10-GHz clock differential phase shift quantum key distribution experiment

This paper reports the first quantum key distribution experi m nt implemented with a 10-GHz clock frequency. We used a 10-GHz a ctively mode-locked fiber laser as a source of short coherent pulses a nd single photon detectors based on frequency up-conversion in perio dically poled lithium niobate waveguides. The use of short pulses and lowjitter upconversion detectors significantly reduced the bit errors c aused by detector dark counts even after long-distance transmission of a weak coherent state pulse. We employed the differential phase shift quantum key distribution protocol, and generated sifted keys at a rate of 3.7 kbit/s ov er a 105 km fiber with a bit error rate of 9.7%. © 2006 Optical Society of America OCIS codes: (270.0270) Quantum optics; (060.0060) Fiber optics and opt ical communications References and links 1. N. Gisin, G. Ribordy, W. Tittel and H. Zbinden, “Quantum cr yptography,” Rev. Mod. Phys. 74, 145-195 (2002). 2. P. D. Townsend, “Secure key distribution system based on q ua tum cryptography” Electron. Lett. 30 809 (1994). 3. G. Ribordy, J. D. Gautier, N. Gisin, O. Guinnard and H. Zbin de , “Automated ‘plug & play’ quantum key distribution,” Electron. Lett. 34 2116 (1998). 4. M. Bourennane, F. Gibson, A. Karlsson, A. Hening, P. Jonss , T. Tsegaye, D. Ljunggren and E. Sundberg, “Experiments on long wavelength (1550 nm) “plug and play” quan t m cryptography systems,” Opt. Express 4 383 (1999). 5. D. Stucki, 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 (2002). 6. A. Yoshizawa, R. Kaji and H. Tsuchida,“10.5 km fiber-optic quantum key distribution at 1550 nm with a key rate of 45 kHz,” Jpn. J. Appl. Phys. 43 (2004) L735. 7. T. Honjo, K. Inoue and H. Takahashi, “Differential-phase -shift quantum key distribution experiment with a planar light-wave circuit Mach-Zehnder interferometer,” Opt. Let t. 29, 2797 (2004). 8. 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). 9. C. Gobby, Z. L. Yuan and A. J. Shields, “Quantum key distrib ution over 122 km of standard telecom fiber,” Appl. Phys. Lett.84 3762-3764 (2004). 10. R. T. Thew, S. Tanzilli, L. Krainer, S. C. Zeller, A. Rocha s, I. Rech, S. Cova, H. Zbinden and N. Gisin, “Low-jitter up-conversion detectors for telecom wavelength QKD,” New J . Phys.8 32 (2006). 11. K. Inoue, E. Waks and Y. Yamamoto, “Differential phase shif t quantum key distribution,” Phys. Rev. Lett. 89, 037902 (2002). #73420 $15.00 USD Received 26 July 2006; revised 12 September 2006; accepted 13 September 2006 (C) 2006 OSA 2 October 2006 / Vol. 14, No. 20 / OPTICS EXPRESS 9522 12. K. Inoue, E. Waks and Y. Yamamoto, “Differential-phase-sh ift quantum key distribution using coherent light,” Phys. Rev. A68, 022317 (2003). 13. K. Inoue and T. Honjo, “Robustness of differential-phas e-shift quantum key distribution against photon-numbersplitting attack,” Phys. Rev. A71, 042305 (2005). 14. E. Diamanti, H. Takesue, T. Honjo, K. Inoue, and Y. Yamamoto, “Performance of various quantum-keydistribution systems using 1.55μm up-conversion single-photon detectors,” Phys. Rev. A 72, 052311 (2005). 15. E. Waks, H. Takesue and Y. Yamamoto, “Security of different ial-phase-shift quantum key distribution against individual attacks,” Phys. Rev. A73, 012344 (2006). 16. C. Langrock, E. Diamanti, R. V. Roussev, Y. Yamamoto, M. M. Fe jer, and H. Takesue, “Highly efficient singlephoton detection at communication wavelengths by use of upcon version in reverse-proton-exchanged periodically poled LiNbO3 waveguides,” Opt. Lett., 30, 1725 (2005).


Introduction
Fiber-based quantum key distribution (QKD) systems have been studied very intensively in recent years [1].Since the first QKD experiment over an optical fiber spool [2], many QKD systems have been demonstrated [3,4,5,6].Currently, intensive efforts are being made to increase the key generation rate and distribution distance.Fiber-based QKD experiments with a 1-GHz clock [7,8] and long-distance QKD over >100 km of fiber [8,9] have already been reported.
The main factor that limited the key distribution distance in previous experiments was bit errors caused by detector dark counts.The most straightforward way to increase the secure key distribution distance is to reduce the dark counts.Another effective approach is to increase the timing resolution of the whole system, which means that we use shorter pulses for photon transmission and photon detectors with shorter timing jitters.In such a system, the dark counts are randomly distributed in the time domain, but the detected signal counts are concentrated in small time segments.As a result, we can effectively increase the signal to noise ratio, which results in fewer bit errors.
A simple and effective way to increase the key generation rate is to increase the clock rate of the system.Since a 10-Gbit/s system is already in practical use in current (classical) optical communication, many components designed for such high-speed optical communication systems can be used to realize a 10-GHz clock QKD system.The biggest problem for such a system is the timing jitter of the single photon detectors.For example, the detectors based on frequency up-conversion in a periodically poled lithium niobate (PPLN) waveguide used in [8] had a timing jitter of ∼500 ps, which is too large for a 10-GHz clock system.Recently, a single photon interference experiment using up-conversion detectors with improved jitter has been reported [10].
In this paper, we report the first DPS-QKD system with a 10-GHz clock frequency.We used a 10-GHz actively mode-locked laser as a coherent pulse source.As regards the detectors, we used up-conversion detectors with improved jitter characteristics.The short pulses from the mode-locked laser and the low jitter characteristic of the detector improved the time resolution of the system, which resulted in a significant reduction of the dark count contribution to the bit errors.As a result, we successfully generated 3.7-kbit/s sifted keys over 105 km of fiber with 9.7% error rate.

Differential phase shift quantum key distribution protocol
Figure 1 shows a schematic diagram of DPS-QKD [11,12].Alice modulates the phase of each pulse emitted from a coherent pulse source by {0, π} using a phase modulator.The pulse train is then attenuated so that the average photon number per pulse is smaller than one (typically 0.2), and transmitted over an optical fiber.The output pulses from the fiber are received by Bob. Bob is equipped with a 1-bit delayed Mach-Zehnder interferometer whose two output ports are connected to single photon detectors 1 and 2. When the phase difference between two adjacent pulses is 0 (π), Bob observes a click at detector 1 (2).Since the average photon number per pulse is much less than 1, Bob observes clicks only occasionally.Bob records time instances in which he observed clicks, and which detector clicked.After detecting the photons, Bob discloses the time instances in which he observed clicks, while holding the which-detector information secret.Alice knows the phase differences at the particular time instances from her original modulation data, which are completely correlated to the which-detector information that Bob obtained in his measurement.As a result, Alice and Bob can construct an identical random bit string by allocating phase difference 0 as bit 0 and π as bit 1, which can be used later as a key for one-time pad cryptography.
In terms of a quantum mechanical description, DPS-QKD protocol is described as follows.If we assume the coherence time of the laser source as being infinite, the state that Alice prepares is expressed as where N, φ k and M are the total number of time slots, the classical phase modulation at time slot k (= {0, π}), and the number of photons in N time slots, respectively.The phase difference between adjacent time slots φ k+1 − φ k corresponds to bit "0" or "1".Since the average number of photons per pulse is set at much smaller than 1, the number of photons M is much smaller than the number of phase differences, N − 1.This means that it is impossible to reconstruct the whole wavefunction including N − 1 phase differences with M(< N − 1) measurements.Thus, the security of DPS-QKD is based on the non-orthogonality of a wavefunction spanned by many time slots.A merit of DPS-QKD is its robustness against photon number splitting attack, even though it uses a coherent light source [8,13,14].Security of DPS-QKD is proven against general individual attack [15], which makes DPS-QKD an attractive solution for constructing longdistance QKD systems with currently available technologies.

Generation of coherent pulse train at 10-GHz clock frequency
We used an actively mode-locked fiber laser operated at 10.0 GHz (Calmar Optocom PSL-10) as a coherent pulse source.The full width at half maximum (FWHM) of the pulses was 10 ps.A typical pulse train observed using a sampling oscilloscope with a 53 GHz bandwidth is shown in Fig. 2. The side peak observed in each pulse is probably due to the non-ideal response of the photodetector.To confirm that the phase coherence was preserved between adjacent pulses, we input the pulse train into a 1-bit delayed Mach-Zehnder interferometer with 100 ps delay time whose output ports were connected to two optical power meters.When the phase difference induced by the interferometer was adjusted to obtain a dark fringe at one of the ports, the ratio of the two output powers was ∼20 dB, which is probably limited by the crosstalk of the interferometer.We then applied a phase modulation with an alternating pattern (0π0π0π..), by which we switched the port where the majority of light was output.Here too, the ratio of the two output powers was ∼20 dB.This implies that the error caused by imperfect interferometry in a QKD experiment is suppressed to ∼1%.This value is similar to that observed in our previous QKD experiments with a 1-GHz clock frequency using coherent pulses generated by modulating CW semiconductor laser light with an external intensity modulator [7,8].A schematic diagram of the up-conversion detector is shown in Fig. 3 [16].A 1550-nm signal photon was combined with 1319-nm CW pump light from a Nd-YAG laser via a wavelength division multiplexing (WDM) fiber coupler, and input into a PPLN waveguide.The wavelength of the signal photon was converted to 713 nm through the sum frequency generation process in the PPLN waveguide.The output light from the PPLN waveguide was input into a wavelength filter to suppress the second harmonic signal of the pump (0.66 µm), and then reflected by a dichroic mirror to separate long-wavelength photons (1.3 and 1.5 µm).The reflected light is then input into a prism to further suppress the pump and SHG components, and finally focused onto a low-jitter Si-APD (MPD photon counting detector module).When we input a ∼100-mW pump light, we obtained a peak quantum efficiency of ∼8 %.However, as reported in [16], dark counts caused by the spurious nonlinear effect increased quadratically as the pump power increased.Therefore, in the following QKD experiments, we set the quantum efficiencies of the up-conversion detectors at relatively small values, to enable us to obtain a better signal to noise ratio.

Up-conversion detectors
We measured the timing jitter of the up-conversion detectors.We input pulses with a 3-ps FWHM and a 1-GHz repetition frequency, and obtained a histogram of the detected signal.A typical histogram is shown in Fig. 4(a), where the count rate was at around 300,000 cps.The FWHM was ∼30 ps, which is sufficiently smaller than the 100 ps time interval of the 10-GHz clock system.However, a long tail was observed, which constituted a major source of bit errors in the QKD experiments.To evaluate the tail, we measured both the FWHM and the full width at tenth maximum (FWTM) as a function of count rate.The result is shown in Fig. 4(b).Both FWHM and FWTM increased as the count rate increased.In particular, the FWTM increased significantly when the count rate approached 1 MHz.This means that the error increases significantly when the transmission loss is small or the quantum efficiencies of the detectors are high.

QKD experiments
We undertook QKD experiments using the setup shown in Fig. 1.Alice and Bob were located in the same room, and fiber transmission was undertaken using spools of dispersion shifted fiber with a zero dispersion wavelength of 1550 nm.The phase modulator was driven at a bit rate of 10 Gbit/s by a pseudo-random bit sequence signal from a high-speed pulse pattern generator (Anritsu MP1765A).We used a Mach-Zehnder interferometer fabricated using planar lightwave circuit (PLC) technology, which was developed for 10-Gbit/s differential phase shift keying

Fig. 2 .
Fig. 2. 10-GHz pulse train from a fiber mode-locked laser monitored by a sampling oscilloscope with a 53 GHz bandwidth.

Fig. 4 .
Fig. 4. (a) Typical histogram of detection signals from the up-conversion detector at a count rate of 300,000.(b) Full widths at half maximum and tenth maximum as a function of count rate.