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Synchronization of free-space quantum key distribution
Optics Communications 275 (2007) 486–490 www.elsevier.com/locate/optcom
Synchronization of free-space quantum key distribution Qing-Lin Wu, Zheng-Fu Han *, Er-Long Miao, Yun Liu, Yi-Min Dai, Guang-Can Guo Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China Received 21 November 2006; received in revised form 22 March 2007; accepted 23 March 2007
Abstract In this paper, it is investigated that how the atmosphere effects on the synchronization accuracy in free-space quantum key distribution (QKD). We measured the synchronization error of a free-space QKD in our near-ground platform. According to experimental results and theoretical calculations, we deduce that the intensity fluctuation of synchronization light due to atmosphere disturbance contributes far more to the synchronization accuracy than others. By using the constant fraction discrimination method, the synchronization error of the free-space QKD, passing through the aerosphere, can be limited within 300 ps which meets the synchronization requirement of a satellite-to-ground QKD system. Ó 2007 Elsevier B.V. All rights reserved. Keywords: Free-space quantum key distribution; Synchronization; Synchronization accuracy
1. Introduction Until now, quantum key distribution (QKD) is the only method to distribute a key with unconditional security through a public channel [1,2]. Originated from Bennett and Brassard’s protocol [1], experimental QKD demonstrations have been performed over 184.6 km via optical cable [3–5]. However, it is still difficult to distribute the quantum key through more than 200 km with fiber due to the losses and the low single-photon detection efficiency. Free-space QKD is now attracting increasing attention [6–8] because of its low-transmission loss. However, in free-space, the beam path is open so any background radiation can enter the system as noise, especially in the satellite-to-ground QKD. In fact, the background light plays a dominant role to the quantum-bit error rate (QBER) in free-space QKD [9]. There are three major methods to shield against the background noise [9], one of which is the time gate filtering. In order to decrease the number of background photons, as well as the dark counts, most of the time the single-photon detector (SPD) is in the off mode. Only when the signal *
Corresponding author. Tel.: +86 551 3607342; fax: +86 551 3606828. E-mail address: [email protected] (Z.-F. Han).
0030-4018/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2007.03.068
photons are expected to arrive is a narrow time gate opened to allow them to enter the SPD, thus noise photons arriving outside the time window are blocked. The narrower the time gate is, the more efficiency this method can obtain. However, a narrow time gate requires precise knowledge of the signal photon’s arrival time, that is, a precise synchronization between the sender and receiver is critically required. Therefore, it is one of the crucial technologies to realize a precise synchronization in long distance free-space QKD. To date, there are two ways to achieve this. One is to utilize stabilized local clocks and software-controlled phase-lock loop driven by the detected photon signal [10] or by the ultra precise global position system (GPS) signal [8]. The other method is to make use of a periodic bright pulse of a different wavelength as precursor to open a time gate for the subsequent signal photon [6]. The former has only a key rate of several hundreds bits per second and needs a timing adjustment, while the latter has a key rate limited only by the attenuated signal pulses and is very easy to realize in practice. In this paper, we prefer the latter and study the influence of the atmosphere on the synchronization accuracy of the free-space QKD in our own platform. Furthermore, a constant fraction discrimination technique is introduced, which can provide a
Q.-L. Wu et al. / Optics Communications 275 (2007) 486–490
sub-nanosecond synchronization accuracy for long distance free-space QKD. In the precursor light pulse synchronization [6], the transmitter first emits a strong light pulse, which acts as a synchronization light (SL) on each clock cycle. After a certain time delay, Dt, a data pulse is launched towards the receiver. At receiver, the arrival time of the SL is used as a reference time to turn on a timing gate in which a QKD data pulse is expected. The time delay between the reference time and the timing gate is also set to Dt exactly. In general, the SL is detected by a photodetector (PD) and an edge triggered discriminator (ETD) to generate the time reference, as shown in Fig. 1a. The amplitude of the output of the PD is directly proportional to the intensity of the light. When the leading edge of this pulse rises to the settled threshold, the ETD yields the timing pulse. The propagation of SL is quite stable in such steady and closed circumstance like optical fiber. However, in free-space, the intensity of the SL varies due to the atmospheric disturbance [11–13], so does the pulse height of the output of PD. This consequentially results in a random time jitter of the time reference, which is known as the synchronization accuracy or the synchronization error. For example, the time reference travels from the time t1 to t2 when the pulse amplitude of PD fluctuates from A1 to A2 (Fig. 1b). The synchronization error is determined by the time jitter t 2 t 1.
487
on the ground, where the effect of atmosphere is even more severe than that of high altitude. The transmitter (Fig. 2a) was designed round a 50 mm diameter transmit telescope. On each cycle of a 1 MHz clock (SRS DG535) the laser diode (LD) emitted a 650 nm SL pulse with the pulse width of 2.5 ns. After focused and aligned, the light beam arrived at the transmitting telescope via a spatial filter (F). In order to ease optimizing the focusing of the receiver, a continuous wave alignment laser was also fed through the spatial filter by a beam splitter (BS). The beam from the filter was expanded in the transmit telescope to a collimated beam with a diameter of 40 mm full width at half maximum (FWHM). The whole transmitting system was mounted on a 50 cm diameter breadboard, attached to a sturdy tripod. The receiver system (Fig. 2b) consisted of a 203 mm diameter commercial telescope (Meade LX200). A photodetector (SPD052) with a bandwidth of 350 MHz was coupled to the back of the telescope after a spatial filter (F) to detect the SL. The output of PD triggered a ETD with a settled threshold to generate the time reference. The transmitter was installed in a room (20 m above ground) located in the Dongpu island (100 m above sea level) in Hefei, China. The receiver was placed in a lakefront house, which located 1.5 km away from the transmitter. 3. Experimental section
It is well known that both the transmission losses and the atmosphere disturbance decrease rapidly with the increase of an altitude [14,15], and recent long distance free-space QKD were all carried out over 2100 m above sea level [6–8]. We put both the transmitter and the receiver
In order to decrease the effects of background lights, the experiment was performed at night. A high speed oscilloscope (Tek TDS7404, 4 GHz bandwidth) was used to measure the time jitter of the timing pulse, which comes from a homemade ETD. The threshold of ETD is set to 300 mV, which is less than the minimum amplitude of input pulse and is greater than any baseline noise. The measured time jitter is about 211 ps (FWHM), as shown in Fig. 3a. The
Fig. 1. Generation of synchronization timing pulse (a) and synchronization error (b). Sync Light is synchronization light, PD is a photodetector, A1 and A2 are amplitudes of the output of PD and ETD is an edge triggered discriminator.
Fig. 2. System diagram of transmitter (a) and receiver (b). LD is a laser diode, BS is a beam splitter, F is a spatial filter, PD is a photodetector, T_Telescope is a transmitting telescope and R_Telescope is a receiving telescope.
2. Experimental setup
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Fig. 3. Synchronization timing error: (a) 1.5 km and (b) 3 km. CFD is a constant fraction discriminator and ETD is an edge triggered discriminator.
above result contains the jitter from the oscilloscope and the clock. In order to quantificationally estimate the synchronization timing error caused only by the atmosphere, we adjusted the above one-way system to a return system. A reflecting mirror instead of the receiver was placed in the lakefront house while the receiver was placed at the side of the transmitter, so the transmission distance reaches 3 km. The clock generated two outputs simultaneously, one was used to drive the laser diode while the other was acted as the oscilloscope’s external trigger. Therefore, both the jitter of oscilloscope and that of clock can be eliminated in such configuration. The synchronization timing error at the distance of 3 km is about 352 ps (FWHM), as shown in Fig. 3b. The threshold of ETD is 130 mV, which is selected similar to that of 1.5 km link distance. It can be seen that the timing error for an ETD increases rapidly as the distance between transmitter and receiver increases.
(ORTEC Trump-PCI) at distance of 1.5 km and 3 km, respectively, as shown in Fig. 4. According to Young et al. [16], the pulse broadening due to atmosphere disturbance is neglectable for a light pulse in duration of 2.5 ns, so we can consider that the pulse shape is invariable during the transmission. The jitter originated from the amplitude fluctuation can be calculated by assuming the output of 2
x
PD is a Gaussian waveform GðxÞ ¼ V e 2r2 , where V is the pulse amplitude corresponding to the x-axis of pulse height distribution curve, and r equals 1.062 ns for a pulse with the width of 2.5 ns. In order to calculate the jitter, two pulse heights, V1 and V2, which correspond to the half maxim counts of the pulse height distribution curve, are x
2
chosen. Then we obtain the functions G1 ðxÞ ¼ V 1 e 2r2 x2 and G2 ðxÞ ¼ V 2 e2r2 . For a settled threshold Vth, we can get two equations 2
V1e
4. Discussion
x2 2r
¼ V th
ð1Þ
¼ V th
ð2Þ
and
4.1. Source of synchronization timing error While traveling in atmosphere, both the intensity and the pulse shape of the SL vary due to the atmosphere disturbance [11]. Therefore, the pulse height and the pulse shape of the PD will change consequently, which directly cause the timing error. The pulse height distribution of the PD was measured using a pulse height analyzer
2
V2e
x2 2r
The solutions of Eqs. (1) and (2), X1 and X2, represent the emergence moment of the reference time. Then we can obtain the time jitter Dt = jX2j jX1j. For example, from Fig. 4, V1 and V2 are 0.4 V and 0.447 V at the distance of 1.5 km. Together with the threshold Vth = 0.3 V and r = 1.062 ns, we obtain the following solutions of
Fig. 4. Pulse height distribution of PD: (a) 1.5 km and (b) 3 km.
Q.-L. Wu et al. / Optics Communications 275 (2007) 486–490
Eqs. (1) and (2): X1 = 0.720 ns and X2 = 0.917 ns. The jitter Dt = 197 ps, which has a error of 6.7% compared to the measured value (211 ps). It can be seen that the synchronization error comes mainly from the intensity fluctuation of the synchronization light due to the atmosphere disturbance. 4.2. Minimize the synchronization timing error The output of ETD fluctuates consequentially with the unstable input pulse height against the settled threshold. A constant fraction discriminator (CFD) can be used to minimize the effect of amplitude fluctuations in the input signal. The trigger time of a CFD is nearly independent of the amplitude of input pulse, as shown in Fig. 5 [17]. The input signal, with an amplitude of A, feeds into a delay line and an attenuator simultaneously, as shown in Fig. 5a. The delayed signal Af(t td) and the attenuated signal PAf(t) are sending to a zero cross discriminator Dz, where td is the delay time of the delay line and P is the attenuate coefficient of the attenuator. P is usually set between 0.1 and 0.5 in most conditions [17]. The zero cross discriminator, Dz, flips when Af ðt td Þ ¼ PAf ðtÞ
ð3Þ
The delay time is selected to ensure td P (1 P)tr, where tr is the rise time of the input pulse [17]. We can then deduce from Eq. (3) that the trigger time is independent of amplitude and therefore is immune to amplitude fluctuation. An EDT, triggered by the input signal, is used to pre-
489
vent zero cross noise from mistriggering the zero cross discriminator Dz [17]. The threshold of ETD, Vth, is less than the minimum amplitude of input pulse and is greater than any baseline noise. Waveforms of all signals are shown in Fig. 5b. According to the above discussion, a CFD can be used to decrease the synchronization error, which comes mainly from the amplitude fluctuation. A homemade CFD with a attenuate coefficient of 0.2 is selected in our experiment. The threshold, Vth, is 300 mV and 130 mV for 1.5 km and 3 km link distance respectively. The jitters measured for 1.5 km and 3 km link distance are 95 ps (Fig. 3a) and 119 ps (Fig. 3b) respectively. It can be seen that the timing error decreases rapidly with a CFD. Furthermore, this error rises slightly with the increase of distance for a CFD. According to the above results, we can see that the jitter changes 24 ps while the distance increases 1.5 km for a CFD. We can then calculate the error increment is about 136 ps when the distance changed from 1.5 km to 10 km. Together with the 95 ps of 1.5 km, the error of a 10 km link distance is 231 ps. Taking into account other factors, we can estimate that the synchronization error can be limited within 300 ps for a free-space QKD passing through the aerosphere, which has a virtual thickness of 10 km. 5. Conclusions In this paper, we have discussed the synchronization method using precursor light pulse in free-space QKD. We have also evaluated factors that decrease the synchronization accuracy and ways to overcome them. Experimental results and calculation show that, the synchronization error comes mainly from the intensity fluctuation of synchronization light. Furthermore, this error increases rapidly with the increase of distance for an ETD while rises slightly for a CFD. Based on the measured data and extrapolation, we can deduce that the synchronization error of a 10 km free-space QKD can be limited less than 300 ps, which provides a sufficient synchronization accuracy for long distance free-space QKD, especially satellite-to-ground QKD. Acknowledgments The program is supported by the National Natural Science Foundation of China under Grant No. 60537020, the National Fundamental Research Program of China under Grant No. 6012503, and the Knowledge Innovation Project of Chinese Academy of Sciences.
Fig. 5. (a) System diagram of CFD. The input signal, Af(t), feeds into a delay line, an attenuator and an ETD simultaneous. Vp, the output of ETD Dp, acts as the enable signal of the zero cross discriminator Dz. VD is the differential input of Dz and equals to the delayed signal Af(t td) subtract the attenuated signal PAf(t). Vo is the output of CFD. (b) Waveforms of CFD. Waveforms in solid and dashed line represent two input signals with different amplitude. The CFD always triggers at the moment tT, which is regardless of amplitude fluctuations of input signals.
References [1] C.H. Bennett, G. Brassard, in: Proceedings of the IEEE International Conference Computers, Systems and Signal, 1984, p. 175. [2] A.K. Ekert, Phys. Rev. Lett. 67 (1991) 661. [3] X.-F. Mo, B. Zhu, Z.-F. Han, et al., Opt. Lett. 30 (2005) 2632.
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[4] C. Gobby, Z.L. Yuan, A.J. Shields, J. Appl. Phys. Lett. 84 (2004) 3762. [5] P.A. Hiskett, D. Rosenberg, C.G. Peterson, et al., New J. Phys. 8 (2006) 193. [6] R.J. Hughes, J.E. Nordholt, D. Derkacs, et al., New J. Phys. 4 (2002) 43. [7] C. Kurtsiefer, P. Zarda, M. Halder, et al., Nature 419 (2002) 450. [8] R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, et al., quant-ph/ 0607182. [9] E.-L. Miao, Z.-F. Han, S.-S. Gong, et al., New J. Phys. 7 (2005) 215. [10] J.G. Rarity, P.R. Tapster, P.M. Gorman, J. Mod. Opt. 48 (2001) 1887.
[11] H.H. Su, M.A. Plonus, J. Opt. Soc. Am. 61 (1971) 2. [12] C.H. Liu, in: V.I. Tatarskii (Ed.), Wave Propagation in Random Media (Scintillation), Taylor & Francis, 1993. [13] A.K. Majumdar, J.C. Ricklin, Proc. SPIE 5892 (2005) 58920K. [14] L. Eltermann, AFCRL-68-0153, AFCRL Environmental Research Paper 285, 1968. [15] V.L. Mironov, Laser Beam Propagation in Turbulence Atmosphere, Nauka, Moscow, 1981. [16] C.Y. Young, L.C. Andrews, A. Ishimaru, Appl. Opt. 37 (1998) 7655. [17] P.W. Nicholson, Nuclear Electronics, John Wiley & Sons, 1974.
Synchronization of free-space quantum key distribution Qing-Lin Wu, Zheng-Fu Han *, Er-Long Miao, Yun Liu, Yi-Min Dai, Guang-Can Guo Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China Received 21 November 2006; received in revised form 22 March 2007; accepted 23 March 2007
Abstract In this paper, it is investigated that how the atmosphere effects on the synchronization accuracy in free-space quantum key distribution (QKD). We measured the synchronization error of a free-space QKD in our near-ground platform. According to experimental results and theoretical calculations, we deduce that the intensity fluctuation of synchronization light due to atmosphere disturbance contributes far more to the synchronization accuracy than others. By using the constant fraction discrimination method, the synchronization error of the free-space QKD, passing through the aerosphere, can be limited within 300 ps which meets the synchronization requirement of a satellite-to-ground QKD system. Ó 2007 Elsevier B.V. All rights reserved. Keywords: Free-space quantum key distribution; Synchronization; Synchronization accuracy
1. Introduction Until now, quantum key distribution (QKD) is the only method to distribute a key with unconditional security through a public channel [1,2]. Originated from Bennett and Brassard’s protocol [1], experimental QKD demonstrations have been performed over 184.6 km via optical cable [3–5]. However, it is still difficult to distribute the quantum key through more than 200 km with fiber due to the losses and the low single-photon detection efficiency. Free-space QKD is now attracting increasing attention [6–8] because of its low-transmission loss. However, in free-space, the beam path is open so any background radiation can enter the system as noise, especially in the satellite-to-ground QKD. In fact, the background light plays a dominant role to the quantum-bit error rate (QBER) in free-space QKD [9]. There are three major methods to shield against the background noise [9], one of which is the time gate filtering. In order to decrease the number of background photons, as well as the dark counts, most of the time the single-photon detector (SPD) is in the off mode. Only when the signal *
Corresponding author. Tel.: +86 551 3607342; fax: +86 551 3606828. E-mail address: [email protected] (Z.-F. Han).
0030-4018/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2007.03.068
photons are expected to arrive is a narrow time gate opened to allow them to enter the SPD, thus noise photons arriving outside the time window are blocked. The narrower the time gate is, the more efficiency this method can obtain. However, a narrow time gate requires precise knowledge of the signal photon’s arrival time, that is, a precise synchronization between the sender and receiver is critically required. Therefore, it is one of the crucial technologies to realize a precise synchronization in long distance free-space QKD. To date, there are two ways to achieve this. One is to utilize stabilized local clocks and software-controlled phase-lock loop driven by the detected photon signal [10] or by the ultra precise global position system (GPS) signal [8]. The other method is to make use of a periodic bright pulse of a different wavelength as precursor to open a time gate for the subsequent signal photon [6]. The former has only a key rate of several hundreds bits per second and needs a timing adjustment, while the latter has a key rate limited only by the attenuated signal pulses and is very easy to realize in practice. In this paper, we prefer the latter and study the influence of the atmosphere on the synchronization accuracy of the free-space QKD in our own platform. Furthermore, a constant fraction discrimination technique is introduced, which can provide a
Q.-L. Wu et al. / Optics Communications 275 (2007) 486–490
sub-nanosecond synchronization accuracy for long distance free-space QKD. In the precursor light pulse synchronization [6], the transmitter first emits a strong light pulse, which acts as a synchronization light (SL) on each clock cycle. After a certain time delay, Dt, a data pulse is launched towards the receiver. At receiver, the arrival time of the SL is used as a reference time to turn on a timing gate in which a QKD data pulse is expected. The time delay between the reference time and the timing gate is also set to Dt exactly. In general, the SL is detected by a photodetector (PD) and an edge triggered discriminator (ETD) to generate the time reference, as shown in Fig. 1a. The amplitude of the output of the PD is directly proportional to the intensity of the light. When the leading edge of this pulse rises to the settled threshold, the ETD yields the timing pulse. The propagation of SL is quite stable in such steady and closed circumstance like optical fiber. However, in free-space, the intensity of the SL varies due to the atmospheric disturbance [11–13], so does the pulse height of the output of PD. This consequentially results in a random time jitter of the time reference, which is known as the synchronization accuracy or the synchronization error. For example, the time reference travels from the time t1 to t2 when the pulse amplitude of PD fluctuates from A1 to A2 (Fig. 1b). The synchronization error is determined by the time jitter t 2 t 1.
487
on the ground, where the effect of atmosphere is even more severe than that of high altitude. The transmitter (Fig. 2a) was designed round a 50 mm diameter transmit telescope. On each cycle of a 1 MHz clock (SRS DG535) the laser diode (LD) emitted a 650 nm SL pulse with the pulse width of 2.5 ns. After focused and aligned, the light beam arrived at the transmitting telescope via a spatial filter (F). In order to ease optimizing the focusing of the receiver, a continuous wave alignment laser was also fed through the spatial filter by a beam splitter (BS). The beam from the filter was expanded in the transmit telescope to a collimated beam with a diameter of 40 mm full width at half maximum (FWHM). The whole transmitting system was mounted on a 50 cm diameter breadboard, attached to a sturdy tripod. The receiver system (Fig. 2b) consisted of a 203 mm diameter commercial telescope (Meade LX200). A photodetector (SPD052) with a bandwidth of 350 MHz was coupled to the back of the telescope after a spatial filter (F) to detect the SL. The output of PD triggered a ETD with a settled threshold to generate the time reference. The transmitter was installed in a room (20 m above ground) located in the Dongpu island (100 m above sea level) in Hefei, China. The receiver was placed in a lakefront house, which located 1.5 km away from the transmitter. 3. Experimental section
It is well known that both the transmission losses and the atmosphere disturbance decrease rapidly with the increase of an altitude [14,15], and recent long distance free-space QKD were all carried out over 2100 m above sea level [6–8]. We put both the transmitter and the receiver
In order to decrease the effects of background lights, the experiment was performed at night. A high speed oscilloscope (Tek TDS7404, 4 GHz bandwidth) was used to measure the time jitter of the timing pulse, which comes from a homemade ETD. The threshold of ETD is set to 300 mV, which is less than the minimum amplitude of input pulse and is greater than any baseline noise. The measured time jitter is about 211 ps (FWHM), as shown in Fig. 3a. The
Fig. 1. Generation of synchronization timing pulse (a) and synchronization error (b). Sync Light is synchronization light, PD is a photodetector, A1 and A2 are amplitudes of the output of PD and ETD is an edge triggered discriminator.
Fig. 2. System diagram of transmitter (a) and receiver (b). LD is a laser diode, BS is a beam splitter, F is a spatial filter, PD is a photodetector, T_Telescope is a transmitting telescope and R_Telescope is a receiving telescope.
2. Experimental setup
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Q.-L. Wu et al. / Optics Communications 275 (2007) 486–490
Fig. 3. Synchronization timing error: (a) 1.5 km and (b) 3 km. CFD is a constant fraction discriminator and ETD is an edge triggered discriminator.
above result contains the jitter from the oscilloscope and the clock. In order to quantificationally estimate the synchronization timing error caused only by the atmosphere, we adjusted the above one-way system to a return system. A reflecting mirror instead of the receiver was placed in the lakefront house while the receiver was placed at the side of the transmitter, so the transmission distance reaches 3 km. The clock generated two outputs simultaneously, one was used to drive the laser diode while the other was acted as the oscilloscope’s external trigger. Therefore, both the jitter of oscilloscope and that of clock can be eliminated in such configuration. The synchronization timing error at the distance of 3 km is about 352 ps (FWHM), as shown in Fig. 3b. The threshold of ETD is 130 mV, which is selected similar to that of 1.5 km link distance. It can be seen that the timing error for an ETD increases rapidly as the distance between transmitter and receiver increases.
(ORTEC Trump-PCI) at distance of 1.5 km and 3 km, respectively, as shown in Fig. 4. According to Young et al. [16], the pulse broadening due to atmosphere disturbance is neglectable for a light pulse in duration of 2.5 ns, so we can consider that the pulse shape is invariable during the transmission. The jitter originated from the amplitude fluctuation can be calculated by assuming the output of 2
x
PD is a Gaussian waveform GðxÞ ¼ V e 2r2 , where V is the pulse amplitude corresponding to the x-axis of pulse height distribution curve, and r equals 1.062 ns for a pulse with the width of 2.5 ns. In order to calculate the jitter, two pulse heights, V1 and V2, which correspond to the half maxim counts of the pulse height distribution curve, are x
2
chosen. Then we obtain the functions G1 ðxÞ ¼ V 1 e 2r2 x2 and G2 ðxÞ ¼ V 2 e2r2 . For a settled threshold Vth, we can get two equations 2
V1e
4. Discussion
x2 2r
¼ V th
ð1Þ
¼ V th
ð2Þ
and
4.1. Source of synchronization timing error While traveling in atmosphere, both the intensity and the pulse shape of the SL vary due to the atmosphere disturbance [11]. Therefore, the pulse height and the pulse shape of the PD will change consequently, which directly cause the timing error. The pulse height distribution of the PD was measured using a pulse height analyzer
2
V2e
x2 2r
The solutions of Eqs. (1) and (2), X1 and X2, represent the emergence moment of the reference time. Then we can obtain the time jitter Dt = jX2j jX1j. For example, from Fig. 4, V1 and V2 are 0.4 V and 0.447 V at the distance of 1.5 km. Together with the threshold Vth = 0.3 V and r = 1.062 ns, we obtain the following solutions of
Fig. 4. Pulse height distribution of PD: (a) 1.5 km and (b) 3 km.
Q.-L. Wu et al. / Optics Communications 275 (2007) 486–490
Eqs. (1) and (2): X1 = 0.720 ns and X2 = 0.917 ns. The jitter Dt = 197 ps, which has a error of 6.7% compared to the measured value (211 ps). It can be seen that the synchronization error comes mainly from the intensity fluctuation of the synchronization light due to the atmosphere disturbance. 4.2. Minimize the synchronization timing error The output of ETD fluctuates consequentially with the unstable input pulse height against the settled threshold. A constant fraction discriminator (CFD) can be used to minimize the effect of amplitude fluctuations in the input signal. The trigger time of a CFD is nearly independent of the amplitude of input pulse, as shown in Fig. 5 [17]. The input signal, with an amplitude of A, feeds into a delay line and an attenuator simultaneously, as shown in Fig. 5a. The delayed signal Af(t td) and the attenuated signal PAf(t) are sending to a zero cross discriminator Dz, where td is the delay time of the delay line and P is the attenuate coefficient of the attenuator. P is usually set between 0.1 and 0.5 in most conditions [17]. The zero cross discriminator, Dz, flips when Af ðt td Þ ¼ PAf ðtÞ
ð3Þ
The delay time is selected to ensure td P (1 P)tr, where tr is the rise time of the input pulse [17]. We can then deduce from Eq. (3) that the trigger time is independent of amplitude and therefore is immune to amplitude fluctuation. An EDT, triggered by the input signal, is used to pre-
489
vent zero cross noise from mistriggering the zero cross discriminator Dz [17]. The threshold of ETD, Vth, is less than the minimum amplitude of input pulse and is greater than any baseline noise. Waveforms of all signals are shown in Fig. 5b. According to the above discussion, a CFD can be used to decrease the synchronization error, which comes mainly from the amplitude fluctuation. A homemade CFD with a attenuate coefficient of 0.2 is selected in our experiment. The threshold, Vth, is 300 mV and 130 mV for 1.5 km and 3 km link distance respectively. The jitters measured for 1.5 km and 3 km link distance are 95 ps (Fig. 3a) and 119 ps (Fig. 3b) respectively. It can be seen that the timing error decreases rapidly with a CFD. Furthermore, this error rises slightly with the increase of distance for a CFD. According to the above results, we can see that the jitter changes 24 ps while the distance increases 1.5 km for a CFD. We can then calculate the error increment is about 136 ps when the distance changed from 1.5 km to 10 km. Together with the 95 ps of 1.5 km, the error of a 10 km link distance is 231 ps. Taking into account other factors, we can estimate that the synchronization error can be limited within 300 ps for a free-space QKD passing through the aerosphere, which has a virtual thickness of 10 km. 5. Conclusions In this paper, we have discussed the synchronization method using precursor light pulse in free-space QKD. We have also evaluated factors that decrease the synchronization accuracy and ways to overcome them. Experimental results and calculation show that, the synchronization error comes mainly from the intensity fluctuation of synchronization light. Furthermore, this error increases rapidly with the increase of distance for an ETD while rises slightly for a CFD. Based on the measured data and extrapolation, we can deduce that the synchronization error of a 10 km free-space QKD can be limited less than 300 ps, which provides a sufficient synchronization accuracy for long distance free-space QKD, especially satellite-to-ground QKD. Acknowledgments The program is supported by the National Natural Science Foundation of China under Grant No. 60537020, the National Fundamental Research Program of China under Grant No. 6012503, and the Knowledge Innovation Project of Chinese Academy of Sciences.
Fig. 5. (a) System diagram of CFD. The input signal, Af(t), feeds into a delay line, an attenuator and an ETD simultaneous. Vp, the output of ETD Dp, acts as the enable signal of the zero cross discriminator Dz. VD is the differential input of Dz and equals to the delayed signal Af(t td) subtract the attenuated signal PAf(t). Vo is the output of CFD. (b) Waveforms of CFD. Waveforms in solid and dashed line represent two input signals with different amplitude. The CFD always triggers at the moment tT, which is regardless of amplitude fluctuations of input signals.
References [1] C.H. Bennett, G. Brassard, in: Proceedings of the IEEE International Conference Computers, Systems and Signal, 1984, p. 175. [2] A.K. Ekert, Phys. Rev. Lett. 67 (1991) 661. [3] X.-F. Mo, B. Zhu, Z.-F. Han, et al., Opt. Lett. 30 (2005) 2632.
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