The feasibility of geostationary satellite-to-ground quantum key distribution

Physics Letters A 361 (2007) 29–32 www.elsevier.com/locate/pla

The feasibility of geostationary satellite-to-ground quantum key distribution Er-Long Miao ∗ , Zheng-Fu Han ∗ , Tao Zhang, Guang-Can Guo Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China Received 10 July 2006; received in revised form 1 September 2006; accepted 6 September 2006 Available online 22 September 2006 Communicated by P.R. Holland

Abstract The feasibility and technology requirements of geostationary (GEO) satellite-to-ground free space quantum key distribution (QKD) are investigated. The losses budget and bit rates of the system show that GEO satellite-to-ground QKD is feasible and a globe secure QKD network can be set up through this system. © 2006 Elsevier B.V. All rights reserved. PACS: 03.67.Dd; 03.65.Ta; 89.70.+c Keywords: Quantum key distribution; Geostationary satellite

1. Introduction Quantum key distribution (QKD) is one of the most exciting technologies in the new century. Its security is based on the laws of nature and is, in principle, absolutely secure against any computational improvement. Point to point QKD has been realized in fiber [1,2] and free space [3–8]. Now some commercial products are available and QKD network has attracted great interests of many groups [9–13]. In Europe, more than 40 groups collaborate in the project “development of a globe network for secure communication based on quantum cryptography” (SECOQC) [14]. United States and UK are also developing a worldwide quantum cryptography system [15]. 2. Free space QKD based on satellite However, it is difficult to distribute the quantum key more than 200 km because of the losses in fiber and the single photon detecting efficiency. To set up a worldwide QKD network, only transmission through fiber is not enough. Low loss transmitting medium and high efficiency detector are two ways to extend the * Corresponding authors. Tel.: +86 0551 3607342; fax: +86 0551 3606828.

E-mail addresses: [email protected] (E.-L. Miao), [email protected] (Z.-F. Han). 0375-9601/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2006.09.013

secure distance and improve the bit rate. Free space QKD has attracted lots of attention for its low transmission losses. After the efforts of several groups [3–8], Los Alamos national lab realized free space QKD exceeding 10 km in 2002 first [7] and Kurtsiefer and Rarity extended the distance to 23.4 km on the top of Alps [8], which exceeded more than an air mass distance. Recently, 144 km free space QKD has been reported in [16]. There is no technological bottleneck in principle to distribute QKD between satellite and ground [17] if only considering atmosphere-transmitting losses. Once QKD through satellite is realized, local QKD network based on fiber can be connected and a globe secure network will be established. Rarity et al. [18] proposed three schemes to realize satelliteto-ground QKD in 2002. It shows that satellite-to-ground QKD is feasible in principle with current technology. In [19], background light noises were especially analyzed and the results indicate that satellite to ground QKD can be realized at least in night. In all these papers, low earth satellite (LEO) is considered better than others for the shorter transmitting distance. In fact, geostationary satellite (GEO) is also a good candidate for QKD from space to ground [20]. In this Letter, we investigate the feasibility of QKD based on GEO satellite and analyze the losses variation with the pointing accuracy. Technology requirements and successful transmission in different situations are listed.

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3. QKD based on GEO satellite In order to set up the quantum communication channel, pointing, acquisition and tracking (ATP) system has to be applied to set up an optical link between satellite and earth station. The link ranges and duration depend on the allowed elevation parameter as seen from the ground. For LEO satellite, acquisition time of 2 minutes is needed and link duration of only 200 s (average) per day are expected for performing a quantum communication link experiment [21]. In addition, the distance varying from several hundreds to thousands kilometers and the pointing angle coverage exceeding 140◦ give a stringent requirement for the speed and stability of the ATP system. For a GEO satellite, the position is relatively stable to the earth, the distance changes only several kilometers, and the pointing angle is nearly fixed, so acquisition and tracking system is much easier and more precise than that for LEO satellite. Further more, the link duration is always available and the communication can be performed whenever the background light noises are low enough [19]. GEO satellite is accused for its high losses for the long transmitting distance. In fact, most loses come from low collecting efficiency because of the big spot size and the relatively small collecting telescope, which make most energy lost outside the telescope. Now diffraction limit telescope can be made, and the beam can transmit with the diffraction limit angle. While the turbulence of atmosphere can lead to both spreading and wandering of the laser beam, and the typical wander is approximately 10 to 100 µrad. So the field view of receiving telescope is set to 10 to 100 µrad here. If we put the sender on the GEO satellite and the receiver on the ground, the atmosphere turbulence will cause the beam spreading about 0.1 to 1 meter (here we take atmosphere height as 10 km, because 90% of the atmosphere mass is below 10 km). As we will see in the next section this beam spread is small in comparison to the beam expansion from diffraction. With precise pointing accuracy, the losses will be low enough for practical application. In addition, background noises are always a big problem for free space QKD [19]. Because of the relatively stationary position to the earth, atom filter, whose bandwidth is about 0.01 nm, can be used to filter out most the noises at other wavelength, and there is no Doppler effect to worry about. Time-gate filter is another way to decrease the background noise as well as the dark counts. When signal photon comes, the detector opens a narrow time gate. The photons in the gate will be detected and the photons out the gate will be omitted. This method decreases the noise photons outside the time gate. Now 1 ns time-gate can be used in the single photon detector (SPD) [6,22]. Small field view of the telescope is very important to reduce the background noises. Stray light and the light sources out of the field view will be blocked out the system.

racy has been reached [23]. If the pointing accuracy is θ , then the diffraction angle is set to 2θ to guarantee the collecting telescope within the laser spot. The divergence half-angle θ of Gaussian beam with radius ω0 (1/e2 ) is given by θ=

λ , πω0

(1)

where λ is the laser wavelength and ω0 is half of the collimating telescope’s diameter. Using a telescope with a diameter D = 2λ πθ on the GEO satellite, the required diffraction angle can be reached. For example, here we use 650 nm laser with 1 µrad transmitter pointing angle, then the sender telescope diameter is about 0.5 meter. The laser transmits from satellite to the ground and is collected by ground telescope. If a large Gaussian beam of diameter 2ω is intercept with small diameter telescope DT , then the collected fraction is   DT2 2DT2 . ≈ η = 1 − exp − (2) (2ω2 ) 2ω2 The distance L between GEO satellite and ground is about 36 000 km, and the spot size after transmitting 36 000 km is L∗ 2θ . In order to receive the signals from the satellite, ATP system of sender pointing accuracy better than θ is required. Here we take the receiving telescope diameter DT = 1 m, according to (2), and the losses for the limited area of receiving telescope are calculated and the curve is plotted in Fig. 1. It shows losses increase from 20 to 40 db when pointing accuracy varies from 0.2 to 2 µrad. If atmosphere transmittance is 60%, SPD efficiency is 70%, photon per pulse is 0.1, and couple efficiency is 80%, then the signal photons per pulse received by ground can be calculated. Fig. 1 shows the received photons per pulse as a function of the transmitter pointing accuracy. Precise transmitter pointing accuracy greatly improves the receiving efficiency. Submicroradian angular resolution is necessary for the beam steering. With 0.2 µrad transmitter pointing accuracy, the collecting telescope can receive about 3.3 × 10−4 photons per pulse. If the clock rate is 10 MHz, then the bit rate is 3300 bits per sec-

4. Losses budgets of GEO satellite We know from previous space optical communication experiments that pointing accuracies of < 5 µrad is easy to be achieved from space [18]. In ETS-VI, 1.6 µrad pointing accu-

Fig. 1. Telescope receiving losses A (in dB) and signal photons received per pulse B as a function of pointing accuracy.

E.-L. Miao et al. / Physics Letters A 361 (2007) 29–32

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Table 1 Noise photons received per pulse are listed in different situation. NPR/pulse means noise photons received per pulse Circumstance condition Sunny cloud Sunny fog Relative brightness Typical brightness (W/Sr m2 µm) NPR/pulse θ = 100 µrad B = 0.01 nm t = 3 ns θ = 100 µrad B = 0.01 nm t = 1 ns θ = 10 µrad B = 0.01 nm t = 3 ns θ = 10 µrad B = 0.01 nm t = 1 ns

Sunny atmosphere Full moon

New moon

Star

1.0 150

10−1

10−2

10−5

15

1.5

1.5 × 10−3

10−6

1.5 × 10−4

10−7 1.5 × 10−5

3.7 × 10−1

3.7 × 10−2

3.7 × 10−3

3.7 × 10−6

3.7 × 10−7

3.7 × 10−8 + 3.7 × 10−8

1.2 × 10−1

1.2 × 10−2

1.2 × 10−3

1.2 × 10−6 + 1.2 × 10−8

1.2 × 10−7 + 1.2 × 10−8

1.2 × 10−8 + 1.2 × 10−8

3.7 × 10−3

3.7 × 10−4

3.7 × 10−5

3.7 × 10−8 + 3.7 × 10−10

3.7 × 10−9 + 3.7 × 10−10

3.7 × 10−10 + 3.7 × 10−10

1.2 × 10−3

1.2 × 10−4

1.2 × 10−5

1.2 × 10−8 + 1.2 × 10−10

1.2 × 10−9 + 1.2 × 10−10

1.2 × 10−10 + 1.2 × 10−10

ond. While high precise pointing accuracy needs application of adaptive optics to reduce the atmosphere turbulence affection, this will be a big challenge to the system. 5. Background noise of the system Another problem is the background noise secure QKD allows at most 11% error rate in theory [24]. According to [19], the contributions of the background noises to the system can be calculated by the formula (3): Pb = Hb × Ωfov × Arec × Bfilter ,

(3)

Hb is the brightness of sky background and its unit is W/m2 Sr µm. Arec , Ωfov and Bfilter are the area of receiving telescope, receiving field and the filter bandwidth, respectively. Here Bfilter is 0.01 nm for the application of atom filter, and the receiving telescope’s aperture is 1 m (Arec = 0.785 m2 ). Considering the atmosphere turbulence, Ωfov is 10 to 100 µrad. Given the luminance of the background, noise photons received by earth station per pulse can be calculated. Here we take 5% error rate as the feasible secure limit of this system [25,26], which means the noise counts must be less than 5% of the signal counts per pulse. According to Fig. 1, the received photons per pulse vary from 3 × 10−4 to 3 × 10−6 depending on the pointing accuracy. Therefore, the system can tolerate background noise counts up to 1.5 × 10−5 − 1.5 × 10−7 per pulse. Compare to the background noise, we can deduce the requirements and situations for the system to be realized employing state-of-art technology. With dark counts of 25 counts/s silicon based SPD and 2 µrad pointing accuracy, the system can tolerate a background noise of up to 1.5 × 10−7 counts per pulse. Table 1 shows the noise photons received per pulse in different background. At the right side of the black line, QKD based on GEO satellite can be realized, which means QKD through GEO satellite is feasible at least at night. If the clock rate is 10 MHz and transmission time is 6 hours per day, then the total bits can be calculated and the results are plotted in Fig. 2.

Fig. 2. The total bits received per day as a function of the pointing accuracy.

When the pointing accuracy is 0.2 µrad, the total bit rate is about 70 M per day. If the sub-microradian pointing accuracy can be reached, QKD through GEO satellite is more promising in future.

6. Conclusion

GEO satellite QKD has special advantages in the space to ground QKD. Results show that pointing accuracy is a key factor to decrease the losses. With the development of space technology, pointing accuracy and stability will be greatly improved and the losses will be low enough for practical application. Now new single photon detector that has higher efficiency, faster speed and lower dark counts than avalanche photon detector (APD) has been used in a 50 km fiber QKD [27]. With all these development, globe QKD network through satellite will come true in near future.

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Acknowledgements This work was funded by the National Fundamental Research Program of China (grant No. 2001CB309301), National Natural Science Foundation of China (grant No. 60121503) and the Innovation Program of the Chinese Academy of Sciences. References [1] D. Stucki, N. Gisin, O. Guinnard, G. Ribordy, H. Zbinden, New J. Phys. 4 (2002) 41. [2] X.F. Mo, B. Zhu, Z.F. Han, Y.Z. Gui, G.C. Guo, Opt. Lett. 30 (2005) 2632. [3] W.T. Buttler, R.J. Hughes, P.G. Kwiat, G.G. Luther, G.L. Morgan, J.E. Nordholt, C.G. Peterson, C.M. Simmons, Phys. Rev. A 57 (1998) 2319. [4] W.T. Buttler, R.J. Hughes, P.G. Kwiat, S.K. Lamoreaux, G.G. Luther, G.L. Morgan, J.E. Nordholt, C.G. Peterson, C.M. Simmons, Phys. Rev. Lett. 81 (1998) 3283. [5] R.J. Hughes, W.T. Buttler, P.G. Kwiat, S.K. Lamoreaux, G.L. Morgan, J.E. Nordholt, C.G. Peterson, J. Mod. Opt. 47 (2000) 549. [6] W.T. Buttler, R.J. Hughes, S.K. Lamoreaux, G.L. Morgan, J.E. Nordholt, C.G. Peterson, Phys. Rev. Lett. 84 (2000) 5652. [7] R.J. Hughes, J.E. Nordholt, D. Derkacs, C.G. Peterson, New J. Phys. 4 (2002) 43. [8] C. Kurtsiefer, P. Zarda, M. Halder, H. Weinfurter, P. Gorman, P.R. Tapster, J.G. Rarity, Nature 419 (2002) 450. [9] R.M. Gingrich, P. Kok, H. Lee, Phys. Rev. Lett. 91 (2003) 217901.

[10] [11] [12] [13] [14] [15] [16] [17]

[18] [19] [20] [21] [22] [23] [24] [25] [26] [27]

G.P. Guo, G.C. Guo, Phys. Lett. A 318 (2003) 337. A.E. Kozhekin, K. Molmer, E. Polzik, Phys. Rev. A 62 (2000) 033809. E. Biham, B. Huttuer, T. Mor, Phys. Rev. A 54 (1996) 2651. P. Xue, C.F. Li, G.C. Guo, Phys. Rev. A 65 (2002) 022317. http://www.obs-azur.fr/gemini/equipes/dm_v1/ActualiteInterne/ELIPS2_ Space_QUEST.pdf . C. Elliott, A. Colvin, quant-ph/0503058. R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, quant-ph/0607182. J.E. Nordholt, R.J. Hughes, G.L. Morgan, C.G. Peterson, C.C. Wipf, in: Proceedings of the SPIE—The International Society for Optical Engineering, vol. 4635, 2002, pp. 116–126. J.G. Rarity, P.R. Tapster, P.M. Gorman, P. Knight, New J. Phys. 4 (2002) 82. E.L. Miao, Z.F. Han, T. Zhang, G.C. Guo, New J. Phys. 7 (2005) 215. R.J. Hughes, W.T. Buttler, P.G. Kwiat, S.K. Lamoreaux, G.L. Morgan, J.E. Nordholt, C.G. Peterson, IEEE Aerospace Conf. Proc. 1 (2000) 191. M. Pfennigbauer, M. Aspelmeyer, J. Opt. Networking 4 (2005) 9. J.G. Rarity, P.M. Gorman, P.R. Tapster, J. Mod. Opt. 48 (2001) 1887. M. Toyoshima, Opt. Eng. 40 (5) (2001) 827. N. Gisin, G. Ribordy, W. Tittel, H. Zbinden, Rev. Mod. Phys. 74 (2002) 145. N. Lutkenhaus, Phys. Rev. A 61 (2000) 052304. J. Calsamiglia, S.M. Barnett, N. Lutkenhaus, Phys. Rev. A 65 (2002) 012312. D. Rosenberg, S.W. Nam, Appl. Phys. Lett. 88 (2006) 021108.