## After-pulse-discarding in single-photon detection to reduce bit errors in quantum key distribution

Optics Express, Vol. 11, Issue 11, pp. 1303-1309 (2003)

http://dx.doi.org/10.1364/OE.11.001303

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### Abstract

We demonstrate fiber-optic quantum key distribution (QKD) at 1550 nm using single-photon detectors operating at 5 MHz. Such high-speed single-photon detectors are essential to the realization of efficient QKD. However, after-pulses increase bit errors. In the demonstration, we discard after-pulses by measuring time intervals of detection events. For a fiber length of 10.5 km, we have achieved a key rate of 17 kHz with an error of 2%.

© 2003 Optical Society of America

## 1. Introduction

## 2. Single-photon detectors

8. A. Yoshizawa, R. Kaji, and H. Tsuchida, “Quantum efficiency evaluation method for gated mode single photon detector,” Electron. Lett. **38**, 1468–1469 (2002). [CrossRef]

*p*

_{interval}(

*Δt*) denote the probability of finding

*Δt*among those measured. Also, let

*p*

_{after-pulse}(

*Δt*) denote the (conditional) probability that an after-pulse is observed after

*Δt*following a previous avalanche. Then, one finds that for each interval

*Δt*=

_{n}*n*/ν with

*n*=1,2,3…

*η*is a quantum efficiency and

*µ*is an average of photons per incoming pulse. The probability of finding no after-pulses within an interval of

*Δt*can be written as (

_{n}*n*=2,3,4…)

*p*

_{after-pulse}(

*Δt*) ~ 0,

_{n}*c*(

*Δt*) becomes

_{n}*n*-independent, enabling us to determine

*η*from the slope of ln

*p*

_{interval}(

*Δt*). Here, ln stands for natural logarithm. Furthermore, considering that

_{n}*c*(

*Δt*

_{1})=1,

*p*

_{after-pulse}(Δ

*t*) is calculated by substituting the estimated value of

_{n}*η*into Eq. (1). In the following, two single-photon detectors (D0 and D1) operating at ν=5 MHz are evaluated. Figure 1 shows ln

*p*

_{interval}(

*Δt*) of D0 measured at

_{n}*µ*=0.015. After-pulses are observed as a nonlinear decrease of the measured data for

*Δt*<10µs. However, for longer intervals, ln

_{n}*p*

_{interval}(

*Δt*) decreases linearly, yielding a quantum efficiency of

_{n}*η*=13%. Figure 2 shows ln

*p*

_{interval}(Δ

*t*) of D1 measured at the same value of

_{n}*µ*. Figure 3 shows the calculated

*p*

_{after-pulse}(

*Δt*), where solid and open circles correspond to those of D0 and D1, respectively. Although they have different probabilities for

_{n}*Δt*<4 µs, each after-pulse is mostly found within 10 µs following a previous avalanche. Table 1 summarizes operating conditions and evaluation results of D0 and D1. Here,

_{n}*d*

_{thermal}and

*d*

_{after-pulse}are dark-count probabilities per gate resulting from thermally excited carriers and after-pulses, respectively. The former is evaluated after excluding after-pulses by measuring time intervals of dark counts and discarding those with

*Δt*<10 µs (=

_{n}*Δt*

_{after-puse}). The remaining dark counts are found with a probability of

*d*

_{thermal}exp(-

*d*

_{thermal}ν

*Δt*

_{after-pulse}), which becomes nearly equal to

*d*

_{thermal}if

*d*

_{thermal}ν

*Δt*

_{after-pulse}≪1. Then, the difference between the dark-count probabilities per gate with and without discarding after-pulses coincides with

*d*

_{after-pulse}.

## 4. Results and discussion

*Δt*<

_{n}*Δt*

_{discard}. Solid circles are the measured results while open circles are corresponding key rates. For

*Δt*

_{discard}<5 µs, after-pulses are effectively discarded, leading to a significant decrease in QBER. However, if

*Δt*

_{discard}exceeds 5 µs, the QBER slowly decreases and then becomes

*Δt*

_{discard}-independent. Meanwhile, the key rate shows an exponential decrease such that

*k*=

*ηµ*exp[-(

*αL*+

*β*)/10]. Note that

*η*is a quantum efficiency of Bob’s single-photon detector (D0) whereas

*µ*is an average of photons of the signal pulse measured by Alice.

*α*is a fiber loss in dB/km;

*L*is a fiber length (km) and

*β*is an internal loss (dB) of Bob’s system. In the demonstration,

*η*=13%,

*µ*=0.05,

*α*=0.21,

*L*=10.5 and

*β*=3. A curve in Fig. 5 is obtained by substituting those parameters into Eq. (3). Figure 6 shows the measured results corresponding to D1. A curve in this figure is also obtained by substituting the same parameters as D0 except that

*η*=11% into Eq. (3). Approximately, the QBER can be written as

*p*

_{after-pulse}~ 0 for

*Δt*>10 µs whereas others are presented as solid and open circles in Fig. 3. The third term on the right-hand side of this equation is the QBER induced by backscattered photons from the signal and reference pulses in the quantum channel, internal reflections at Bob’s system and other imperfections of optical and electrical components. In the demonstration,

_{n}*e*

_{others}~1% and is independent of

*Δt*

_{discard}. Open squares in Figs. 5 and 6 are those calculated with Eq. (4), agreeing with the results obtained in QKD experiments (solid circles). Since the key rate decreases with

*Δt*

_{discard}, we have to properly determine

*Δt*

_{discard}for D0 and D1. For example, if we choose

*Δt*

_{discard}=7.6 µs for D0 and 5 µs for D1, respectively, the total key rate becomes 17 kHz with an error of 2%.

## 5. Summary

## References and links

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

2. | P. A. Hiskett, G. Bonfrate, G. S. Buller, and P. D. Townsend, “Eighty kilometer transmission experiment using an InGaAs/InP SPAD-based quantum cryptography receiver operating at 1.55 µm,” J. Mod. Opt. |

3. | P. A. Hiskett, J. M. Smith, G. S. Buller, and P. D. Townsend, “Low-noise single-photon detection at wavelength 1.55 µm,” Electron. Lett. |

4. | M. Bourennane, A. Karlsson, J. P. Ciscar, and M. Mathes, “Single-photon counters in the telecommunication wavelength region of 1550 nm for quantum information processing,” J. Mod. Opt. |

5. | D. Stucki, G. Ribordy, A. Stefanov, H. Zbinden, J. G. Rarity, and T. Wall, “Photon counting for quantum key distribution with Peltier cooled InGaAs/InP APDs,” J. Mod. Opt. |

6. | A. Yoshizawa, R. Kaji, and H. Tsuchida, “A method of discarding after-pulses in single-photon detection for quantum key distribution,” Jpn. J. Appl. Phys. |

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

8. | A. Yoshizawa, R. Kaji, and H. Tsuchida, “Quantum efficiency evaluation method for gated mode single photon detector,” Electron. Lett. |

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

10. | D. S. Bethune and W. P. Risk, “An autocompensating fiber-optic quantum cryptography system based on polarization splitting of light,” IEEE J. Quantum Electron. |

11. | C. H. Bennett and G. Brassard, “Quantum Cryptography: Public Key Distribution and Coin Tossing,” in |

**OCIS Codes**

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

(270.0270) Quantum optics : Quantum optics

**ToC Category:**

Research Papers

**History**

Original Manuscript: April 16, 2003

Revised Manuscript: May 16, 2003

Published: June 2, 2003

**Citation**

Akio Yoshizawa, R. Kaji, and H. Tsuchida, "After-pulse-discarding in single-photon detection to reduce bit errors in quantum key distribution," Opt. Express **11**, 1303-1309 (2003)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-11-1303

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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. A. Hiskett, G. Bonfrate, G. S. Buller and P. D. Townsend, �??Eighty kilometer transmission experiment using an InGaAs/InP SPAD-based quantum cryptography receiver operating at 1.55 m,�?? J. Mod. Opt. 48, 1957-1966 (2001).
- P. A. Hiskett, J. M. Smith, G. S. Buller and P. D. Townsend, �??Low-noise single-photon detection at wavelength 1.55 m,�?? Electron. Lett. 37, 1081-1082 (2001). [CrossRef]
- M. Bourennane, A. Karlsson, J. P. Ciscar and M. Mathes, �??Single-photon counters in the telecommunication wavelength region of 1550 nm for quantum information processing,�?? J. Mod. Opt. 48, 1983-1995 (2001).
- D. Stucki, G. Ribordy, A. Stefanov, H. Zbinden, J. G. Rarity and T. Wall, �??Photon counting for quantum key distribution with Peltier cooled InGaAs/InP APDs,�?? J. Mod. Opt. 48, 1967-1981 (2001). [CrossRef]
- A. Yoshizawa, R. Kaji and H. Tsuchida, �??A method of discarding after-pulses in single-photon detection for quantum key distribution,�?? Jpn. J. Appl. Phys. 41, 6016-6017 (2002). [CrossRef]
- D. Stuchi, N. Gisin, O. Guinnard, G. Ribordy and H. Zbinden, �??Quantum key distribution over 67 km with a plug & play system,�?? New J. Phys. 4, 41.1-41.8 (2002).
- A. Yoshizawa, R. Kaji and H. Tsuchida, �??Quantum efficiency evaluation method for gated mode single photon detector,�?? Electron. Lett. 38, 1468-1469 (2002). [CrossRef]
- C. H. Bennett, �??Quantum cryptography using any two nonorthogonal states,�?? Phys. Rev. Lett. 68, 3121-3124 (1992). [CrossRef] [PubMed]
- D. S. Bethune and W. P. Risk, �??An autocompensating fiber-optic quantum cryptography system based on polarization splitting of light,�?? IEEE J. Quantum Electron. 36, 340-347 (2000). [CrossRef]
- C. H. Bennett and G. Brassard, �??Quantum Cryptography: Public Key Distribution and Coin Tossing,�?? in Proc. of IEEE Inter. Conf. on Computers and Signal Processing, Bangalore, India (Institute of Electrical and Electronics Engineers, New York, 1984), pp. 175-179.

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