April 15, 2010 / Vol. 35, No. 8 / OPTICS LETTERS
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Quantum key distribution based on phase encoding in long-distance communication fiber Shi-Hai Sun,1 Hai-Qiang Ma,2 Jia-Jia Han,1 Lin-Mei Liang,1,* and Cheng-Zu Li1 1 Department of Physics, National University of Defense Technology, Changsha 410073, China School of Sciences, Beijing University of Posts and Telecommunications, Beijing 100876, China *Corresponding author:
[email protected]
2
Received January 6, 2010; revised March 11, 2010; accepted March 11, 2010; posted March 19, 2010 (Doc. ID 122151); published April 14, 2010 A robust two-way quantum key distribution system based on phase encoding is demonstrated in 50 km and 100 km commercial communication fiber. The system can automatically compensate for birefringence effects and remain stable over 23 h. A low quantum bit error rate and high visibility are obtained. Furthermore, the storage fiber is unnecessary and train of pulses is only needed in the test with 100 km fiber. © 2010 Optical Society of America OCIS codes: 270.5568, 060.2330.
Quantum key distribution (QKD) can establish unconditional secret key between two remote parties, Alice and Bob, the security of which is guaranteed by quantum mechanics. Since the first protocol, BB84 scheme, was proposed [1] and then demonstrated [2], many QKD schemes have been proposed and implemented in free space [3,4] or fiber [5–10]. In fiber systems, phase encoding is widely adopted, and the pulses can travel through a one-way [5–8] or two-way [9,10] scheme. A one-way scheme encounters the problem of compensation for birefringence. To resolve this, Muller et al. proposed a two-way plug-and-play scheme [9] in which the birefringence is compensated automatically. However, in this scheme, where pulses travel back and forth, Rayleigh backscattering (RBS) puts strong limitations on its performance [10]. Although it can be overcome by introducing storage fiber in Alice’s station and replacing continuous pulses with trains of pulses [11,12], the efficiency is reduced. In this Letter, we demonstrate a robust two-way QKD scheme in 50 km and 100 km fiber, and both the two phase modulators used by Alice and Bob are polarization sensitive. Compared with other two-way schemes, storage fiber is unnecessary and continuous pulse mode can be used in the test with 50 km fiber. The average visibility is 96.2% with a standard deviation of 0.64% in our test over 23 h. Train of pulses is needed only when tested with 100 km fiber. To the best of our knowledge, this is the first time that the QKD is implemented in 100 km with a two-way system. The experimental setup is shown in Fig. 1. Pulses from the LD are divided equally into two parts by a BS, denoted as P1 and P2. P1 arrives PBS1 directly. It has been controlled to be horizontally polarized by PC1 to guarantee it can pass through PBS1 totally. Then it will travel down to a Faraday mirror and come back vertically polarized, then reflected into the QC by PBS2. Since PM1 is polarization sensitive, P2 is controlled to be horizontally polarized so that it can pass through PM1 totally and be transmitted to the QC by PBS2. Thus P2 will travel through the QC and arrive at Alice’s security region at first, and then P1 does. The interval between P1 and P2 is decided 0146-9592/10/081203-3/$15.00
by the length of the DL. In other two-way systems with a Faraday mirror [9,10], the PM should be polarization insensitive in Alice’s region. However, the PM currently used is polarization sensitive. Thus we replace the FM with a fiber loop connected via PBS3 and containing an FR [13]. When arriving at PBS3, pulses are divided into two parts. The vertical polarization part is reflected to the FR and then passes through PM2. The horizontal polarization part is transmitted to PM2 directly and then rotated by FR. To reduce the fluctuation of phase induced by PM at different times, the two parts divided by PBS3 is set to arrive at PM2 at the same time, where P2 is modulated and P1 does not. Before the pulses are reflected back to the QC, the intensity of the pulses must be attenuated to the secure level by Att.2. Under the effect of PBS3 and the FR, the polarization state of the outgoing pulses is orthogonal to that of the incoming pulses. Thus they will take the other path at Bob’s station and arrive at the BS at the same time where they interfere. Since both of them travel through the same path, their polarization state will be the same, and the interference is affected only by the difference of the modulated phase in PM1 and PM2. We now present an analysis of polarization states through the QKD process. The Jones matrix of a Faraday mirror, TFM, and the Jones matrix, T, of a round trip through a birefringent fiber element terminated by a Faraday rotator mirror are given by [6]
Fig. 1. (Color online) Schematic diagram of experimental system. LD, laser diode; Att., attenuator; PC, polarization controller; CIR, circulator; BS, beam splitter; PBS, polarization beam splitter; FM, Faraday mirror; PM, phase modulator; DL, delay line; FR, 90° Faraday rotator; QC, quantum channel. © 2010 Optical Society of America
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OPTICS LETTERS / Vol. 35, No. 8 / April 15, 2010
TFM =
冋
0
−1
−1
0
册
Thus the total effect of Alice’s setups is given by
ឈ ·T ·T ជ = exp共i兲TFM , T=T FM
3 3 TA共兲 = P21 · FR−共90 ° 兲 · PM2 · P13
共1兲
ឈ and T ជ are the backward and forward Jones where T matrices along the fiber, respectively, and is the phase shift due to birefringence effects of the fiber. Thus when the input is linearly polarized, the polarization of the outgoing state is orthogonal to that of the incoming state despite the birefringence. In our scheme the PBS and FR are used in Alice’s station whose effect is equal to that of the FM. The Jones matrix of FR is given by FR±共兲 =
冋
cos共兲
⫿sin共兲
±sin共兲
cos共兲
册
,
共2兲
where is the rotation angle and ⫾ represents that the direction of the FR magnetic field vector H is in the same (⫹) or opposite (⫺) direction to the light.
冋 册 冋 册 冋 册冋 册 冋 册冋 册 冋 册 0 0
3 3 + P31 · PM2 · FR+共90 ° 兲 · P12 =
⫻ ⫻
0
1
−1 0
exp共i兲
0 −1
0 0
1
0 1
0
1 0
0 0
+
= exp共i兲
0 1
1 0
0 0
exp共i兲
0
−1
−1
0
, 共3兲
where Pijs is the Jones matrix of the sth PBS and the subscript represents that the photons input from port i and output from port j, and the definition of port 1, 2, and 3 is given in Fig. 1. is the phase modulated by PM2. It is clearly shown that the total effect is equal to an FM. Therefore, the polarization states of P1 and P2 when they travel back to the BS are given by
2 2 1 1 ឈ · T 共0兲 · T ឈ ·T ·T ជ QC兲 · P21 ជ DL兲 · P31 兩P1典 = PM1共B兲 · P13 · 共T · P12 · 共T · Ein = exp关i共B + 1兲兴Ein , QC A DL FM
共4a兲
1 1 2 2 ឈ ·T ·T ឈ · T 共 兲 · T ជ DL兲 · P21 ជ QC兲 · P31 · 共T · P12 · 共T · PM1共0兲 · Ein = exp关i共A + 2兲兴Ein , 兩P2典 = P13 DL FM QC A A
共4b兲
where Ein is the input Jones vector at Bob’s side, which is horizontal polarization state; B and A are the phase modulated by PM1 and PM2, respectively; and 1 and 2 are the induced phase for P1 and P2, respectively, when they travel through the total path. Thus the interference output can be written as Iout = ␥兩exp关i共B + 1兲兴 + exp关i共A + 2兲兴兩2Iin = 2␥关1 + cos共⌬AB + ⌬12兲兴Iin = 2␥关1 + cos共⌬AB兲兴Iin ,
共5兲
where ␥ is the factor that describes the total loss of the system, ⌬AB = A − B, and ⌬12 = 1 − 2. The third equality is true because the pulses from P1 and P2 travel the same path. Thus the visibility is given by V=
out out − Imin Imax out out Imax + Imin
,
共6兲
To test the performance of our scheme, we implement QKD with the system shown in Fig. 1. The intensity of pulses generated by a 1550 nm short-pulse distributed-feedback laser (id300, id Quantique, Switzerland) is attenuated by Att.1 to a very low level that can reduce efficiently RBS coming from the QC. The repetition frequency of the laser is 2 MHz. To satisfy security constraints, the pulses are attenuated by Att.2 to 0.3 photon/pulse when leaving Alice’s secure zone. When the pulses travel back, two single photon detectors (id201, id Quantique, Switzerland)
are used to detect the signal photons, whose darkcount rate is 1.65⫻ 10−6 / ns with a gate width of 2.5 ns and an efficiency of 10%. Homemade electronic chips are used to synchronize all the optical setups. As is well known, photon number splitting (PNS) attack [14,15] is currently technologically unfeasible and can be defeated by the decoy state method [16–18]; we did not consider the open door left to PNS attack, since there is no additional technological difficulty for the decoy state method and the optimized pulse intensity can be reach up to 0.5 photon/pulse, which is higher than our choice of 0.3 photon/pulse. With the setups described above, we test our scheme in the lab with 50 km and 100 km fiber. In other two-way schemes [9,10], storage fiber and train of pulses must be introduced to reduce RBS. However, in our experiment, the storage fiber is not necessary, and the train of pulses is only needed in the test with 100 km fiber. This is for two reasons: one is that the homemade electronic chips, but not the laser, are used for synchronization, so the power of the outgoing pulses from the laser can be attenuated to a very low level that the count rate caused by RBS is reduced; the other reason is that our scheme is polarization dependent for the return photons, for example, when P1 return to PBS2, it will be transmitted totally, but RBS photons are partly transmitted, even they arrive at PBS2 at the same time with P1, the same is true for P2, and therefore the count rate coming from RBS is reduced again. The average visibility tested over 23 h with continuous pulse mode in 50 km fiber, as shown in Fig. 2, is 96.2% with a stan-
April 15, 2010 / Vol. 35, No. 8 / OPTICS LETTERS
Fig. 2. (Color online) Visibility of experimental system as a function of time. VPM1 ⫽ 0 and VPM2 ⫽ V0, where V0 is the half-wave voltage of the PM. The continuous pulse mode is adopted.
dard deviation of 0.64%. Correspondingly, the QKD experiment over 50 km fiber obtains a raw key rate of 172 Hz with a quantum bit error rate (QBER) of 2.54%. When the efficiency of detector is changed to 15%, the raw key rate becomes 268.5 Hz with a QBER of 3.39%. When the distance reaches 100 km, the dispersion of the fiber and the time jitter of the electronic setups will contribute to the increasing of final QBER, since a fraction of signal photons are dispersed out of the detection gate. The standard fibers used here introduce a chromatic dispersion of 17 ps/ nm at 1550 nm; thus the pulse width of the laser pulse with a spectral width of 0.6 nm will be broadened to 2.04 ns. Also, the time jitter of the electronic setups used here is about 1 ns. Therefore, the gain of the signal photons will be reduced rapidly, and RBS will limit the performance of our scheme. Thus the train of pulses is adopted here. However, storage fiber is still unneeded. We test the count rate coming from RBS and find that it comes mainly from the first half part of the QC. Therefore, the number of signal pulses for each train and the time of waiting are decided by the length of QC, which can be written as Ln
Lfn N=
c
,
twait =
c
,
共7兲
where L is the length of QC, f is the repeation frequency of synchronous signal, n is the refraction index of fiber, and c is the light velocity in vacuum. By using the train of pulse, the count rate caused by RBS can be reduced to the level of dark count. At the same time, the gate of the detector has to broaden to 5 ns, and the intensity of pulses is also increased to 0.6 photon/pulse. Under these conditions, the raw key rate is 101 Hz with a QBER of 12.81%. Although the QBER has exceeded 11%, which is the security limit for one-way postprocessing, it can be improved by using a Bragg grating device or fiber filter to reduce the spectral width of the laser or using two-way
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postprocessing [19], whose security limit is at least 20%, to distill the final key. In summary, a robust two-way QKD scheme in 50 km and 100 km fiber is demonstrated. The system can remain stable for a long time with low QBER. Storage fiber is unnecessary, and train of pulses is only needed in 100 km fiber. Although Alice and Bob sit in the same lab in our experiment, our method can be extended to the case with the station really 100 km apart by using an almost 100 km cable or another fiber to transmit synchronized signal and then using our homemade electronic chips, which can delay electronic signal with 1 ns accuracy, to modulate synchronized time carefully. As for Trojan horse attacks [20] and Faraday effects [21], the former can be defeated with additional technical method, and the latter is small in practical case; thus they do not affect the practicability of our system. The authors thank W.-T. Liu and W. Wu for their helpful advice and comments. H.-Q. Ma is supported by the National Natural Science Foundation of China (NSFC) grant 10805006. References 1. C. H. Bennett and G. Brassard, Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing (IEEE, 1984), pp. 175–179. 2. C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, J. Cryptology 5, 3 (1992). 3. R. J. Hughes, J. E. Nordholt, D. Derkacs, and C. G. Peterson, New J. Phys. 4, 43 (2002). 4. C. Kurtsiefer, P. Zarda, M. Halder, H. Weinfurter, P. M. Gorman, P. R. Tapster, and J. G. Rarity, Nature 419, 450 (2002). 5. H.-Q. Ma, J.-L. Zhao, and L.-A. Wu, Opt. Lett. 32, 698 (2007). 6. X.-F. Mo, B. Zhu, Z.-F. Han, Y.-Z. Gui, and G.-C. Guo, Opt. Lett. 30, 2632 (2005). 7. Z. L. Yuan, A. R. Dixon, J. F. Dynes, A. W. Sharpe, and A. J. Shields, Appl. Phys. Lett. 92, 201104 (2008). 8. W.-T. Liu, W. Wu, L.-M. Liang, C.-Z. Li, and J.-M. Yuan, Chin. Phys. Lett. 32, 287 (2006). 9. A. Muller, T. Herzog, B. Huttner, W. Tittel, H. Zbinden, and N. Gisin, Appl. Phys. Lett. 70, 793 (1997). 10. D. Subacius, A. Zavriyev, and A. Trifonov, Appl. Phys. Lett. 86, 011103 (2005). 11. D. Stucki, N. Gisin, O. Guinnard, G. Ribordy, and H. Zbinden, New J. Phys. 4, 41 (2002). 12. X. Peng, H. Jiang, and H. Guo, J. Phys. B 41, 085509 (2008). 13. R. D. Esman and M. J. Marrone, IEEE Trans. Microwave Theory Tech. 43, 2208 (1995). 14. M. Dušek, O. Haderka, and M. Hendrych, Opt. Commun. 169, 103 (1999). 15. G. Brassard, N. Lütkenhaus, T. Mor, and B. C. Sanders, Phys. Rev. Lett. 85, 1330 (2000). 16. W.-Y. Hwang, Phys. Rev. Lett. 91, 057901 (2003). 17. H.-K. Lo, X.-F. Ma, and K. Chen, Phys. Rev. Lett. 94, 230504 (2005). 18. X.-B. Wang, Phys. Rev. Lett. 94, 230503 (2005). 19. N. Gisin and S. Wolf, Phys. Rev. Lett. 83, 4200 (1999). 20. J.-C. Boileau, D. Gottesman, R. Laflamme, D. Poulin, and R. W. Spekkens, Phys. Rev. Lett. 92, 017901 (2004). 21. A. Mecozzi, C. Antonelli, and M. Brodsky, Opt. Lett. 33, 1476 (2008).
