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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 11, Iss. 11 — Jun. 2, 2003
  • pp: 1303–1309
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After-pulse-discarding in single-photon detection to reduce bit errors in quantum key distribution

A. Yoshizawa, R. Kaji, and H. Tsuchida  »View Author Affiliations


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

pinterval(Δtn)=c(Δtn)e(n1)ημ[(1eημ)+pafterpulse(Δtn)]
(1)

Here, ν is a repetition frequency; 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 Δtn can be written as (n=2,3,4…)

c(Δtn)=Πk=1n1[1pafterpulse(Δtn)].
(2)

Fig. 1. ln p interval(Δtn) of D0.
Fig. 2. ln p interval(Δtn) of D1.

Table 1. Operating conditions and evaluation results of single-photon detectors

table-icon
View This Table
Fig. 3. p after-pulse versus Δtn.

3. Quantum key distribution

3.1 Quantum channel

3.2 Clock sharing

Figure 4 also shows how to share the clock between Alice and Bob. A gain-switched laser diode (LD2) produces a sequence of light pulses at a repetition frequency of 1 MHz, each having a width of 50 ps with a bandwidth of 10 nm centered at 1550 nm. To synchronize LD1 with LD2, a two-channel synthesized function generator (SFG) is used, which also triggers a delay generator (DG) whose outputs become timing signals for gated-mode operation of D0 and D1. Alice detects clock pulses sent by Bob via DSF2 with a conventional avalanche photodiode (C-APD), whose output pulse is converted into a square wave with a frequency of 1 MHz, which becomes a reference signal of a frequency synthesizer (FS). A sinusoidal wave with a frequency of 10 MHz is generated from FS, and is applied as a time-base signal to an arbitrary wave function generator, which is used as PRNG. Since the signal/reference pulse and the clock pulse are transmitted through separate fibers, the difference in temperature between DSF1 and DSF2 will cause the relative temporal walk-off between those pulses. However, such a walk-off is estimated to be ~0.6 ns/K [2

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. 48, 1957–1966 (2001).

], and is not a significant problem because it is much smaller than the width of the voltage pulse applied to PM (=50 ns). Compared with the signal and reference pulses, the clock pulse is strong enough to produce a large number of backscattered photons. The presented system prevents those photons from entering single-photon detectors. Thus, only half of backscattered photons from the signal and reference pulses (much weaker than the clock pulse) become bit errors in QKD.

Fig. 4. Experimental setup for quantum key distribution. LD1 and LD2: gain-switched laser diodes, PC: polarization controller, PBS1 and PBS2: polarizing beam splitters, HWP: half-wave plate, QWP: quarter-wave plate, M: mirror, DL: delay line, FRM: Faraday rotator mirror, D0 and D1: single-photon detectors, SFG: synthesized function generator, DG: delay generator, PM: phase modulator, C-APD: conventional avalanche photodiode, PRNG: pseudo-random number generator, AT: attenuator, DSF1 and DSF2: dispersion-shifted single-mode fibers, FS: frequency synthesizer.

4. Results and discussion

Figure 5 shows the quantum bit-error rate (QBER) of D0 after discarding detection events with intervals Δtn<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

r=kvexp(kvΔtdiscard).
(3)

Here, k=ηµexp[-(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

Fig. 5. Measured and calculated quantum bit-error rates (solid circles and open squares, respectively) and corresponding key rates (open circles) of D0.
Fig. 6. Measured and calculated quantum bit-error rates (solid circles and open squares, respectively) and corresponding key rates (open circles) of D1.
eqberdthermal2k+12n=11kpafterpulse(Δtdiscard+Δtn)+eothers.
(4)

In this equation, the first and second terms on the right-hand side express contributions to bit errors of thermally excited carriers and after-pulses, respectively. In the following calculation, we assume that p after-pulse ~ 0 for Δtn>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, 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

We have demonstrated fiber-optic quantum key distribution at 1550 nm using single-photon detectors operating at 5 MHz. After-pulses are discarded by measuring time intervals of detection events, leading to a significant reduction of the quantum bit-error rate. For a fiber length of 10.5 km, we have achieved a key rate of 17 kHz with an error of 2%.

References and links

1.

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

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. 48, 1957–1966 (2001).

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. 37, 1081–1082 (2001). [CrossRef]

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. 48, 1983–1995 (2001).

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. 48, 1967–1981 (2001). [CrossRef]

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. 41, 6016–6017 (2002). [CrossRef]

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. 4, 41.1–41.8 (2002).

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]

9.

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

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. 36, 340–347 (2000). [CrossRef]

11.

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.

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

  1. N. Gisin, G. Ribordy, W. Tittel and H. Zbinden, �??Quantum cryptography,�?? Rev. Mod. Phys. 74, 145-195 (2002). [CrossRef]
  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 m,�?? J. Mod. Opt. 48, 1957-1966 (2001).
  3. 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]
  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. 48, 1983-1995 (2001).
  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. 48, 1967-1981 (2001). [CrossRef]
  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. 41, 6016-6017 (2002). [CrossRef]
  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. 4, 41.1-41.8 (2002).
  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]
  9. C. H. Bennett, �??Quantum cryptography using any two nonorthogonal states,�?? Phys. Rev. Lett. 68, 3121-3124 (1992). [CrossRef] [PubMed]
  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. 36, 340-347 (2000). [CrossRef]
  11. 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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