Abstract

Quantum key distribution (QKD) is a method for exchanging keys between two parties (Alice and Bob) with an absolute level of security in the ideal scenario. QKD systems are vulnerable to hacking through secondary emissions of photons by SPAD detectors, known as backflash. In this work, we derive an information leakage probability model for the scenario of QKD in a free space communication (FSO) system, and suggest a method for its minimization.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Quantum key distribution (QKD) is a method of transferring a secret key between two parties with the aid of quantum mechanics in order to achieve secure communication. Practical QKD systems have been explored for over a decade and are used commercially [1]. However, while QKD is theoretically secure, actual physical devices have weak points that can be exploited by a third party [2–4]. A promising implementation of QKD is free space optical communication over ground (FSO) [5,6] or with satellite or ground-air communication [7–11]. This adds complications due to stochastic jitter and vibration of the pointing direction of the optical system, and this must be taken into account when designing a system in order to reduce the probability of attacks.

One such vulnerability is backflash [12–16]. QKD systems typically use single photons to convey the information. The most common method of detection today is single photon avalanche photodiodes (SPADs). In order to count single photons the SPAD diode is operated in Geiger mode; that is, reverse-biased above the breakdown voltage. As a result the signal photoelectron can create an avalanche. The sender, Alice, sends a photon to the receiver, Bob, which is detected with his SPAD. However, as a result of the avalanche caused by the incoming photon, the SPAD can emit a secondary photon which could be detected by a third party, Eve, who could gain information from it. This secondary emission, called backflash, is quenched along with the avalanche itself when the detector bias is lowered below the breakdown voltage. Thus, the backflash intensity strongly depends on the parameter settings of the quenching electronics [3,12]. From previous measurements [12,16] a lower bound for the probability of detecting backflash was found to be 0.4%. Given that these APDs have a nominal detection efficiency of about 10%, the backflash could contain at least 0.04 photons emerging from the devices. This may result in a considerable amount of information leakage that has to be considered in practical QKD implementations. Information may be obtained regarding detector type as well as other optical components through which the photons pass, which could contain information about the signal. The performance of FSO communication through the atmosphere could degrade due to atmospheric turbulence [17–19] and pointing error [20–25]. Here in this paper, we analyze the effect of pointing error on the performance of information leakage due to backflash.

2. Scenario under consideration

In this work we assume that Alice is located on a static platform on the ground, while Bob is located on a less stable platform such as a laser satellite system [21] or skyscraper [22] and suffers from jitter and vibration. First we analyze the probability for Eve to detect a backflash photon in a free space configuration. Till now these calculations have been made for table top configurations. However, real FSO suffer from jitter and vibration of the optical system pointing direction. Therefore, we also calculate the probability as affected by pointing loss assuming that Bob is on a vibrating platform. Figure 1 shows the general scenario under consideration. Alice sends a message to Bob through free space over a distance Z1. Eve, who is at a distance of Z2 from Bob, tries to intercept backflash photons.

 

Fig. 1 QKD scheme with eavesdropper. Alice sends a signal to Bob, and Bob’s detector releases backflash photons that are intercepted by Eve.

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3. Theory

We assume that Bob is on a vibrating platform and as a result there will be a random pointing error. The vibration and jitter of the pointing angle are typical of an FSO system such as laser satellite communication [21] or urban FSO [22]. In a satellite system the vibrations have internal and external causes. The external sources are structure deformations due to gradients of temperature, and inhomogeneities of gravitational force through the satellite orbit. The internal sources are electronic noise in the tracking and pointing system, and operation of subsystem on the satellite such as antenna pointing system, thruster operation, and solar array driver. In urban FSO, the causes can include building sway as a result of strong winds, thermal expansion, and weak earthquakes [22].

The probability for Bob to receive a photon which Alice transmitted as a function of θ, the pointing direction error angle, and of Z1, the distance between Alice and Bob, is given [21–23] by

PBob(θ)=K1L(θ)GBob,
where K1 is a constant, L(ϑ) the pointing loss factor, and GBob is the gain of Bob’s telescope. GBob is equal to (π dBob/λ)2 [24] where dBob is the unobscured circular aperture diameter of Bob’s telescope, and λ is the wavelength. K1 is given by
K1=ηqPAliceGAliceηAliceηBobLA(Z1)Z12(λ4π)2
where PAlice is the probability to transmit a photon, ηq is quantum efficiency, ηAlice, ηBob are optical efficiencies, GAlice is Alice’s telescope gain, and LA is atmospheric loss. GAlice is equal to (π dAlice/λ)2 [24] where dAlice is the unobscured circular aperture diameter of Alice’s telescope.

The pointing loss factor is [22]

L(θ)=exp(GBobθ2).
To find the average probability for Bob to detect a photon, we calculate the effect of the pointing loss, as follows. The azimuth and elevation pointing error angle θH and θV are normally distributed, with probability density functionfθV(θV),fθH(θH). The radial pointing error angle is the root square sum of the azimuth and elevation angles
θ=θV2+θH2.
Based on symmetry we can assume that,
σV=σH=σ.
In our model Bob is on a mobile platform such as a satellite. σ describes the vibration amplitude of the pointing system of the satellite. We assume that the azimuth and elevation processes are independent and identically distributed so the radial pointing error angle model is Rayleigh distributed with probability density [22,23]
fθ(θ)=θσ2exp(θ22σ2).
In this case the average probability for Bob to absorb a photon is
PBob¯=0PBob(θ)f(θ)dθ.
From Eqs. (1), (6), and (7) integration gives
PBob¯=GKBob11+2GBobσ2,
The probability for Eve to receive a photon due to backflash as a function of pointing direction error angle α and of Z2, the distance between Bob and Eve, is
PEve(α,θV,θH,θ)=K2PBob(θ)L((θV+α)2+θH2)GBob
where the constant K2 is given by
K2=ηBackflashηqηBobGEveηEveLA(Z2)Z22(λB4π)2
and ηbackflash is the probability of backflash due to absorption of photon, ηEve and GEve are Eve’s optical efficiency and telescope gain respectively and λb is the backflash wavelength. (We assume that λB is equal to λ due to the receiver optical filter).
PEve¯(α)=PEve(α,θV,θH)fθV(θV)fθH(θH)dθVdθH.
In order to obtain a closed form expression, we assume that α -> 0. In practical terms this means that the eavesdropper on the ground is close to Alice. Plugging in Eqs. (4) and (9), we expand as follows:
PEve¯=limα0K3GBob20exp(GBobθ2)2θσ2exp(θ22σ2)dθ
where
K3=K1K2.
Then we integrate
PEve¯(GBob)=K30θGBob2exp(θ2a)dθ
where we have defined
a=(2GBob+12σ2).
Integration gives
PEve¯=GBob2K31+4GBobσ2.
From Eqs. (8) and (16) the ratio between the detection probability of Eve and Bob is given by
PEve¯PBob¯=K2GBob1+2GBobσ21+4GBobσ2.
The two probabilities are at different scales but the trend is clear. Obviously as Bob's gain increases his probability of detection increases, but for increased security it could be better not to strive for maximum gain but for a point where gain is sufficient for communication purposes while Eve's probability for backflash detection is minimal.

4. Numerical calculation

A numerical simulation was performed, with typical parameters of the system described in Table 1. In Fig. 2 it is easy to see that Bob's probability is saturated quickly. It is also clear from a physical point of view (energy conservation) that this value cannot increase without bound. Figure 4 depicts the ratio PEve¯PBob¯. From this figure it is clear that the increase of PEve¯ cannot be restrained by the increase of PBob¯. One conclusion is that the appropriate strategy is to use the minimum gain that provides the acceptable performance for Bob's probability to detect a photon. In Fig. 3 it is easy to see that Eve's probability continues to grow exponentially.

Tables Icon

Table 1. Simulation Parameters

 

Fig. 2 Bob's probability to detect a photon as a function of Bob's telescope gain.

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Fig. 3 Eve's probability to detect a photon as a function of Bob's telescope gain.

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Fig. 4 Probability ratio PEve¯PBob¯ as a function of Bob's telescope gain.

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5. Summary and conclusion

In conclusion, we have analyzed the probability for an eavesdropper to detect backflash photons emitted from a receiver on a moving platform. This analysis can benefit system design, as follows. The probability for the eavesdropping increases with Bob’s gain, but as we have shown, this probability is not a linear function and the region of leakage has been identified: the probability begins to increase steeply only at a gain of about 1013 for Bob, and zooming in to examine the ratio of probabilities between Eve and Bob, one finds a steep increase at 2*1013. This should be taken into account in system design, constraining Bob’s gain to provide maximal efficiency within the range that will minimize the possibility of information leakage.

Funding

NATO, Science for Peace and Security program, project G5263, “Analysis, design and implementation of an end-to-end 400 km QKD link.”

References

1. P. W. Shor and J. Preskill, “Simple proof of security of the BB84 quantum key distribution protocol,” Phys. Rev. Lett. 85(2), 441–444 (2000). [CrossRef]   [PubMed]  

2. L. Lydersen, C. Wiechers, C. Wittmann, D. Elser, J. Skaar, and V. Makarov, “Hacking commercial quantum cryptography systems by tailored bright illumination,” Nat. Photonics 4(10), 686–689 (2010). [CrossRef]  

3. A. Meda, I. P. Degiovanni, A. Tosi, Z. L. Yuan, G. Brida, and M. Genovese, “Quantum key distribution security threat: the backflash light case.” in Quantum Technologies 2018, vol. 10674, p. 1067418. International Society for Optics and Photonics, 2018.

4. K. Wei, H. Liu, H. Ma, X. Yang, Y. Zhang, Y. Sun, J. Xiao, and Y. Ji, “Feasible attack on detector-device-independent quantum key distribution,” Sci. Rep. 7(1), 449 (2017). [CrossRef]   [PubMed]  

5. P. V. Trinh and A. T. Pham, “Design and secrecy performance of novel two-way free-space QKD protocol using standard FSO systems.” In Communications (ICC), 2017 IEEE International Conference on, pp. 1–6. IEEE, 2017. [CrossRef]  

6. W. S. Rabinovich, R. Mahon, M. S. Ferraro, P. G. Goetz, M. Bashkansky, R. E. Freeman, J. Reintjes, and J. L. Murphy, “Free space quantum key distribution using modulating retro-reflectors,” Opt. Express 26(9), 11331–11351 (2018). [CrossRef]   [PubMed]  

7. J. A. Grieve, R. Bedington, Z. Tang, R. C. M. R. B. Chandrasekara, A. Ling, C. M. R. B. Chandrasekara, and A. Ling, “SpooQySats: CubeSats to demonstrate quantum key distribution technologies,” Acta Astronaut. 151, 103–106 (2018). [CrossRef]  

8. G. Vallone, D. Bacco, D. Dequal, S. Gaiarin, V. Luceri, G. Bianco, and P. Villoresi, “Experimental satellite quantum communications,” Phys. Rev. Lett. 115(4), 040502 (2015). [CrossRef]   [PubMed]  

9. J. G. Rarity, P. R. Tapster, P. M. Gorman, and P. Knight, “Ground to satellite secure key exchange using quantum cryptography,” New J. Phys. 4(1), 82 (2002). [CrossRef]  

10. X. Han, H.-L. Yong, P. Xu, W.-Y. Wang, K.-X. Yang, H.-J. Xue, W.-Q. Cai, J.-G. Ren, C.-Z. Peng, and J.-W. Pan, “Point-ahead demonstration of a transmitting antenna for satellite quantum communication,” Opt. Express 26(13), 17044–17055 (2018). [CrossRef]   [PubMed]  

11. S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L. H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017). [CrossRef]   [PubMed]  

12. A. Meda, I. P. Degiovanni, A. Tosi, Z. Yuan, G. Brida, and M. Genovese, “Quantifying backflash radiation to prevent zero-error attacks in quantum key distribution,” Light Sci. Appl. 6(6), e16261 (2017). [CrossRef]   [PubMed]  

13. P. V. P. Pinheiro, P. Chaiwongkhot, S. Sajeed, R. T. Horn, J.-P. Bourgoin, T. Jennewein, N. Lütkenhaus, and V. Makarov, “Eavesdropping and countermeasures for backflash side channel in quantum cryptography.” arXiv preprint arXiv:1804.10317 (2018).

14. Y. Shi, J. Z. J. Lim, H. S. Poh, P. K. Tan, P. A. Tan, A. Ling, and C. Kurtsiefer, “Breakdown flash at telecom wavelengths in InGaAs avalanche photodiodes,” Opt. Express 25(24), 30388–30394 (2017). [CrossRef]   [PubMed]  

15. P. V. P. Pinheiro, P. Chaiwongkhot, S. Sajeed, R. T. Horn, J.-P. Bourgoin, T. Jennewein, N. Lütkenhaus, and V. Makarov, “Eavesdropping and countermeasures for backflash side channel in quantum cryptography.” arXiv preprint arXiv:1804.10317 (2018).

16. A. Lacaita, S. Cova, A. Spinelli, and F. Zappa, “Photon‐assisted avalanche spreading in reach‐through photodiodes,” Appl. Phys. Lett. 62(6), 606–608 (1993). [CrossRef]  

17. M. Gabay and S. Arnon, “Quantum key distribution by a free-space MIMO system,” J. Lightwave Technol. 24(8), 3114–3120 (2006). [CrossRef]  

18. M. Li, Y. Hong, Y. Song, and X. Zhang, “Effect of controllable parameter synchronization on the ensemble average bit error rate of space-to-ground downlink chaos laser communication system,” Opt. Express 26(3), 2954–2964 (2018). [CrossRef]   [PubMed]  

19. M. Gabay and S. Arnon, “Effect of turbulence on a quantum-key distribution scheme based on transformation from the polarization to the time domain: laboratory experiment,” Opt. Eng. 44(4), 045002 (2005). [CrossRef]  

20. J. Yin, Y. Cao, Y.-H. Li, S.-K. Liao, L. Zhang, J.-G. Ren, W.-Q. Cai, W.-Y. Liu, B. Li, H. Dai, G.-B. Li, Q.-M. Lu, Y.-H. Gong, Y. Xu, S.-L. Li, F.-Z. Li, Y.-Y. Yin, Z. Q. Jiang, M. Li, J. J. Jia, G. Ren, D. He, Y. L. Zhou, X. X. Zhang, N. Wang, X. Chang, Z. C. Zhu, N. L. Liu, Y. A. Chen, C. Y. Lu, R. Shu, C. Z. Peng, J. Y. Wang, and J. W. Pan, “Satellite-based entanglement distribution over 1200 kilometers,” Science 356(6343), 1140–1144 (2017). [CrossRef]   [PubMed]  

21. S. Arnon and N. S. Kopeika, “Laser satellite communication network-vibration effect and possible solutions,” Proc. IEEE 85(10), 1646–1661 (1997). [CrossRef]  

22. S. Arnon, “Effects of atmospheric turbulence and building sway on optical wireless-communication systems,” Opt. Lett. 28(2), 129–131 (2003). [CrossRef]   [PubMed]  

23. F. Yang, J. Cheng, and T. A. Tsiftsis, “Free-space optical communication with nonzero boresight pointing errors,” IEEE Trans. Commun. 62(2), 713–725 (2014). [CrossRef]  

24. C.-C. Chen and C. S. Gardner, “Impact of random pointing and tracking errors on the design of coherent and incoherent optical intersatellite communication links,” IEEE Trans. Commun. 37(3), 252–260 (1989). [CrossRef]  

25. J. G. Ren, P. Xu, H. L. Yong, L. Zhang, S. K. Liao, J. Yin, W. Y. Liu, W. Q. Cai, M. Yang, L. Li, K. X. Yang, X. Han, Y. Q. Yao, J. Li, H. Y. Wu, S. Wan, L. Liu, D. Q. Liu, Y. W. Kuang, Z. P. He, P. Shang, C. Guo, R. H. Zheng, K. Tian, Z. C. Zhu, N. L. Liu, C. Y. Lu, R. Shu, Y. A. Chen, C. Z. Peng, J. Y. Wang, and J. W. Pan, “Ground-to-satellite quantum teleportation,” Nature 549(7670), 70–73 (2017). [CrossRef]   [PubMed]  

References

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  1. P. W. Shor and J. Preskill, “Simple proof of security of the BB84 quantum key distribution protocol,” Phys. Rev. Lett. 85(2), 441–444 (2000).
    [Crossref] [PubMed]
  2. L. Lydersen, C. Wiechers, C. Wittmann, D. Elser, J. Skaar, and V. Makarov, “Hacking commercial quantum cryptography systems by tailored bright illumination,” Nat. Photonics 4(10), 686–689 (2010).
    [Crossref]
  3. A. Meda, I. P. Degiovanni, A. Tosi, Z. L. Yuan, G. Brida, and M. Genovese, “Quantum key distribution security threat: the backflash light case.” in Quantum Technologies 2018, vol. 10674, p. 1067418. International Society for Optics and Photonics, 2018.
  4. K. Wei, H. Liu, H. Ma, X. Yang, Y. Zhang, Y. Sun, J. Xiao, and Y. Ji, “Feasible attack on detector-device-independent quantum key distribution,” Sci. Rep. 7(1), 449 (2017).
    [Crossref] [PubMed]
  5. P. V. Trinh and A. T. Pham, “Design and secrecy performance of novel two-way free-space QKD protocol using standard FSO systems.” In Communications (ICC), 2017 IEEE International Conference on, pp. 1–6. IEEE, 2017.
    [Crossref]
  6. W. S. Rabinovich, R. Mahon, M. S. Ferraro, P. G. Goetz, M. Bashkansky, R. E. Freeman, J. Reintjes, and J. L. Murphy, “Free space quantum key distribution using modulating retro-reflectors,” Opt. Express 26(9), 11331–11351 (2018).
    [Crossref] [PubMed]
  7. J. A. Grieve, R. Bedington, Z. Tang, R. C. M. R. B. Chandrasekara, A. Ling, C. M. R. B. Chandrasekara, and A. Ling, “SpooQySats: CubeSats to demonstrate quantum key distribution technologies,” Acta Astronaut. 151, 103–106 (2018).
    [Crossref]
  8. G. Vallone, D. Bacco, D. Dequal, S. Gaiarin, V. Luceri, G. Bianco, and P. Villoresi, “Experimental satellite quantum communications,” Phys. Rev. Lett. 115(4), 040502 (2015).
    [Crossref] [PubMed]
  9. J. G. Rarity, P. R. Tapster, P. M. Gorman, and P. Knight, “Ground to satellite secure key exchange using quantum cryptography,” New J. Phys. 4(1), 82 (2002).
    [Crossref]
  10. X. Han, H.-L. Yong, P. Xu, W.-Y. Wang, K.-X. Yang, H.-J. Xue, W.-Q. Cai, J.-G. Ren, C.-Z. Peng, and J.-W. Pan, “Point-ahead demonstration of a transmitting antenna for satellite quantum communication,” Opt. Express 26(13), 17044–17055 (2018).
    [Crossref] [PubMed]
  11. S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L. H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
    [Crossref] [PubMed]
  12. A. Meda, I. P. Degiovanni, A. Tosi, Z. Yuan, G. Brida, and M. Genovese, “Quantifying backflash radiation to prevent zero-error attacks in quantum key distribution,” Light Sci. Appl. 6(6), e16261 (2017).
    [Crossref] [PubMed]
  13. P. V. P. Pinheiro, P. Chaiwongkhot, S. Sajeed, R. T. Horn, J.-P. Bourgoin, T. Jennewein, N. Lütkenhaus, and V. Makarov, “Eavesdropping and countermeasures for backflash side channel in quantum cryptography.” arXiv preprint arXiv:1804.10317 (2018).
  14. Y. Shi, J. Z. J. Lim, H. S. Poh, P. K. Tan, P. A. Tan, A. Ling, and C. Kurtsiefer, “Breakdown flash at telecom wavelengths in InGaAs avalanche photodiodes,” Opt. Express 25(24), 30388–30394 (2017).
    [Crossref] [PubMed]
  15. P. V. P. Pinheiro, P. Chaiwongkhot, S. Sajeed, R. T. Horn, J.-P. Bourgoin, T. Jennewein, N. Lütkenhaus, and V. Makarov, “Eavesdropping and countermeasures for backflash side channel in quantum cryptography.” arXiv preprint arXiv:1804.10317 (2018).
  16. A. Lacaita, S. Cova, A. Spinelli, and F. Zappa, “Photon‐assisted avalanche spreading in reach‐through photodiodes,” Appl. Phys. Lett. 62(6), 606–608 (1993).
    [Crossref]
  17. M. Gabay and S. Arnon, “Quantum key distribution by a free-space MIMO system,” J. Lightwave Technol. 24(8), 3114–3120 (2006).
    [Crossref]
  18. M. Li, Y. Hong, Y. Song, and X. Zhang, “Effect of controllable parameter synchronization on the ensemble average bit error rate of space-to-ground downlink chaos laser communication system,” Opt. Express 26(3), 2954–2964 (2018).
    [Crossref] [PubMed]
  19. M. Gabay and S. Arnon, “Effect of turbulence on a quantum-key distribution scheme based on transformation from the polarization to the time domain: laboratory experiment,” Opt. Eng. 44(4), 045002 (2005).
    [Crossref]
  20. J. Yin, Y. Cao, Y.-H. Li, S.-K. Liao, L. Zhang, J.-G. Ren, W.-Q. Cai, W.-Y. Liu, B. Li, H. Dai, G.-B. Li, Q.-M. Lu, Y.-H. Gong, Y. Xu, S.-L. Li, F.-Z. Li, Y.-Y. Yin, Z. Q. Jiang, M. Li, J. J. Jia, G. Ren, D. He, Y. L. Zhou, X. X. Zhang, N. Wang, X. Chang, Z. C. Zhu, N. L. Liu, Y. A. Chen, C. Y. Lu, R. Shu, C. Z. Peng, J. Y. Wang, and J. W. Pan, “Satellite-based entanglement distribution over 1200 kilometers,” Science 356(6343), 1140–1144 (2017).
    [Crossref] [PubMed]
  21. S. Arnon and N. S. Kopeika, “Laser satellite communication network-vibration effect and possible solutions,” Proc. IEEE 85(10), 1646–1661 (1997).
    [Crossref]
  22. S. Arnon, “Effects of atmospheric turbulence and building sway on optical wireless-communication systems,” Opt. Lett. 28(2), 129–131 (2003).
    [Crossref] [PubMed]
  23. F. Yang, J. Cheng, and T. A. Tsiftsis, “Free-space optical communication with nonzero boresight pointing errors,” IEEE Trans. Commun. 62(2), 713–725 (2014).
    [Crossref]
  24. C.-C. Chen and C. S. Gardner, “Impact of random pointing and tracking errors on the design of coherent and incoherent optical intersatellite communication links,” IEEE Trans. Commun. 37(3), 252–260 (1989).
    [Crossref]
  25. J. G. Ren, P. Xu, H. L. Yong, L. Zhang, S. K. Liao, J. Yin, W. Y. Liu, W. Q. Cai, M. Yang, L. Li, K. X. Yang, X. Han, Y. Q. Yao, J. Li, H. Y. Wu, S. Wan, L. Liu, D. Q. Liu, Y. W. Kuang, Z. P. He, P. Shang, C. Guo, R. H. Zheng, K. Tian, Z. C. Zhu, N. L. Liu, C. Y. Lu, R. Shu, Y. A. Chen, C. Z. Peng, J. Y. Wang, and J. W. Pan, “Ground-to-satellite quantum teleportation,” Nature 549(7670), 70–73 (2017).
    [Crossref] [PubMed]

2018 (4)

2017 (6)

J. Yin, Y. Cao, Y.-H. Li, S.-K. Liao, L. Zhang, J.-G. Ren, W.-Q. Cai, W.-Y. Liu, B. Li, H. Dai, G.-B. Li, Q.-M. Lu, Y.-H. Gong, Y. Xu, S.-L. Li, F.-Z. Li, Y.-Y. Yin, Z. Q. Jiang, M. Li, J. J. Jia, G. Ren, D. He, Y. L. Zhou, X. X. Zhang, N. Wang, X. Chang, Z. C. Zhu, N. L. Liu, Y. A. Chen, C. Y. Lu, R. Shu, C. Z. Peng, J. Y. Wang, and J. W. Pan, “Satellite-based entanglement distribution over 1200 kilometers,” Science 356(6343), 1140–1144 (2017).
[Crossref] [PubMed]

K. Wei, H. Liu, H. Ma, X. Yang, Y. Zhang, Y. Sun, J. Xiao, and Y. Ji, “Feasible attack on detector-device-independent quantum key distribution,” Sci. Rep. 7(1), 449 (2017).
[Crossref] [PubMed]

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L. H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

A. Meda, I. P. Degiovanni, A. Tosi, Z. Yuan, G. Brida, and M. Genovese, “Quantifying backflash radiation to prevent zero-error attacks in quantum key distribution,” Light Sci. Appl. 6(6), e16261 (2017).
[Crossref] [PubMed]

Y. Shi, J. Z. J. Lim, H. S. Poh, P. K. Tan, P. A. Tan, A. Ling, and C. Kurtsiefer, “Breakdown flash at telecom wavelengths in InGaAs avalanche photodiodes,” Opt. Express 25(24), 30388–30394 (2017).
[Crossref] [PubMed]

J. G. Ren, P. Xu, H. L. Yong, L. Zhang, S. K. Liao, J. Yin, W. Y. Liu, W. Q. Cai, M. Yang, L. Li, K. X. Yang, X. Han, Y. Q. Yao, J. Li, H. Y. Wu, S. Wan, L. Liu, D. Q. Liu, Y. W. Kuang, Z. P. He, P. Shang, C. Guo, R. H. Zheng, K. Tian, Z. C. Zhu, N. L. Liu, C. Y. Lu, R. Shu, Y. A. Chen, C. Z. Peng, J. Y. Wang, and J. W. Pan, “Ground-to-satellite quantum teleportation,” Nature 549(7670), 70–73 (2017).
[Crossref] [PubMed]

2015 (1)

G. Vallone, D. Bacco, D. Dequal, S. Gaiarin, V. Luceri, G. Bianco, and P. Villoresi, “Experimental satellite quantum communications,” Phys. Rev. Lett. 115(4), 040502 (2015).
[Crossref] [PubMed]

2014 (1)

F. Yang, J. Cheng, and T. A. Tsiftsis, “Free-space optical communication with nonzero boresight pointing errors,” IEEE Trans. Commun. 62(2), 713–725 (2014).
[Crossref]

2010 (1)

L. Lydersen, C. Wiechers, C. Wittmann, D. Elser, J. Skaar, and V. Makarov, “Hacking commercial quantum cryptography systems by tailored bright illumination,” Nat. Photonics 4(10), 686–689 (2010).
[Crossref]

2006 (1)

2005 (1)

M. Gabay and S. Arnon, “Effect of turbulence on a quantum-key distribution scheme based on transformation from the polarization to the time domain: laboratory experiment,” Opt. Eng. 44(4), 045002 (2005).
[Crossref]

2003 (1)

2002 (1)

J. G. Rarity, P. R. Tapster, P. M. Gorman, and P. Knight, “Ground to satellite secure key exchange using quantum cryptography,” New J. Phys. 4(1), 82 (2002).
[Crossref]

2000 (1)

P. W. Shor and J. Preskill, “Simple proof of security of the BB84 quantum key distribution protocol,” Phys. Rev. Lett. 85(2), 441–444 (2000).
[Crossref] [PubMed]

1997 (1)

S. Arnon and N. S. Kopeika, “Laser satellite communication network-vibration effect and possible solutions,” Proc. IEEE 85(10), 1646–1661 (1997).
[Crossref]

1993 (1)

A. Lacaita, S. Cova, A. Spinelli, and F. Zappa, “Photon‐assisted avalanche spreading in reach‐through photodiodes,” Appl. Phys. Lett. 62(6), 606–608 (1993).
[Crossref]

1989 (1)

C.-C. Chen and C. S. Gardner, “Impact of random pointing and tracking errors on the design of coherent and incoherent optical intersatellite communication links,” IEEE Trans. Commun. 37(3), 252–260 (1989).
[Crossref]

Arnon, S.

M. Gabay and S. Arnon, “Quantum key distribution by a free-space MIMO system,” J. Lightwave Technol. 24(8), 3114–3120 (2006).
[Crossref]

M. Gabay and S. Arnon, “Effect of turbulence on a quantum-key distribution scheme based on transformation from the polarization to the time domain: laboratory experiment,” Opt. Eng. 44(4), 045002 (2005).
[Crossref]

S. Arnon, “Effects of atmospheric turbulence and building sway on optical wireless-communication systems,” Opt. Lett. 28(2), 129–131 (2003).
[Crossref] [PubMed]

S. Arnon and N. S. Kopeika, “Laser satellite communication network-vibration effect and possible solutions,” Proc. IEEE 85(10), 1646–1661 (1997).
[Crossref]

Bacco, D.

G. Vallone, D. Bacco, D. Dequal, S. Gaiarin, V. Luceri, G. Bianco, and P. Villoresi, “Experimental satellite quantum communications,” Phys. Rev. Lett. 115(4), 040502 (2015).
[Crossref] [PubMed]

Bashkansky, M.

Bedington, R.

J. A. Grieve, R. Bedington, Z. Tang, R. C. M. R. B. Chandrasekara, A. Ling, C. M. R. B. Chandrasekara, and A. Ling, “SpooQySats: CubeSats to demonstrate quantum key distribution technologies,” Acta Astronaut. 151, 103–106 (2018).
[Crossref]

Bianco, G.

G. Vallone, D. Bacco, D. Dequal, S. Gaiarin, V. Luceri, G. Bianco, and P. Villoresi, “Experimental satellite quantum communications,” Phys. Rev. Lett. 115(4), 040502 (2015).
[Crossref] [PubMed]

Brida, G.

A. Meda, I. P. Degiovanni, A. Tosi, Z. Yuan, G. Brida, and M. Genovese, “Quantifying backflash radiation to prevent zero-error attacks in quantum key distribution,” Light Sci. Appl. 6(6), e16261 (2017).
[Crossref] [PubMed]

Cai, W. Q.

J. G. Ren, P. Xu, H. L. Yong, L. Zhang, S. K. Liao, J. Yin, W. Y. Liu, W. Q. Cai, M. Yang, L. Li, K. X. Yang, X. Han, Y. Q. Yao, J. Li, H. Y. Wu, S. Wan, L. Liu, D. Q. Liu, Y. W. Kuang, Z. P. He, P. Shang, C. Guo, R. H. Zheng, K. Tian, Z. C. Zhu, N. L. Liu, C. Y. Lu, R. Shu, Y. A. Chen, C. Z. Peng, J. Y. Wang, and J. W. Pan, “Ground-to-satellite quantum teleportation,” Nature 549(7670), 70–73 (2017).
[Crossref] [PubMed]

Cai, W.-Q.

X. Han, H.-L. Yong, P. Xu, W.-Y. Wang, K.-X. Yang, H.-J. Xue, W.-Q. Cai, J.-G. Ren, C.-Z. Peng, and J.-W. Pan, “Point-ahead demonstration of a transmitting antenna for satellite quantum communication,” Opt. Express 26(13), 17044–17055 (2018).
[Crossref] [PubMed]

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L. H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

J. Yin, Y. Cao, Y.-H. Li, S.-K. Liao, L. Zhang, J.-G. Ren, W.-Q. Cai, W.-Y. Liu, B. Li, H. Dai, G.-B. Li, Q.-M. Lu, Y.-H. Gong, Y. Xu, S.-L. Li, F.-Z. Li, Y.-Y. Yin, Z. Q. Jiang, M. Li, J. J. Jia, G. Ren, D. He, Y. L. Zhou, X. X. Zhang, N. Wang, X. Chang, Z. C. Zhu, N. L. Liu, Y. A. Chen, C. Y. Lu, R. Shu, C. Z. Peng, J. Y. Wang, and J. W. Pan, “Satellite-based entanglement distribution over 1200 kilometers,” Science 356(6343), 1140–1144 (2017).
[Crossref] [PubMed]

Cao, Y.

J. Yin, Y. Cao, Y.-H. Li, S.-K. Liao, L. Zhang, J.-G. Ren, W.-Q. Cai, W.-Y. Liu, B. Li, H. Dai, G.-B. Li, Q.-M. Lu, Y.-H. Gong, Y. Xu, S.-L. Li, F.-Z. Li, Y.-Y. Yin, Z. Q. Jiang, M. Li, J. J. Jia, G. Ren, D. He, Y. L. Zhou, X. X. Zhang, N. Wang, X. Chang, Z. C. Zhu, N. L. Liu, Y. A. Chen, C. Y. Lu, R. Shu, C. Z. Peng, J. Y. Wang, and J. W. Pan, “Satellite-based entanglement distribution over 1200 kilometers,” Science 356(6343), 1140–1144 (2017).
[Crossref] [PubMed]

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L. H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Chandrasekara, C. M. R. B.

J. A. Grieve, R. Bedington, Z. Tang, R. C. M. R. B. Chandrasekara, A. Ling, C. M. R. B. Chandrasekara, and A. Ling, “SpooQySats: CubeSats to demonstrate quantum key distribution technologies,” Acta Astronaut. 151, 103–106 (2018).
[Crossref]

Chandrasekara, R. C. M. R. B.

J. A. Grieve, R. Bedington, Z. Tang, R. C. M. R. B. Chandrasekara, A. Ling, C. M. R. B. Chandrasekara, and A. Ling, “SpooQySats: CubeSats to demonstrate quantum key distribution technologies,” Acta Astronaut. 151, 103–106 (2018).
[Crossref]

Chang, X.

J. Yin, Y. Cao, Y.-H. Li, S.-K. Liao, L. Zhang, J.-G. Ren, W.-Q. Cai, W.-Y. Liu, B. Li, H. Dai, G.-B. Li, Q.-M. Lu, Y.-H. Gong, Y. Xu, S.-L. Li, F.-Z. Li, Y.-Y. Yin, Z. Q. Jiang, M. Li, J. J. Jia, G. Ren, D. He, Y. L. Zhou, X. X. Zhang, N. Wang, X. Chang, Z. C. Zhu, N. L. Liu, Y. A. Chen, C. Y. Lu, R. Shu, C. Z. Peng, J. Y. Wang, and J. W. Pan, “Satellite-based entanglement distribution over 1200 kilometers,” Science 356(6343), 1140–1144 (2017).
[Crossref] [PubMed]

Chen, C.-C.

C.-C. Chen and C. S. Gardner, “Impact of random pointing and tracking errors on the design of coherent and incoherent optical intersatellite communication links,” IEEE Trans. Commun. 37(3), 252–260 (1989).
[Crossref]

Chen, X.-W.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L. H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Chen, Y. A.

J. Yin, Y. Cao, Y.-H. Li, S.-K. Liao, L. Zhang, J.-G. Ren, W.-Q. Cai, W.-Y. Liu, B. Li, H. Dai, G.-B. Li, Q.-M. Lu, Y.-H. Gong, Y. Xu, S.-L. Li, F.-Z. Li, Y.-Y. Yin, Z. Q. Jiang, M. Li, J. J. Jia, G. Ren, D. He, Y. L. Zhou, X. X. Zhang, N. Wang, X. Chang, Z. C. Zhu, N. L. Liu, Y. A. Chen, C. Y. Lu, R. Shu, C. Z. Peng, J. Y. Wang, and J. W. Pan, “Satellite-based entanglement distribution over 1200 kilometers,” Science 356(6343), 1140–1144 (2017).
[Crossref] [PubMed]

J. G. Ren, P. Xu, H. L. Yong, L. Zhang, S. K. Liao, J. Yin, W. Y. Liu, W. Q. Cai, M. Yang, L. Li, K. X. Yang, X. Han, Y. Q. Yao, J. Li, H. Y. Wu, S. Wan, L. Liu, D. Q. Liu, Y. W. Kuang, Z. P. He, P. Shang, C. Guo, R. H. Zheng, K. Tian, Z. C. Zhu, N. L. Liu, C. Y. Lu, R. Shu, Y. A. Chen, C. Z. Peng, J. Y. Wang, and J. W. Pan, “Ground-to-satellite quantum teleportation,” Nature 549(7670), 70–73 (2017).
[Crossref] [PubMed]

Chen, Y.-A.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L. H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Cheng, J.

F. Yang, J. Cheng, and T. A. Tsiftsis, “Free-space optical communication with nonzero boresight pointing errors,” IEEE Trans. Commun. 62(2), 713–725 (2014).
[Crossref]

Cova, S.

A. Lacaita, S. Cova, A. Spinelli, and F. Zappa, “Photon‐assisted avalanche spreading in reach‐through photodiodes,” Appl. Phys. Lett. 62(6), 606–608 (1993).
[Crossref]

Dai, H.

J. Yin, Y. Cao, Y.-H. Li, S.-K. Liao, L. Zhang, J.-G. Ren, W.-Q. Cai, W.-Y. Liu, B. Li, H. Dai, G.-B. Li, Q.-M. Lu, Y.-H. Gong, Y. Xu, S.-L. Li, F.-Z. Li, Y.-Y. Yin, Z. Q. Jiang, M. Li, J. J. Jia, G. Ren, D. He, Y. L. Zhou, X. X. Zhang, N. Wang, X. Chang, Z. C. Zhu, N. L. Liu, Y. A. Chen, C. Y. Lu, R. Shu, C. Z. Peng, J. Y. Wang, and J. W. Pan, “Satellite-based entanglement distribution over 1200 kilometers,” Science 356(6343), 1140–1144 (2017).
[Crossref] [PubMed]

Degiovanni, I. P.

A. Meda, I. P. Degiovanni, A. Tosi, Z. Yuan, G. Brida, and M. Genovese, “Quantifying backflash radiation to prevent zero-error attacks in quantum key distribution,” Light Sci. Appl. 6(6), e16261 (2017).
[Crossref] [PubMed]

Deng, L.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L. H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Dequal, D.

G. Vallone, D. Bacco, D. Dequal, S. Gaiarin, V. Luceri, G. Bianco, and P. Villoresi, “Experimental satellite quantum communications,” Phys. Rev. Lett. 115(4), 040502 (2015).
[Crossref] [PubMed]

Elser, D.

L. Lydersen, C. Wiechers, C. Wittmann, D. Elser, J. Skaar, and V. Makarov, “Hacking commercial quantum cryptography systems by tailored bright illumination,” Nat. Photonics 4(10), 686–689 (2010).
[Crossref]

Ferraro, M. S.

Freeman, R. E.

Gabay, M.

M. Gabay and S. Arnon, “Quantum key distribution by a free-space MIMO system,” J. Lightwave Technol. 24(8), 3114–3120 (2006).
[Crossref]

M. Gabay and S. Arnon, “Effect of turbulence on a quantum-key distribution scheme based on transformation from the polarization to the time domain: laboratory experiment,” Opt. Eng. 44(4), 045002 (2005).
[Crossref]

Gaiarin, S.

G. Vallone, D. Bacco, D. Dequal, S. Gaiarin, V. Luceri, G. Bianco, and P. Villoresi, “Experimental satellite quantum communications,” Phys. Rev. Lett. 115(4), 040502 (2015).
[Crossref] [PubMed]

Gardner, C. S.

C.-C. Chen and C. S. Gardner, “Impact of random pointing and tracking errors on the design of coherent and incoherent optical intersatellite communication links,” IEEE Trans. Commun. 37(3), 252–260 (1989).
[Crossref]

Genovese, M.

A. Meda, I. P. Degiovanni, A. Tosi, Z. Yuan, G. Brida, and M. Genovese, “Quantifying backflash radiation to prevent zero-error attacks in quantum key distribution,” Light Sci. Appl. 6(6), e16261 (2017).
[Crossref] [PubMed]

Goetz, P. G.

Gong, Y.-H.

J. Yin, Y. Cao, Y.-H. Li, S.-K. Liao, L. Zhang, J.-G. Ren, W.-Q. Cai, W.-Y. Liu, B. Li, H. Dai, G.-B. Li, Q.-M. Lu, Y.-H. Gong, Y. Xu, S.-L. Li, F.-Z. Li, Y.-Y. Yin, Z. Q. Jiang, M. Li, J. J. Jia, G. Ren, D. He, Y. L. Zhou, X. X. Zhang, N. Wang, X. Chang, Z. C. Zhu, N. L. Liu, Y. A. Chen, C. Y. Lu, R. Shu, C. Z. Peng, J. Y. Wang, and J. W. Pan, “Satellite-based entanglement distribution over 1200 kilometers,” Science 356(6343), 1140–1144 (2017).
[Crossref] [PubMed]

Gorman, P. M.

J. G. Rarity, P. R. Tapster, P. M. Gorman, and P. Knight, “Ground to satellite secure key exchange using quantum cryptography,” New J. Phys. 4(1), 82 (2002).
[Crossref]

Grieve, J. A.

J. A. Grieve, R. Bedington, Z. Tang, R. C. M. R. B. Chandrasekara, A. Ling, C. M. R. B. Chandrasekara, and A. Ling, “SpooQySats: CubeSats to demonstrate quantum key distribution technologies,” Acta Astronaut. 151, 103–106 (2018).
[Crossref]

Guo, C.

J. G. Ren, P. Xu, H. L. Yong, L. Zhang, S. K. Liao, J. Yin, W. Y. Liu, W. Q. Cai, M. Yang, L. Li, K. X. Yang, X. Han, Y. Q. Yao, J. Li, H. Y. Wu, S. Wan, L. Liu, D. Q. Liu, Y. W. Kuang, Z. P. He, P. Shang, C. Guo, R. H. Zheng, K. Tian, Z. C. Zhu, N. L. Liu, C. Y. Lu, R. Shu, Y. A. Chen, C. Z. Peng, J. Y. Wang, and J. W. Pan, “Ground-to-satellite quantum teleportation,” Nature 549(7670), 70–73 (2017).
[Crossref] [PubMed]

Han, X.

X. Han, H.-L. Yong, P. Xu, W.-Y. Wang, K.-X. Yang, H.-J. Xue, W.-Q. Cai, J.-G. Ren, C.-Z. Peng, and J.-W. Pan, “Point-ahead demonstration of a transmitting antenna for satellite quantum communication,” Opt. Express 26(13), 17044–17055 (2018).
[Crossref] [PubMed]

J. G. Ren, P. Xu, H. L. Yong, L. Zhang, S. K. Liao, J. Yin, W. Y. Liu, W. Q. Cai, M. Yang, L. Li, K. X. Yang, X. Han, Y. Q. Yao, J. Li, H. Y. Wu, S. Wan, L. Liu, D. Q. Liu, Y. W. Kuang, Z. P. He, P. Shang, C. Guo, R. H. Zheng, K. Tian, Z. C. Zhu, N. L. Liu, C. Y. Lu, R. Shu, Y. A. Chen, C. Z. Peng, J. Y. Wang, and J. W. Pan, “Ground-to-satellite quantum teleportation,” Nature 549(7670), 70–73 (2017).
[Crossref] [PubMed]

He, D.

J. Yin, Y. Cao, Y.-H. Li, S.-K. Liao, L. Zhang, J.-G. Ren, W.-Q. Cai, W.-Y. Liu, B. Li, H. Dai, G.-B. Li, Q.-M. Lu, Y.-H. Gong, Y. Xu, S.-L. Li, F.-Z. Li, Y.-Y. Yin, Z. Q. Jiang, M. Li, J. J. Jia, G. Ren, D. He, Y. L. Zhou, X. X. Zhang, N. Wang, X. Chang, Z. C. Zhu, N. L. Liu, Y. A. Chen, C. Y. Lu, R. Shu, C. Z. Peng, J. Y. Wang, and J. W. Pan, “Satellite-based entanglement distribution over 1200 kilometers,” Science 356(6343), 1140–1144 (2017).
[Crossref] [PubMed]

He, Z. P.

J. G. Ren, P. Xu, H. L. Yong, L. Zhang, S. K. Liao, J. Yin, W. Y. Liu, W. Q. Cai, M. Yang, L. Li, K. X. Yang, X. Han, Y. Q. Yao, J. Li, H. Y. Wu, S. Wan, L. Liu, D. Q. Liu, Y. W. Kuang, Z. P. He, P. Shang, C. Guo, R. H. Zheng, K. Tian, Z. C. Zhu, N. L. Liu, C. Y. Lu, R. Shu, Y. A. Chen, C. Z. Peng, J. Y. Wang, and J. W. Pan, “Ground-to-satellite quantum teleportation,” Nature 549(7670), 70–73 (2017).
[Crossref] [PubMed]

Hong, Y.

Hu, T.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L. H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Huang, Y.-M.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L. H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Ji, Y.

K. Wei, H. Liu, H. Ma, X. Yang, Y. Zhang, Y. Sun, J. Xiao, and Y. Ji, “Feasible attack on detector-device-independent quantum key distribution,” Sci. Rep. 7(1), 449 (2017).
[Crossref] [PubMed]

Jia, J. J.

J. Yin, Y. Cao, Y.-H. Li, S.-K. Liao, L. Zhang, J.-G. Ren, W.-Q. Cai, W.-Y. Liu, B. Li, H. Dai, G.-B. Li, Q.-M. Lu, Y.-H. Gong, Y. Xu, S.-L. Li, F.-Z. Li, Y.-Y. Yin, Z. Q. Jiang, M. Li, J. J. Jia, G. Ren, D. He, Y. L. Zhou, X. X. Zhang, N. Wang, X. Chang, Z. C. Zhu, N. L. Liu, Y. A. Chen, C. Y. Lu, R. Shu, C. Z. Peng, J. Y. Wang, and J. W. Pan, “Satellite-based entanglement distribution over 1200 kilometers,” Science 356(6343), 1140–1144 (2017).
[Crossref] [PubMed]

Jia, J.-J.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L. H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Jiang, X.-J.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L. H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Jiang, Z. Q.

J. Yin, Y. Cao, Y.-H. Li, S.-K. Liao, L. Zhang, J.-G. Ren, W.-Q. Cai, W.-Y. Liu, B. Li, H. Dai, G.-B. Li, Q.-M. Lu, Y.-H. Gong, Y. Xu, S.-L. Li, F.-Z. Li, Y.-Y. Yin, Z. Q. Jiang, M. Li, J. J. Jia, G. Ren, D. He, Y. L. Zhou, X. X. Zhang, N. Wang, X. Chang, Z. C. Zhu, N. L. Liu, Y. A. Chen, C. Y. Lu, R. Shu, C. Z. Peng, J. Y. Wang, and J. W. Pan, “Satellite-based entanglement distribution over 1200 kilometers,” Science 356(6343), 1140–1144 (2017).
[Crossref] [PubMed]

Knight, P.

J. G. Rarity, P. R. Tapster, P. M. Gorman, and P. Knight, “Ground to satellite secure key exchange using quantum cryptography,” New J. Phys. 4(1), 82 (2002).
[Crossref]

Kopeika, N. S.

S. Arnon and N. S. Kopeika, “Laser satellite communication network-vibration effect and possible solutions,” Proc. IEEE 85(10), 1646–1661 (1997).
[Crossref]

Kuang, Y. W.

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J. G. Ren, P. Xu, H. L. Yong, L. Zhang, S. K. Liao, J. Yin, W. Y. Liu, W. Q. Cai, M. Yang, L. Li, K. X. Yang, X. Han, Y. Q. Yao, J. Li, H. Y. Wu, S. Wan, L. Liu, D. Q. Liu, Y. W. Kuang, Z. P. He, P. Shang, C. Guo, R. H. Zheng, K. Tian, Z. C. Zhu, N. L. Liu, C. Y. Lu, R. Shu, Y. A. Chen, C. Z. Peng, J. Y. Wang, and J. W. Pan, “Ground-to-satellite quantum teleportation,” Nature 549(7670), 70–73 (2017).
[Crossref] [PubMed]

Yang, X.

K. Wei, H. Liu, H. Ma, X. Yang, Y. Zhang, Y. Sun, J. Xiao, and Y. Ji, “Feasible attack on detector-device-independent quantum key distribution,” Sci. Rep. 7(1), 449 (2017).
[Crossref] [PubMed]

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J. G. Ren, P. Xu, H. L. Yong, L. Zhang, S. K. Liao, J. Yin, W. Y. Liu, W. Q. Cai, M. Yang, L. Li, K. X. Yang, X. Han, Y. Q. Yao, J. Li, H. Y. Wu, S. Wan, L. Liu, D. Q. Liu, Y. W. Kuang, Z. P. He, P. Shang, C. Guo, R. H. Zheng, K. Tian, Z. C. Zhu, N. L. Liu, C. Y. Lu, R. Shu, Y. A. Chen, C. Z. Peng, J. Y. Wang, and J. W. Pan, “Ground-to-satellite quantum teleportation,” Nature 549(7670), 70–73 (2017).
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J. G. Ren, P. Xu, H. L. Yong, L. Zhang, S. K. Liao, J. Yin, W. Y. Liu, W. Q. Cai, M. Yang, L. Li, K. X. Yang, X. Han, Y. Q. Yao, J. Li, H. Y. Wu, S. Wan, L. Liu, D. Q. Liu, Y. W. Kuang, Z. P. He, P. Shang, C. Guo, R. H. Zheng, K. Tian, Z. C. Zhu, N. L. Liu, C. Y. Lu, R. Shu, Y. A. Chen, C. Z. Peng, J. Y. Wang, and J. W. Pan, “Ground-to-satellite quantum teleportation,” Nature 549(7670), 70–73 (2017).
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S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L. H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
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J. G. Ren, P. Xu, H. L. Yong, L. Zhang, S. K. Liao, J. Yin, W. Y. Liu, W. Q. Cai, M. Yang, L. Li, K. X. Yang, X. Han, Y. Q. Yao, J. Li, H. Y. Wu, S. Wan, L. Liu, D. Q. Liu, Y. W. Kuang, Z. P. He, P. Shang, C. Guo, R. H. Zheng, K. Tian, Z. C. Zhu, N. L. Liu, C. Y. Lu, R. Shu, Y. A. Chen, C. Z. Peng, J. Y. Wang, and J. W. Pan, “Ground-to-satellite quantum teleportation,” Nature 549(7670), 70–73 (2017).
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J. Yin, Y. Cao, Y.-H. Li, S.-K. Liao, L. Zhang, J.-G. Ren, W.-Q. Cai, W.-Y. Liu, B. Li, H. Dai, G.-B. Li, Q.-M. Lu, Y.-H. Gong, Y. Xu, S.-L. Li, F.-Z. Li, Y.-Y. Yin, Z. Q. Jiang, M. Li, J. J. Jia, G. Ren, D. He, Y. L. Zhou, X. X. Zhang, N. Wang, X. Chang, Z. C. Zhu, N. L. Liu, Y. A. Chen, C. Y. Lu, R. Shu, C. Z. Peng, J. Y. Wang, and J. W. Pan, “Satellite-based entanglement distribution over 1200 kilometers,” Science 356(6343), 1140–1144 (2017).
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J. G. Ren, P. Xu, H. L. Yong, L. Zhang, S. K. Liao, J. Yin, W. Y. Liu, W. Q. Cai, M. Yang, L. Li, K. X. Yang, X. Han, Y. Q. Yao, J. Li, H. Y. Wu, S. Wan, L. Liu, D. Q. Liu, Y. W. Kuang, Z. P. He, P. Shang, C. Guo, R. H. Zheng, K. Tian, Z. C. Zhu, N. L. Liu, C. Y. Lu, R. Shu, Y. A. Chen, C. Z. Peng, J. Y. Wang, and J. W. Pan, “Ground-to-satellite quantum teleportation,” Nature 549(7670), 70–73 (2017).
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S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L. H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
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Figures (4)

Fig. 1
Fig. 1 QKD scheme with eavesdropper. Alice sends a signal to Bob, and Bob’s detector releases backflash photons that are intercepted by Eve.
Fig. 2
Fig. 2 Bob's probability to detect a photon as a function of Bob's telescope gain.
Fig. 3
Fig. 3 Eve's probability to detect a photon as a function of Bob's telescope gain.
Fig. 4
Fig. 4 Probability ratio P Eve ¯ P Bob ¯ as a function of Bob's telescope gain.

Tables (1)

Tables Icon

Table 1 Simulation Parameters

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

P Bob ( θ ) =K 1 L( θ ) G Bob ,
K 1 = η q P Alice G Alice η Alice η Bob L A ( Z 1 ) Z 1 2 ( λ 4 π ) 2
L ( θ )=exp( G Bob θ 2 ).
θ = θ V 2 + θ H 2 .
σ V = σ H = σ .
f θ ( θ )= θ σ 2 exp( θ 2 2 σ 2 ).
P Bob ¯ = 0 P Bob ( θ )f( θ ) dθ.
P Bob ¯ = G K Bob 1 1+2 G Bob σ 2 ,
P Eve ( α, θ V , θ H ,θ ) = K 2 P Bob ( θ )L( ( θ V +α ) 2 + θ H 2 ) G Bob
K 2 = η Backflash η q η Bob G Eve η Eve L A ( Z 2 ) Z 2 2 ( λ B 4 π ) 2
P Eve ¯ ( α )= P Eve ( α, θ V , θ H ) f θ V ( θ V ) f θ H ( θ H )d θ V d θ H .
P Eve ¯ = lim α0 K 3 G Bob 2 0 exp ( G Bob θ 2 ) 2 θ σ 2 exp( θ 2 2 σ 2 )dθ
K 3 = K 1 K 2 .
P Eve ¯ ( G Bob )= K 3 0 θ G Bob 2 exp( θ 2 a ) dθ
a=( 2 G Bob + 1 2 σ 2 ).
P Eve ¯ = G Bob 2 K 3 1+4 G Bob σ 2 .
P Eve ¯ P Bob ¯ = K 2 G Bob 1+2 G Bob σ 2 1+4 G Bob σ 2 .

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