. Qian, “Experimental quantum key distribution with decoy states,” Phys. Rev. Lett. **96**, 070502-1–4 (2006). [CrossRef] [PubMed]

*Q*(

_{ν}^{L}*Y*

^{U}_{0}) are the lower (upper) bounds on the decoy pulse and vacuum transmittances respectively , estimated conservatively as ten standard deviations of

*Q*(

_{ν}*Y*

_{0}) from the measured value ensuring a confidence interval of 1 - 1.5 × 10

^{-23}. The bit errors are assumed to derive from the subset of single photon pulses and the upper bound for the single photon error rate can be written as:

*ε*is the signal error rate and

_{μ}*Y*

^{L}_{0}is the lower bound on the vacuum transmittance (estimated as as ten standard deviations of

*Y*

_{0}from the measured value). The lower bound on the final secure key rate,

*R*can then be determined by the following expression:

^{L}*q*= 0.5 for the BB84 protocol,

*N*is the total number of signal pulses sent by Alice,

_{μ}*f*(

*x*) is the bi-directional error correction efficiency above the Shannon limit is estimated to be

*f*(

*ε*) ∼ 1.10,

_{μ}*H*

_{2}= -

*x*log

_{2}(

*x*)-(1-

*x*)log

_{2}(1-

*x*) is the binary entropy function and the time

*t*is the duration of the key session. The first term in eq. (3) corresponds to error correction; the second term corresponds to the single photon gain modified by privacy amplification (

*H*

_{2}(

*ε*

^{U}_{1})). Although the weak + vacuum decoy protocol is predicted to have an improved performance over the single decoy pulse protocol, recent implementations [14

14. C.-Z. Peng, J. Zhang, D. Yang, W.-B. Gao, H.-Xin. Ma, H. Yin, H.-P. Zeng, T. Yang, X.-B. Wang, and J.-W. Pan, “Experimental long-distance decoy-state quantum key distribution based on polarization encoding,” Phys. Rev. Lett. **98**, 010505-1–4 (2007). [CrossRef] [PubMed]

15. D. Rosenberg, J. W. Harrington, P. R. Rice, P. A. Hiskett, C. G. Peterson, R. J. Hughes, A. E. Lita , S-W. Nam, and J. E. Nordholt, “Long-distance decoy-State quantum key distribution in optical fiber,” Phys. Rev. Lett. **98**, 010505-1–4 (2007). [CrossRef]

## 2. QKD experimental setup

*λ*= 1.55

*μ*m) and clock (

*λ*= 1.3

*μ*m) optical pulses are transmitted. The 1.3

*μ*m clock pulse duration is 5ns with a peak intensity of ∼ 5

*μ*W; average intensity is ∼ 200nW at Alice. The clock pulse over the entire transmission distance does not overlap the (1.55

*μ*m) signal pulses. The signal laser is a distributed feedback type and emits a fixed intensity train of pulses at a repetition rate of 7.143MHz. An intensity modulator is used to produce signal and decoy pulses of differing intensities. The vacuum decoy pulse is produced by omitting trigger pulses to the signal laser. All signal, decoy and vacuum pulses are produced at random times and can have relative occurance probabilities assigned to them. The signal and decoy pulses are attenuated strongly to the single photon level after which a much stronger clock pulse is wavelength division multiplexed with them to provide synchronization between Alice and Bob’s electronics. Customized electronics based on FPGAs were developed in house to drive the QKD optics. An active stabilization technique is employed to ensure continuously running operation. Bob’s detectors are two single photon InGaAs avalanche photodiodes (APDs) cooled to approximately -30

*°*C and characterized to have negligible afterpulsing [16

16. G. Ribordy, J. D. Gautier, H. Zbinden, and N. Gisin, “Performance of InGaAs/InP avalanche photodiodes as gated-mode photon counters,” Appl. Opt. **37**, 2272 (1998). [CrossRef]

^{-4}. Bob’s detector efficiency ∼ 10% and loss ∼ 2.5dB gives rise to an overall efficiency of 5.62 × 10

^{-2}. The weak + vacuum including BB84 protocol was implemented. Numerical simulation to maximize the secure bit rate was performed to yield the optimal intensities of the signal and decoy pulses as

*μ*= 0.55 and

*ν*= 0.098. Numerical simulation also provided the optimal probabilities of pulses: signal

*N*= 0.93, decoy pulse

_{μ}*N*= 0.062 and vacuum pulse

_{ν}*N*

_{0}= 0.016. The session length for each QKD key is selected as 3 × 10

^{6}bits which corresponds to roughly 6 × 10

^{6}detection events by Bob. A total of 3262 sessions were distributed with an average individual session time of ∼ 71 seconds.

## 3. Results

*Q*= 0.01270±0.00078,

_{μ}*Q*= 0.00234±0.00014 where the errors are two standard deviations; for the vacuum transmittance (per pulse),

_{ν}*Y*

_{0}= 1.34±0.20 × 10

^{-4}in good agreement with the measured dark count value of ∼ 1.4 × 10

^{-4}measured prior to the experiment. A small (simultaneous) proportion of fluctuations in

*Q*and

_{μ}*Q*are observed and are attributed to polarization and/or fiber stretcher resets during which photons were temporarily not counted. These obtained transmittances indicates the various optical states had been well prepared and detected. The associated quantum bit error rates of both the signal (

_{ν}*E*) and the non-zero decoy (

_{μ}*E*) are plotted in Fig. 2(b). They are fairly stable and constant. The final secure bit rate is displayed in Fig. 3. A secure bit rate of > 10kbps is observed. The long term drift in the key rate is attributed to long term temperature drift from day through to night (the period is roughly 24 hours) in the laboratory affecting the overall temperature of the 20km fiber spool. In a real world environment the fiber is usually located around 1 meter underground leading to very stable fiber temperatures. This would eliminate this long term drift observed here.

_{ν}12. C. Gobby, Z. L. Yuan, and A. J. Shields, Elec. Lett. “Unconditionally secure quantum key distribution over 50 km of standard telecom fiber,” Electron. Lett. **40**, 1603–1605 (2004). [CrossRef]

13. X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A **72**, 012306-1–15 (2005). [CrossRef]

*N*> 2 have a very small probability of occurring. Hence they will contribute little to the overall photon distribution when the average photon numbers of the signal and decoy states are

*μ*,

*ν*< 1. Additionally, there are practical problems in using more decoy pulses such as a decrease of duty cycle of signal pulses, greater requirements on Alices’ random number generator and more data processing power needed.

11. Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “Unconditionally secure one-way quantum key distribution using decoy pulses,” Appl. Phys. Lett. **90**, 011118-1–3 (2007). [CrossRef]

*Q*/

_{ν}*Q*. If Eve decides to implement a PNS attack, the ratio

_{μ}*Q*/

_{ν}*Q*will dip below the expected value as preferentially more multi-photon signals would be transmitted to Bob (the transmittance

_{μ}*Q*>

_{μ}*Q*due to

_{ν}*μ*>

*ν*). This is displayed in Fig. 4(a)(ii). No secure bit rate is possible with

*Q*/

_{ν}*Q*< 0.13.

_{μ}*Y*

_{0}on the secure bit rate. For the weak plus vacuum protocol implemented here no secure bit rate is possible for

*Y*

_{0}> 10

^{-3}(solid black line). However, if one were to use a single (non-vacuum) decoy protocol (dotted blue line) no secure bit rate would be possible for

*Y*

_{0}> 4.8×10

^{-4}. This shows the power of using more than one decoy pulse. Further insight can be gained by examining the formulae for the weak plus vacuum protocol (eq.(1) & eq.(2)). The magnitudes of the single photon gain (privacy amplification) are greater (smaller) respectively by using the weak + vacuum protocol compared to employing the single pulse protocol. This is manifest through a tighter bound on the single photon gain eq. (1) and the single photon error rate eq. (2). The second term in eq. (2) reduces the overall single photon error rate due to the measurement of the vacuum pulses. In the single decoy pulse protocol this term is zero.

*Y*

_{0}) this effect can be apparent. We are currently working to improve this problem with modifications to the software. However, we note this behaviour does not compromise security as evident from Fig. 4(b)(ii). As can be seen, an increase in

*Y*

_{0}overestimates the amount of privacy amplification and results in a shorter key, hence lower final secure key rate. The final secure key rate is underestimated for this small fraction of keys.

## 4. Conclusions

## Acknowledgements

## References and links

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

2. | C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in |

3. | C. H. Bennett, F. Bessette, G. Brassard, L. Savail, and J. Smolin, “Experimental quantum cryptography,” J. Cryp-tol. |

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

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

6. | X.-B. Wang, “Beating the photon pulse-number-splitting attack in practical quantum cryptography,” Phys. Rev. Lett. |

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

8. | W.-Y. Hwang, “Quantum key distribution with high loss: toward global secure communication,” Phys. Rev. Lett. |

9. | D. Gottesman, H.-K. Lo, N. Lütkenhaus, and J. Preskill, “Security of quantum key distribution with imperfect devices,” Quant. Inf. Comp. |

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

11. | Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “Unconditionally secure one-way quantum key distribution using decoy pulses,” Appl. Phys. Lett. |

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

13. | X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A |

14. | C.-Z. Peng, J. Zhang, D. Yang, W.-B. Gao, H.-Xin. Ma, H. Yin, H.-P. Zeng, T. Yang, X.-B. Wang, and J.-W. Pan, “Experimental long-distance decoy-state quantum key distribution based on polarization encoding,” Phys. Rev. Lett. |

15. | D. Rosenberg, J. W. Harrington, P. R. Rice, P. A. Hiskett, C. G. Peterson, R. J. Hughes, A. E. Lita , S-W. Nam, and J. E. Nordholt, “Long-distance decoy-State quantum key distribution in optical fiber,” Phys. Rev. Lett. |

16. | G. Ribordy, J. D. Gautier, H. Zbinden, and N. Gisin, “Performance of InGaAs/InP avalanche photodiodes as gated-mode photon counters,” Appl. Opt. |

17. | M. Hayashi, “Upper bounds of eavesdropper’s performances in finite-length code with decoy method,” quant-ph/0702250 (2007). |

**OCIS Codes**

(060.4510) Fiber optics and optical communications : Optical communications

(270.0270) Quantum optics : Quantum optics

(270.5290) Quantum optics : Photon statistics

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: May 4, 2007

Revised Manuscript: June 15, 2007

Manuscript Accepted: June 18, 2007

Published: June 22, 2007

**Citation**

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, "Practical quantum key distribution over 60 hours at an optical fiber distance of 20km using weak and vacuum decoy pulses for enhanced security," Opt. Express **15**, 8465-8471 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-13-8465

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### References

- N. Gisin, G. Ribordy, W. Tittel and H. Zbinden, "Quantum cryptography," Rev. Mod. Phys. 74, 145-195 (2002). [CrossRef]
- 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, (IEEE, New York, 1984), pp. 175179.
- C. H. Bennett, F. Bessette, G. Brassard, L. Savail and J. Smolin, "Experimental quantum cryptography," J. Cryptol. 53-28 (1992).
- D. Stucki, N. Gisin, O. Guinnard, G. Ribordy and H. Zbinden, "Quantum key distribution over 67km with a plug & play system," New J. Phys. 4 41.1-41.8 (2002). [CrossRef]
- C. Gobby, Z. L. Yuan and A. J. Shields, "Quantum key distribution over 122km of standard telecom fiber," Appl. Phys. Lett. 84, 3762-3764 (2004). [CrossRef]
- X.-B. Wang, "Beating the photon pulse-number-splitting attack in practical quantum cryptography," Phys. Rev. Lett. 94, 230503-1-4 (2005) and H.-K. Lo, X. Ma and K. Chen, "Decoy state quantum key distribution," Phys. Rev. Lett. 94, 230504-1-4 (2005). [CrossRef] [PubMed]
- G. Brassard, N. L¨utkenhaus, T. Mor and B. C. Sanders, "Limits on practical quantum cryptography," Phys. Rev. Lett. 85, 1330-1333 (2000). [CrossRef] [PubMed]
- W.-Y. Hwang, "Quantum key distribution with high loss: toward global secure communication," Phys. Rev. Lett. 91, 057901-1-4 (2003). [CrossRef] [PubMed]
- D. Gottesman, H.-K. Lo, N. Lutkenhaus and J. Preskill, "Security of quantum key distribution with imperfect devices," Quant. Inf. Comp. 5, 325-360 (2004).
- Y. Zhao, B. Qi, X. Ma, H.-K. Lo and L. Qian, "Experimental quantum key distribution with decoy states," Phys. Rev. Lett. 96, 070502-1-4 (2006). [CrossRef] [PubMed]
- Z. L. Yuan, A. W. Sharpe and A. J. Shields, "Unconditionally secure one-way quantum key distribution using decoy pulses," Appl. Phys. Lett. 90, 011118-1-3 (2007). [CrossRef]
- C. Gobby, Z. L. Yuan and A. J. Shields, Elec. Lett. "Unconditionally secure quantum key distribution over 50 km of standard telecom fiber," Electron. Lett. 40, 1603-1605 (2004). [CrossRef]
- X. Ma, B. Qi, Y. Zhao and H.-K. Lo, "Practical decoy state for quantum key distribution," Phys. Rev. A 72, 012306-1-15 (2005). [CrossRef]
- C.-Z. Peng, J. Zhang, D. Yang, W.-B. Gao, H.-Xin. Ma, H. Yin, H.-P. Zeng, T. Yang, X.-B. Wang and J.-W. Pan, "Experimental long-distance decoy-state quantum key distribution based on polarization encoding," Phys. Rev. Lett. 98, 010505-1-4 (2007). [CrossRef] [PubMed]
- D. Rosenberg, J. W. Harrington, P. R. Rice, P. A. Hiskett, C. G. Peterson, R. J. Hughes, A. E. Lita, S-W. Nam and J. E. Nordholt, "Long-distance decoy-State quantum key distribution in optical fiber," Phys. Rev. Lett. 98, 010505-1-4 (2007). [CrossRef]
- G. Ribordy, J. D. Gautier, H. Zbinden, and N. Gisin, "Performance of InGaAs/InP avalanche photodiodes as gated-mode photon counters," Appl. Opt. 37, 2272 (1998). [CrossRef]
- M. Hayashi, "Upper bounds of eavesdropper’s performances in finite-length code with decoy method," quantph/ 0702250 (2007).

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