## Experimental study of high speed polarization-coding quantum key distribution with sifted-key rates over Mbit/s

Optics Express, Vol. 14, Issue 6, pp. 2062-2070 (2006)

http://dx.doi.org/10.1364/OE.14.002062

Acrobat PDF (184 KB)

### Abstract

We present a quantitative study of various limitations on quantum cryptographic systems operating with sifted-key rates over Mbit/s. The dead time of silicon APDs not only limits the sifted-key rate but also causes correlation between the neighboring key bits. In addition to the well-known count-rate dependent timing jitter in avalanche photo-diode (APD), the faint laser sources, the vertical cavity surface emission lasers (VCSELs) in our system, also induce a significant amount of data-dependent timing jitter. Both the dead time and the data-dependent timing jitter are major limiting factors in designing QKD systems with sifted-key rates beyond Mbit/s.

© 2006 Optical Society of America

## 1. Introduction

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

11. X. Tang, L. Ma, A. Mink, A. Nakassis, B. Hershman, J. Bienfang, R. F. Boisvert, C. Clark, and C. Williams, “High Speed Fiber-Based Quantum Key Distribution using Polarization Encoding,” in Optics and Photonics 2005: Quantum Communications and Quantum Imaging III, Proc. SPIE **5893**, 1-1-1A-9 (2005)

15. K. J. Gordon, V. Fernandez, G. S. Buller, I. Rech, S. D. Cova, and P. D. Townsend, “Quantum key distribution system clocked at 2 GHz,” Opt. Express **13**: 3015–3020 (2005). [CrossRef] [PubMed]

## 2. System configuration

## 3. Results and discussion

11. X. Tang, L. Ma, A. Mink, A. Nakassis, B. Hershman, J. Bienfang, R. F. Boisvert, C. Clark, and C. Williams, “High Speed Fiber-Based Quantum Key Distribution using Polarization Encoding,” in Optics and Photonics 2005: Quantum Communications and Quantum Imaging III, Proc. SPIE **5893**, 1-1-1A-9 (2005)

12. A. Nakassis, J. Bienfang, and C. Williams, “Expeditious reconciliation for practical quantum key distribution,” in Defense and Security Symposium: Quantum Information and Computation II, Proc. SPIE5436, 28–35 (2004). [CrossRef]

### 3.1 Sifted-key rate

*t*

_{dead}) to recover its initial operation state for detection of the next photon. During this period, the bias voltage across the p-n junction of the APD is below the breakdown level and no photon can be detected. Moreover, in most high-speed QKD system, the APDs operate in free-running mode and different APDs works independently from each other so that when one APD is in the dead time the other APD can still detect a photon. In this case, the sifted-key rate can be calculated by

*t*

_{dead}is 50 ns in this experiment and

*R*

_{1}is the detection count rate for each APD. In B92,

*μ*is the mean photon number per pulse sent by Alice. There are some discussions [13

13. D. S. Pearson and C. Elliott, “On the optimal mean photon number for quantum cryptography,” Eprint quant-ph/0403065 (2004), http://arxiv.org/fpt/quant-ph/papers/0403/0403064.pdf

*ν*is the QCTR. The photon detection efficiency

*P*

_{d}of the APDs is 45% at 850 nm according to the manufacturer’s specifications. The quantity

*L*

_{f}represents the optical loss in the transmission fiber and connectors, which is measured to be -3.0 dB. Other optical devices have an additional loss

*L*

_{o}of approximately -2.0 dB. For a given path, the coupler causes 3-dB loss of power (

*L*

_{c}), i.e., photon numbers. The polarization beam splitter further induces 6-dB loss (

*L*

_{p}) for a given path. Ideally, in the B92 protocol the polarization beam splitter blocks all photons in the incompatible bits (bits 1 for PBS in Path 0 and bits 0 for PBS in Path 1), and causes 3-dB loss in average numbers of photons per bit. The photons in incompatible bits could leak though a real PBS but this probability is small and has negligible effect on the sifted key rate. For example a typical PBS has more than 20 dB extinction ratio. In comparison, such imperfect extinction ratio has an important effect on the quantum bit error rate and we will discuss it in the next section.

*t*

_{dead}≪1/

*R*

_{1}. In this case, one can approximate

*R*by 2

*R*

_{1}and therefore,

*R*increases linearly over QCTR. As one further increases QCTR to achieve sifted-key rate beyond Mbit/s, the increase of the sifted-key rate gradually deviates from the linear growth and, at sufficient high QCTRs, the sifted-key rate is ultimately limited by 2/

*t*

_{dead}. Figure 2 shows our measured sifted-key rate and QBER for different QCTRs. The solid line represents the sifted-key rate calculated with Eq. (1) and the dash line represents the sifted-key rate with the linear approximation (

*t*

_{dead}=0). As shown in the figure, the sifted-key rate agrees well with Eq. (1). The figure also shows that our system is operated at the edge of the linear region. The sifted-key rate will be gradually saturated as the QCTR further increases.

*t*

_{dead}with sufficiently high QCTR, the dead time could induce a strong correlation between neighboring sifted key bits. In this region, when one APD is in the dead time, photons can only be detected by the other APD, which generate key bits with different value. Thus the sifted key is not completely random and the security could be potentially degraded. When the QCTR is so high that the sifted-key rate is saturated to 2/

*t*

_{dead}, the firing order of the two APDs can become self-synchronized. In that case, the APDs will come out of their dead time in the same order they entered. When an APD comes out of its dead time there is a high probability of it firing again before any of the other APDs come out of their dead times. This self-synchronized sequence can continue for some time resulting in a burst of non-random sifted keys. One heuristic way to inhibit such events would be disabling all APDs when one fires, until the dead time is over so that detections only occur when all APDs are available. Nevertheless, as can be seen from Fig. 2, our system is currently operating in the linear region and the potential degradation of security is negligible.

### 3.2 QBER

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

14. J. K. Guenter and J. A. Tatum, “Modulating VCSELs,” (Honeywell), http://www.adopco.com/publication/documents/ModulatingVCSELs.pdf.

15. K. J. Gordon, V. Fernandez, G. S. Buller, I. Rech, S. D. Cova, and P. D. Townsend, “Quantum key distribution system clocked at 2 GHz,” Opt. Express **13**: 3015–3020 (2005). [CrossRef] [PubMed]

13. D. S. Pearson and C. Elliott, “On the optimal mean photon number for quantum cryptography,” Eprint quant-ph/0403065 (2004), http://arxiv.org/fpt/quant-ph/papers/0403/0403064.pdf

## 4. Conclusion

*μ*= 0.1 and an error rate of 3.08%. With QCTR below 1 Gbit/s in our system, the sifted-key rate increases approximately linearly over the QCTR. In comparison, at higher QCTR, the dead time can saturate the sifted-key rate and degrade security performance as well. Our results also show that the data-dependent system timing jitter has the major effect on the QBER in a QKD system operating around 1 GHz and beyond. A higher speed system requires a further reduction of both APD dead time and the data-dependent system timing jitter.

## Acknowledgments

## References and links

1. | C. H. Bennet and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” in Proceedings of IEEE International Conference on Computers, Systems and Signal Processing (Institute of Electrical and Electronics Engineers, Bangalore, India,1984), pp. 175–179. |

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

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

4. | J.C. Bienfang, A. J. Gross, A. Mink, B. J. Hershman, A. Nakassis, X. Tang, R. Lum, D. H. Su, and C. W. Clark, “Quantum key distribution with 1.25 Gbps clock synchronization,” Opt. Express. |

5. | J. G. Rarity, P. R. Tapster, and P. M. Gorman, “Secure Free-space key-exchange to 1.9 km and beyond,” J. Mod. Opt. |

6. | C. Elliott, D. Pearson, and G. Troxel, “Quantum cryptography in practice,” in SIGCOMM’ 03: Proceedings of the 2003 Conference on Applications, Technologies, Architectures, and Protocols for Computer Communications (ACM Press, New York, 2003), pp. 227–238. |

7. | D. S. Bethune, M. Navarro, and W. P. Risk, “Enhanced autocompensating quantum cryptography system,” Appl. Opt. |

8. | J. Breguet, A. Muller, and N. Gisin, “Quantum cryptography with polarized photons in optical fibers, experiment and practical limits,” J. of Mod. Opt. , |

9. | P. D. Townsend, “Experimental investigation of the performance limits for first telecommunication-window quantum cryptography system,” IEEE Photon. Technol. Lett. |

10. | K. J. Gordon, V. Fernandez, P. D. Townsend, and G. S. Buller, “A Short Wavelength GigaHertz Clocked FiberOptic Quantum Key Distribution System,” IEEE J. of Quantum Electron. |

11. | X. Tang, L. Ma, A. Mink, A. Nakassis, B. Hershman, J. Bienfang, R. F. Boisvert, C. Clark, and C. Williams, “High Speed Fiber-Based Quantum Key Distribution using Polarization Encoding,” in Optics and Photonics 2005: Quantum Communications and Quantum Imaging III, Proc. SPIE |

12. | A. Nakassis, J. Bienfang, and C. Williams, “Expeditious reconciliation for practical quantum key distribution,” in Defense and Security Symposium: Quantum Information and Computation II, Proc. SPIE5436, 28–35 (2004). [CrossRef] |

13. | D. S. Pearson and C. Elliott, “On the optimal mean photon number for quantum cryptography,” Eprint quant-ph/0403065 (2004), http://arxiv.org/fpt/quant-ph/papers/0403/0403064.pdf |

14. | J. K. Guenter and J. A. Tatum, “Modulating VCSELs,” (Honeywell), http://www.adopco.com/publication/documents/ModulatingVCSELs.pdf. |

15. | K. J. Gordon, V. Fernandez, G. S. Buller, I. Rech, S. D. Cova, and P. D. Townsend, “Quantum key distribution system clocked at 2 GHz,” Opt. Express |

**OCIS Codes**

(030.5260) Coherence and statistical optics : Photon counting

(060.2330) Fiber optics and optical communications : Fiber optics communications

(060.4510) Fiber optics and optical communications : Optical communications

(270.5570) Quantum optics : Quantum detectors

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: January 11, 2006

Revised Manuscript: March 6, 2006

Manuscript Accepted: March 15, 2006

Published: March 20, 2006

**Citation**

Xiao Tang, Lijun Ma, Alan Mink, Anastase Nakassis, Hai Xu, Barry Hershman, Joshua C. Bienfang, David Su, Ronald F. Boisvert, Charles W. Clark, and Carl J. Williams, "Experimental study of high speed polarization-coding quantum key distribution with sifted-key rates over Mbit/s," Opt. Express **14**, 2062-2070 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-6-2062

Sort: Year | Journal | Reset

### References

- C. H. Bennet and G. Brassard, "Quantum cryptography: Public key distribution and coin tossing," in Proceedings of IEEE International Conference on Computers, Systems and Signal Processing (Institute of Electrical and Electronics Engineers, Bangalore, India,1984), pp. 175-179.
- C. H. Bennett, "Quantum cryptography using any two nonorthogonal states," Phys. Rev. Lett. 68, 3121-3124 (1992). [CrossRef] [PubMed]
- N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, "Quantum cryptography," Rev. Mod. Phys. 74, 145-195 (2002). [CrossRef]
- J.C. Bienfang, A. J. Gross, A. Mink, B. J. Hershman, A. Nakassis, X. Tang, R. Lum D. H. Su, C. W. Clark, "Quantum key distribution with 1.25 Gbps clock synchronization," Opt. Express. 7, 2011-2016 (2004). [CrossRef]
- J. G. Rarity, P. R. Tapster and P. M. Gorman, "Secure Free-space key-exchange to 1.9 km and beyond," J. Mod. Opt. 48, 1887-1901 (2001).
- C. Elliott, D. Pearson, and G. Troxel, "Quantum cryptography in practice," in SIGCOMM’ 03: Proceedings of the 2003 Conference on Applications, Technologies, Architectures, and Protocols for Computer Communications (ACM Press, New York, 2003), pp. 227-238.
- D. S. Bethune, M. Navarro, and W. P. Risk, "Enhanced autocompensating quantum cryptography system," Appl. Opt. 41, 1640-1648 (2002). [CrossRef] [PubMed]
- J. Breguet, A. Muller, and N. Gisin, "Quantum cryptography with polarized photons in optical fibers, experiment and practical limits," J. of Mod. Opt., 41, 2405-2412 (1994). [CrossRef]
- P. D. Townsend, "Experimental investigation of the performance limits for first telecommunication-window quantum cryptography system," IEEE Photon. Technol. Lett. 10, 1048-1050 (1998). [CrossRef]
- K. J. Gordon, V. Fernandez, P. D. Townsend, and G. S. Buller, "A Short Wavelength GigaHertz Clocked Fiber-Optic Quantum Key Distribution System," IEEE J. Quantum Electron. 40, 900-908 (2004). [CrossRef]
- X. Tang, L. Ma, A. Mink, A. Nakassis, B. Hershman, J. Bienfang, R. F. Boisvert, C. Clark, and C. Williams, "High Speed Fiber-Based Quantum Key Distribution using Polarization Encoding," in Optics and Photonics 2005: Quantum Communications and Quantum Imaging III, Proc. SPIE 5893, 1A-1-1A-9 (2005)
- A. Nakassis, J. Bienfang, and C. Williams, "Expeditious reconciliation for practical quantum key distribution," in Defense and Security Symposium: Quantum Information and Computation II, Proc. SPIE 5436,28-35 (2004). [CrossRef]
- D. S. Pearson and C. Elliott, "On the optimal mean photon number for quantum cryptography," Eprint quant-ph/0403065 (2004), http://arxiv.org/fpt/quant-ph/papers/0403/0403064.pdf
- J. K. Guenter and J. A. Tatum, "Modulating VCSELs," (Honeywell), http://www.adopco.com/publication/documents/ModulatingVCSELs.pdf.
- K. J. Gordon, V. Fernandez, G. S. Buller, I. Rech, S. D. Cova, and P. D. Townsend, "Quantum key distribution system clocked at 2 GHz," Opt. Express 13,3015-3020 (2005). [CrossRef] [PubMed]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.