Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter September 16, 2019

Adaptive optics benefit for quantum key distribution uplink from ground to a satellite

  • Christopher J. Pugh , Jean-Francois Lavigne , Jean-Philippe Bourgoin , Brendon L. Higgins and Thomas Jennewein EMAIL logo


For quantum communications, the use of Earth-orbiting satellites to extend distances has gained significant attention in recent years, exemplified in particular by the launch of the Micius satellite in 2016. The performance of applied protocols such as quantum key distribution (QKD) depends significantly on the transmission efficiency through the turbulent atmosphere, which is especially challenging for ground-to-satellite uplink scenarios. Adaptive optics (AO) techniques have been used in astronomical, communication, and other applications to reduce the detrimental effects of turbulence for many years, but their applicability to quantum protocols, and their requirements specifically in the uplink scenario, is not well established. Here, we model the effect of the atmosphere on link efficiency between an Earth station and a satellite using an optical uplink and how AO can help recover from loss due to turbulence. Examining both low Earth orbit and geostationary uplink scenarios, we find that a modest link transmissivity improvement of about 3 dB can be obtained in the case of a coaligned downward beacon, while the link can be dramatically improved, up to 7 dB, using an offset beacon, such as a laser guide star. AO coupled with a laser guide star would thus deliver a significant increase in the secret key generation rate of the QKD ground-to-space uplink system, especially as reductions of channel loss have a favourably nonlinear key-rate response within this high-loss regime.

Corresponding author: Thomas Jennewein, Institute for Quantum Computing, University of Waterloo, Waterloo, ON, N2L 3G1, Canada; and Department of Physics and Astronomy, University of Waterloo, Waterloo, ON, N2L 3G1, Canada, E-mail:

Funding source: Canadian Space Agency

Funding source: Industry Canada

Funding source: Province of Ontario

Funding source: NSERC Banting Postdoctoral Fellowships


C.J.P. thanks NSERC and the province of Ontario for funding. B.L.H. acknowledges support from NSERC Banting Postdoctoral Fellowships.

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: Canadian Space Agency, Canadian Institute for Advanced Research, Industry Canada, and the Natural Sciences and Engineering Research Council (NSERC).

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.


[1] N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys., vol. 74, pp. 145–195, 2002, in Google Scholar

[2] V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, et al., “The security of practical quantum key distribution,” Rev. Mod. Phys., vol. 81, pp. 1301–1350, 2009, in Google Scholar

[3] C. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” J. Cryptol., vol. 5, pp. 3–28, 1992, in Google Scholar

[4] J. D. Franson and H. Ilves, “Quantum cryptography using optical fiber,” Appl. Optic., vol. 33, pp. 2949–2954, 1994, in Google Scholar

[5] B. Korzh, C. C. W. Lim, R. Houlmann, et al., “Provably secure and practical quantum key distribution over 307 km of optical fibre,” Nat. Photon., vol. 9, pp. 163–168, 2015, in Google Scholar

[6] H.-L. Yin, T.-Y. Chen, Z.-W. Yu, et al., “Measurement-device-independent quantum key distribution over a 404 km optical fiber,” Phys. Rev. Lett., vol. 117, p. 190501, 2016. in Google Scholar

[7] M. Fürst, H. Weier, T. Schmitt-Manderbach, et al.,“Free-Space Quantum Key Distribution Over 144 km,” in Proc. SPIE, Advanced Free-Space Optical Communication Techniques/Applications II and Photonic Components/Architectures for Microwave Systems and Displays, Stockholm, Sweden, 2006, 6399, p. 63990G. in Google Scholar

[8] R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, et al., “Entanglement-based quantum communication over 144 km,” Nat. Phys., vol. 3, pp. 481–486, 2007, in Google Scholar

[9] J. E. Nordholt, R. J. Hughes, G. L. Morgan, C. G. Peterson, and C. C. Wipf, “Present and future free-space quantum key distribution,” in Proc. SPIE, Free-Space Laser Communication Technologies XIV SPIE, 2002, p. 4635.10.2172/790237Search in Google Scholar

[10] M. Aspelmeyer, T. Jennewein, M. Pfennigbauer, W. R. Leeb, and A. Zeilinger, “Long-distance quantum communication with entangled photons using satellites,” IEEE J. Sel. Top. Quant. Electron., vol. 9, pp. 1541–1551, 2003, in Google Scholar

[11] J. G. Rarity, P. M. Gorman, P. R. Knight, H. Weinfurter, and C. Kurtsiefer, “Quantum communications in space,” in Proc. SPIE, Quantum Communications and Quantum Imaging, 2004, p. 5161.10.1117/12.504744Search in Google Scholar

[12] J. M. Perdigues Armengol, B. Furch, C. Jacinto de Matos, et al., “Quantum communications at ESA: Towards a space experiment on the ISS,” Acta Astronaut., vol. 63, pp. 165–178, 2008, in Google Scholar

[13] T. Jennewein, J.-P. Bourgoin, B. Higgins, et al., “QEYSSAT: A mission proposal for a quantum receiver in space,” in Proc. SPIE, Advances in Photonics of Quantum Computing, Memory, and Communication VII, San Francisco, US, SPIE, 2014, 8997, p. 89970A. in Google Scholar

[14] R. Ursin, T. Jennewein, and A. Zeilinger, “Space-QUEST: Quantum physics and quantum communication in space,” in Proc. SPIE, Quantum Communications Realized II, San Francisco, US, SPIE, 2009, 7236, p. 723609. in Google Scholar

[15] W.-Q. Liao, S.-K. Cai, W.-Y. Liu, et al., “Satellite-to-ground quantum key distribution,” Nature, vol. 549, pp. 43–47, 2017, in Google Scholar

[16] S.-K. Liao, W.-Q. Cai, J. Handsteiner, et al., “Satellite-Relayed Intercontinental Quantum Network,” Phys. Rev. Lett., vol. 120, 2018, Art no. 030501. in Google Scholar

[17] R. Ursin, T. Jennewein, J. Kofler, et al., “Space-quest, experiments with quantum entanglement in space,” EuroPhys. News, vol. 40, pp. 26–29, 2009, in Google Scholar

[18] H. Xin, “Chinese academy takes space under its wing,” Science, vol. 332, p. 904, 2011, in Google Scholar

[19] H. Takenaka, M. Toyoshima, Y. Takayama, Y. Koyama, and M. Akioka,” in 2011 International Conference on Space Optical Systems and Applications, Santa Monica, USA, IEEE, 2011, pp. 113–116.Search in Google Scholar

[20] J.-P. Bourgoin, E. Meyer-Scott, B. L. Higgins, et al., “A comprehensive design and performance analysis of low Earth orbit satellite quantum communication,” New J. Phys., vol. 15, 2013, Art no. 023006, in Google Scholar

[21] L. Xin, Physics World Bristol UK: Physics World, 2016. in Google Scholar

[22] D. Vasylyev, W. Vogel, and F. Moll, “Satellite-mediated quantum atmospheric links,” Phys. Rev. A, vol. 99, 2019, Art no. 053830, in Google Scholar

[23] R. Tyson, Principles of Adaptive Optics, 3rd ed., Boca Raton, CRC Press, 2011.10.1201/EBK1439808580Search in Google Scholar

[24] R. W. Duffner, “Itea,” J. Test. Eval., vol. 29, pp. 341–346, 2008. in Google Scholar

[25] A. Roorda, “Adaptive optics for studying visual function: A comprehensive review,” J. Vis., vol. 11, 2011, in Google Scholar

[26] J. W. Armstrong, C. Yeh, and K. E. Wilson, “Earth-to-deep-space optical communications system with adaptive tilt and scintillation correction by use of near-Earth relay mirrors,” Opt. Lett., vol. 23, 1998, in Google Scholar

[27] C. Petit, N. Vedrenne, M.-T. Velluet, et al., “Investigation on adaptive optics performance from propagation channel characterization with the small optical transponder,” Opt. Eng., vol. 55, p. 111611, 2016, in Google Scholar

[28] M. Chen, C. Liu, D. Rui, and H. Xian, “Performance verification of adaptive optics for satellite-to-ground coherent optical communications at large zenith angle,” Opt. Express, vol. 26, pp. 4230–4242, 2018, in Google Scholar

[29] J. S. Bell, “On the Einstein Podolsky Rosen paradox,” Phys. Phys. Fiz., vol. 1, pp. 195–200, 1964, in Google Scholar

[30] M. Toyoshima, H. Takenaka, and Y. Takayama, “Atmospheric turbulence-induced fading channel model for space-to-ground laser communications links,” Opt. Express, vol. 19, pp. 15965–15975, 2011, in Google Scholar

[31] C. Erven, B. Heim, E. Meyer-Scott, et al., “Studying free-space transmission statistics and improving free-space quantum key distribution in the turbulent atmosphere,” New J. Phys., vol. 14, p. 123018, 2012, in Google Scholar

[32] M. T. Gruneisen, B. A. Sickmiller, M. B. Flanagan, et al., “Errata: Adaptive spatial filtering of daytime sky noise in a satellite quantum key distribution downlink receiver,” Opt. Eng., vol. 55, pp. 1–11, 2016, in Google Scholar

[33] M. T. Gruneisen, M. B. Flanagan, and B. A. Sickmiller, “Modeling satellite-Earth quantum channel downlinks with adaptive-optics coupling to single-mode fibers,” Opt. Eng., vol. 56, pp. 1–17, 2017. in Google Scholar

[34] M. D. Oliker, and M. T. Gruneisen, “How much value does adaptive optics add to a satellite QKD uplink?,” in Quantum Technologies and Quantum Information Science V, vol., 11167, International Society for Optics and Photonics (SPIE), 2019, pp. 10–19.10.1117/12.2537962Search in Google Scholar

[35] C. Pugh, “Free Space Quantum Key Distribution to Moving Platforms,” Ph.D. thesis, University of Waterloo, Waterloo, Canada, 2017.Search in Google Scholar

[36] M. Jeganathan, K. Wilson, and J. R. Lesh, “TDA Progress Report,” vol. 42, pp. 20–32, 1996.Search in Google Scholar

[37] D. L. Fried, “Statistics of a geometric representation of wavefront distortion,” J. Opt. Soc. Am., vol. 55, pp. 1427–1431, 1965, in Google Scholar

[38] R. E. Hufnagel, Digest of Topical Meeting on Optical Propagation Through Turbulence, OSA Technical Digest Series (Optical Society of America, Washinton, D.C.), OSA, 1974. WA1–1–WA1–4.Search in Google Scholar

[39] J. Hardy, Adaptive Optics for Astronomical Telescopes, Oxford, UK: Oxford University Press, 1998.Search in Google Scholar

[40] S. Chueca, B. Garcia-Lorenzo, E. G. Mendizabal, et al., “Input parameters of the HV model above Canarian observatories,” Proc. SPIE, Optics in Atmospheric Propagation and Adaptive Systems VI, Proc. SPIE, 2004, 5237.10.1117/12.511560Search in Google Scholar

[41] R. L. Fante, “Electromagnetic beam propagation in turbulent media,” Proc. IEEE, vol. 63, pp. 1669–1692, 1975, in Google Scholar

[42] H. T. Yura, “Short-term average optical-beam spread in a turbulent medium,” J. Opt. Soc. Am., vol. 63, pp. 567–572, 1973, in Google Scholar

[43] First Sensor, First Sensor PSD Data Sheet, THD, Germany, 2018, pp. DL400–DL407. in Google Scholar

[44] G. A. Tyler, “Bandwidth considerations for tracking through turbulence,” J. Opt. Soc. Am. A, vol. 11, pp. 358–367, 1994, in Google Scholar

[45] J. L. Bufton, “Comparison of vertical profile turbulence structure with stellar observations,” Appl. Optic., vol. 12, pp. 1785–1793, 1973, in Google Scholar

[46] J. L. M. Mohr, R. A. J. Johnston, and P. L. C. Cottrell, “Optical Turbulence measurements and models for Mount John University observatory,” Publ. Astron. Soc. Aust., vol. 27, pp. 347–359, 2010, in Google Scholar

[47] D. L. Fried, “Varieties Of Isoplanatism,” in Proc. SPIE, Imaging through the Atmosphere, Proc. SPIE, 1976, 0075.Search in Google Scholar

[48] S. S. Olivier, C. E. Max, D. T. Gavel, and J. M. Brase, “Tip-tilt compensation - Resolution limits for ground-based telescopes using laser guide star adaptive optics,” Astrophys. J., vol. 407, pp. 428–439, 1993, in Google Scholar

[49] V. N. Mahajan, “Strehl ratio for primary aberrations in terms of their aberration variance,” J. Opt. Soc. Am., vol. 73, pp. 860–861, 1983, in Google Scholar

[50] D. P. Greenwood, “Bandwidth specification for adaptive optics systems*,” J. Opt. Soc. Am., vol. 67, pp. 390–393, 1977, in Google Scholar

[51] F. von Zernike, “Beugungstheorie des schneidenver-fahrens und seiner verbesserten form, der phasenkontrastmethode,” Physica, vol. 1, pp. 689–704, 1934, in Google Scholar

[52] R. J. Noll, “Zernike polynomials and atmospheric turbulence*,” J. Opt. Soc. Am., vol. 66, pp. 207–211, 1976, in Google Scholar

[53] M. Tallon and R. Foy, “Adaptive telescope with laser probe: isoplanatism and cone effect,” Astron. Astrophys., vol. 235, pp. 549–557, 1990. in Google Scholar

[54] E. Meyer-Scott, Z. Yan, A. MacDonald, et al., “How to implement decoy-state quantum key distribution for a satellite uplink with 50-dB channel loss,” Phys. Rev. A, vol. 84, 2011, Art no. 062326, in Google Scholar

Received: 2020-05-14
Accepted: 2020-08-17
Published Online: 2019-09-16
Published in Print: 2020-11-26

© 2020 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 24.2.2024 from
Scroll to top button