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Analysis of atmospheric effects on satellite-based quantum communication: a comparative study

  • Vishal SharmaEmail author
  • Subhashish Banerjee
Article
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Abstract

Quantum key distribution (QKD) is a key exchange protocol which is implemented over free space optical links or optical fiber cable. When direct communication is not possible, QKD is performed over fiber cables, but the imperfections in detectors used at the receiver side and also the material properties of fiber cables limit the long-distance communication. Free space-based QKD is free from such limitations and can pave the way for satellite-based quantum communication to set up a global network for sharing secret messages. To implement free space optical links, it is essential to study the effect of atmospheric turbulence. Here, an analysis is made for satellite-based quantum communication using QKD protocols. We assume two specific attacks, namely PNS (photon number splitting) and IRUD (intercept-resend with unambiguous discrimination), which could be main threats for future QKD-based satellite applications. The key generation rates and the error rates of the considered QKD protocols are presented. Other parameters such as optimum signal and decoy states mean photon numbers are calculated for each protocol and distance. Further, in SARG04 QKD protocol with two decoy states, the optimum signal-state mean photon number is independent of the link distance and is valid for the attacks considered here. This is significant, highlighting its use in a realistic scenario of satellite quantum communication.

Keywords

Free space optics Geometric losses Quantum key distribution Quantum teleportation Satellite applications Space technology Total attenuation Turbulence 

Notes

Acknowledgements

VS would like to thank the Ministry of Human Resource Development, Govt. of India, for offering a doctoral fellowship as a Ph.D. research scholar at Indian Institute of Technology Jodhpur, Rajasthan, India. VS thanks, Professor K. K. Sharma for useful discussions pertaining to the work.

References

  1. 1.
    Bennett, C.H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. In: Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India, 10-19 December 1984, pp. 175–179 (1984)Google Scholar
  2. 2.
    Shenoy, A., Pathak, A., Srikanth, R.: Quantum cryptography: key distribution and beyond. Quanta 6, 1–47 (2017)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Scarani, V., Bechmann-Pasquinucci, H., Cerf, N.J., Dušek, M., Lütkenhaus, N., Peev, M.: The security of practical quantum key distribution. Rev. Mod. Phys. 81(3), 1301 (2009)ADSCrossRefGoogle Scholar
  4. 4.
    Srinatha, N., Omkar, S., Srikanth, R., Banerjee, S., Pathak, A.: The quantum cryptographic switch. Quantum Inf. Process. 13, 59–70 (2014)ADSCrossRefGoogle Scholar
  5. 5.
    Sangouard, N., Simon, C., De Riedmatten, H., Gisin, N.: Quantum repeaters based on atomic ensembles and linear optics. Rev. Mod. Phys. 83(1), 33 (2011)ADSCrossRefGoogle Scholar
  6. 6.
    Bussières, F., Sangouard, N., Afzelius, M., de Riedmatten, H., Simon, C., Tittel, W.: Prospective applications of optical quantum memories. J. Mod. Opt. 60(18), 1519–1537 (2013)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Guha, S., Krovi, H., Fuchs, C.A., Dutton, Z., Slater, J.A., Simon, C., Tittel, W.: Rate-loss analysis of an efficient quantum repeater architecture. Phys. Rev. A 92(2), 022357 (2015)ADSCrossRefGoogle Scholar
  8. 8.
    Munro, W.J., Stephens, A.M., Devitt, S.J., Harrison, K.A., Nemoto, K.: Quantum communication without the necessity of quantum memories. Nat. Photon. 6(11), 777–781 (2012)ADSCrossRefGoogle Scholar
  9. 9.
    Azuma, K., Tamaki, K., Lo, H.-K.: All-photonic quantum repeaters. Nat. Commun. 6, 6787 (2015)ADSCrossRefGoogle Scholar
  10. 10.
    Muralidharan, S., Kim, J., Lütkenhaus, N., Lukin, M.D., Jiang, L.: Ultrafast and fault-tolerant quantum communication across long distances. Phys. Rev. Lett. 112(25), 250501 (2014)ADSCrossRefGoogle Scholar
  11. 11.
    Boone, K., Bourgoin, J.-P., Meyer-Scott, E., Heshami, K., Jennewein, T., Simon, C.: Entanglement over global distances via quantum repeaters with satellite links. Phys. Rev. A 91(5), 052325 (2015)ADSCrossRefGoogle Scholar
  12. 12.
    Thapliyal, K., Pathak, A.: Applications of quantum cryptographic switch: various tasks related to controlled quantum communication can be performed using Bell states and permutation of particles. Quantum Inf. Process. 14(7), 2599–2616 (2015)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Pathak, A.: Elements of Quantum Computation and Quantum Communication. CRC Press, Boca Raton (2013)zbMATHGoogle Scholar
  14. 14.
    Shukla, C., Alam, N., Pathak, A.: Protocols of quantum key agreement solely using Bell states and Bell measurement. Quantum Inf. Process. 13(11), 2391–2405 (2014)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Schmitt-Manderbach, T., Weier, H., Fürst, M., Ursin, R., Tiefenbacher, F., Scheidl, T., Perdigues, J., Sodnik, Z., Kurtsiefer, C., Rarity, J.G., et al.: Experimental demonstration of free-space decoy-state quantum key distribution over 144 km. Phys. Rev. Lett. 98(1), 010504 (2007)ADSCrossRefGoogle Scholar
  16. 16.
    Lo, H.-K., Ma, X., Chen, K.: Decoy state quantum key distribution. Phys. Rev. Lett. 94(23), 230504 (2005)ADSCrossRefGoogle Scholar
  17. 17.
    Wang, X.-B.: Beating the photon-number-splitting attack in practical quantum cryptography. Phys. Rev. Lett. 94(23), 230503 (2005)ADSCrossRefGoogle Scholar
  18. 18.
    Ma, X., Qi, B., Zhao, Y., Lo, H.-K.: Practical decoy state for quantum key distribution. Phys. Rev. A 72(1), 012326 (2005)ADSCrossRefGoogle Scholar
  19. 19.
    Liu, Y., Chen, T.-Y., Wang, J., Cai, W.-Q., Wan, X., Chen, L.-K., Wang, J.-H., Liu, S.-B., Liang, H., Yang, L., et al.: Decoy-state quantum key distribution with polarized photons over 200 km. Opt. Express 18(8), 8587–8594 (2010)ADSCrossRefGoogle Scholar
  20. 20.
    Pugh, C.J., Kaiser, S., Bourgoin, J.-P., Jin, J., Sultana, N., Agne, S., Anisimova, E., Makarov, V., Choi, E., Higgins, B.L., et al.: Airborne demonstration of a quantum key distribution receiver payload. Quantum Sci. Technol. 2(2), 024009 (2017)ADSCrossRefGoogle Scholar
  21. 21.
    Liao, S.-K., Lin, J., Ren, J.-G., Liu, W.-Y., Qiang, J., Yin, J., Li, Y., Shen, Q., Zhang, L., Liang, X.-F., et al.: Space-to-ground quantum key distribution using a small-sized payload on tiangong-2 space lab. Chin. Phys. Lett. 34(9), 090302 (2017)ADSCrossRefGoogle Scholar
  22. 22.
    Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74(1), 145 (2002)ADSzbMATHCrossRefGoogle Scholar
  23. 23.
    Carbonneau, T.H., Wisely, D.R.: Opportunities and challenges for optical wireless: the competitive advantage of free space telecommunications links in today’s crowded marketplace. In: Voice, Video, and Data Communications, pp. 119–128. International Society for Optics and Photonics (1998)Google Scholar
  24. 24.
    Bennett, C.H., Bessette, F., Brassard, G., Salvail, L., Smolin, J.: Experimental quantum cryptography. J. Cryptol. 5(1), 3–28 (1992)zbMATHCrossRefGoogle Scholar
  25. 25.
    Zbinden, H., Gisin, N., Huttner, B., Muller, A., Tittel, W.: Practical aspects of quantum cryptographic key distribution. J. Cryptol. 13(2), 207–220 (2000)zbMATHCrossRefGoogle Scholar
  26. 26.
    Owens, P.C.M., Rarity, J.G., Tapster, P.R., Knight, D., Townsend, P.D.: Photon counting with passively quenched germanium avalanche. Appl. Opt. 33(30), 6895–6901 (1994)ADSCrossRefGoogle Scholar
  27. 27.
    Hughes, R.J., Nordholt, J.E., Derkacs, D., Peterson, C.G.: Practical free-space quantum key distribution over 10 km in daylight and at night. New J. Phys. 4(1), 43 (2002)ADSCrossRefGoogle Scholar
  28. 28.
    Resch, K.J., Lindenthal, M., Blauensteiner, B., Böhm, H.R., Fedrizzi, A., Kurtsiefer, C., Poppe, A., Schmitt-Manderbach, T., Taraba, M., Ursin, R., et al.: Distributing entanglement and single photons through an intra-city, free-space quantum channel. Opt. Express 13(1), 202–209 (2005)ADSCrossRefGoogle Scholar
  29. 29.
    Mayers, D.: Unconditional security in quantum cryptography. J. ACM (JACM) 48(3), 351–406 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  30. 30.
    Shields, A., Yuan, Z.: Key to the quantum industry. Phys. World 20(3), 24 (2007)CrossRefGoogle Scholar
  31. 31.
    Sharbaf, M.S.: Quantum cryptography: an emerging technology in network security. In: Technologies for Homeland Security (HST), 2011 IEEE International Conference on, pp. 13–19. IEEE (2011)Google Scholar
  32. 32.
    Buttler, W.T., Hughes, R.J., Kwiat, P.G., Lamoreaux, S.K., Luther, G.G., Morgan, G.L., Nordholt, J.E., Peterson, C.G., Simmons, C.M.: Practical free-space quantum key distribution over 1 km. Phys. Rev. Lett. 81(15), 3283 (1998)ADSzbMATHCrossRefGoogle Scholar
  33. 33.
    Kurtsiefer, C., Zarda, P., Halder, M., Gorman, P.M., Tapster, P.R., Rarity, J.G., Weinfurter, H.: Long-distance free-space quantum cryptography. In: Photonics Asia 2002, pp. 25–31. International Society for Optics and Photonics (2002)Google Scholar
  34. 34.
    Sharma, V.: Effect of noise on practical quantum communication systems. Def. Sci. J. 66(2), 186–192 (2016)CrossRefGoogle Scholar
  35. 35.
    Omkar, S., Srikanth, R., Banerjee, S.: Dissipative and non-dissipative single-qubit channels: dynamics and geometry. Quantum Inf. Process. 12(12), 3725–3744 (2013)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  36. 36.
    Sharma, V., Sharma, R.: Analysis of spread spectrum in MATLAB. Int. J. Sci. Eng. Res. 5(1), 1899–1902 (2014)Google Scholar
  37. 37.
    Bedington, R., Arrazola, J.M., Ling, A.: Progress in satellite quantum key distribution. NPJ Quantum Inf. 3(1), 30 (2017)ADSCrossRefGoogle Scholar
  38. 38.
    Sharma, V., Shrikant, U., Srikanth, R., Banerjee, S.: Decoherence can help quantum cryptographic security. Quantum Inf. Process. 17(8), 207 (2018)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  39. 39.
    Sharma, V., Banerjee, S.: Analysis of quantum key distribution based satellite communication. In: 2018 9th International Conference on Computing, Communication and Networking Technologies (ICCCNT), pp. 1–5. IEEE (2018)Google Scholar
  40. 40.
    Raj, A.B., Sharma, V., Banerjee, S.: Principles and Applications of Free Space Optical Communication, Chapter 19. ISBN: 978-1-78561-415-6. IET, UK (2018)Google Scholar
  41. 41.
    Khan, I., Heim, B., Neuzner, A., Marquardt, C.: Satellite-Based QKD. Opt. Photon. News Opt. Soc. Am. 29(2), 26–33 (2018)ADSCrossRefGoogle Scholar
  42. 42.
    Calderaro, L., Agnesi, C., Dequal, D., Vedovato, F., Schiavon, M., Santamato, A., Luceri, V., Bianco, G., Vallone, G., Villoresi, P.: Towards quantum communication from global navigation satellite system. ArXiv preprint arXiv:1804.05022 (2018)
  43. 43.
    Yin, J., Cao, Y., Li, Y.-H., Liao, S.-K., Zhang, L., Ren, J.-G., Cai, W.-Q., Liu, W.-Y., Li, B., Dai, H., et al.: Satellite-based entanglement distribution over 1200 kilometers. Science 356(6343), 1140–1144 (2017)CrossRefGoogle Scholar
  44. 44.
    Ren, J.-G., Xu, P., Yong, H.-L., Zhang, L., Liao, S.-K., Yin, J., Liu, W.-Y., Cai, W.-Q., Yang, M., Li, L., et al.: Ground-to-satellite quantum teleportation. Nature 549(7670), 70 (2017)ADSCrossRefGoogle Scholar
  45. 45.
    Liao, S.-K., Cai, W.-Q., Liu, W.-Y., Zhang, L., Li, Y., Ren, J.-G., Yin, J., Shen, Q., Cao, Y., Li, Z.-P., et al.: Satellite-to-ground quantum key distribution. Nature 549(7670), 43 (2017)ADSCrossRefGoogle Scholar
  46. 46.
    Liao, S.-K., Cai, W.-Q., Handsteiner, J., Liu, B., Yin, J., Zhang, L., Rauch, D., Fink, M., Ren, J.-G., Liu, W.-Y., et al.: Satellite-relayed intercontinental quantum network. Phys. Rev. Lett. 120(3), 030501 (2018)ADSCrossRefGoogle Scholar
  47. 47.
    Qi, B., Liu, S., Shen, Q., Liao, S., Cai, W., Lin, Z., Liu, W., Peng, C., An, Q.: A compact readout electronics for the ground station of a quantum communication satellite. IEEE Trans. Nucl. Sci. 62(3), 883–888 (2015)ADSCrossRefGoogle Scholar
  48. 48.
    Rarity, J.G., Tapster, P.R., Gorman, P.M., Knight, P.: Ground to satellite secure key exchange using quantum cryptography. New J. Phys. 4(1), 82 (2002)ADSCrossRefGoogle Scholar
  49. 49.
    Aspelmeyer, M., Jennewein, T., Pfennigbauer, M., Leeb, W.R., Zeilinger, A.: Long-distance quantum communication with entangled photons using satellites. IEEE J. Sel. Top. Quantum Electron. 9(6), 1541–1551 (2003)ADSCrossRefGoogle Scholar
  50. 50.
    Nordholt, J.E., Hughes, R.J., Morgan, G.L., Peterson, C.G., Wipf, C.C.: Present and future free-space quantum key distribution. In: Free-Space Laser Communication Technologies XIV, International Society for Optics and Photonics, vol. 4635, pp. 116–127 (2002)Google Scholar
  51. 51.
    Kurtsiefer, C., Zarda, P., Halder, M., Weinfurter, H., Gorman, P.M., Tapster, P.R., Rarity, J.G.: Quantum cryptography: a step towards global key distribution. Nature 419(6906), 450 (2002)ADSCrossRefGoogle Scholar
  52. 52.
    Hughes, R., Nordholt, J.E., Morgan, G.L., Peterson, C.G.: Free space quantum key distribution over 10 km in daylight and at night. In: Nonlinear Optics: Materials, Fundamentals and Applications. Optical Society of America, FA2 (2002)Google Scholar
  53. 53.
    Pfennigbauer, M., Aspelmeyer, M., Leeb, W., Baister, G., Dreischer, T., Jennewein, T., Neckamm, G., Perdigues, J., Weinfurter, H., Zeilinger, A.: Satellite-based quantum communication terminal employing state-of-the-art technology. J. Opt. Netw. 4(9), 549–560 (2005)CrossRefGoogle Scholar
  54. 54.
    Buttler, W.T., Hughes, R.J., Lamoreaux, S.K., Morgan, G.L., Nordholt, J.E., Peterson, C.G.: Daylight quantum key distribution over 1.6 km. Phys. Rev. Lett. 84(24), 5652 (2000)ADSCrossRefGoogle Scholar
  55. 55.
    Lindenthal, M., Resch, K.J., Blauensteiner, B., Boehm, H.R., Fedrizzi, A., Poppe, A., Taraba, M., et al.: Long-distance free-space distribution of quantum entanglement over Vienna (2005)Google Scholar
  56. 56.
    Fung, C.F., Tamaki, K., Qi, B., Lo, H.-K., Ma, X.: Security proof of quantum key distribution with detection efficiency mismatch. ArXiv preprint arXiv:0802.3788 (2008)
  57. 57.
    Toyoshima, M., Takayama, Y., Klaus, W., Kunimori, H., Fujiwara, M., Sasaki, M.: Free-space quantum cryptography with quantum and telecom communication channels. Acta Astronaut. 63(1–4), 179–184 (2008)ADSCrossRefGoogle Scholar
  58. 58.
    Toyoshima, M., Takayama, Y., Kunimori, H., Takeoka, M., Fujiwara, M., Sasaki, M.: Development of the polarization tracking scheme for free-space quantum cryptography. In: Atmospheric Propagation V, vol. 6951, p. 695101. International Society for Optics and Photonics (2008)Google Scholar
  59. 59.
    Toyoshima, M., Shoji, Y., Takayama, Y., Kunimori, H., Takeoka, M., Fujiwara, M., Sasaki, M.: Conceptual designs of onboard transceivers for ground-to-satellite quantum cryptography. In: Atmospheric Propagation VI, vol. 7324, p. 73240E. International Society for Optics and Photonics (2009)Google Scholar
  60. 60.
    Ursin, R., Tiefenbacher, F., Schmitt-Manderbach, T., Weier, H., Scheidl, T., Lindenthal, M., Blauensteiner, B., Jennewein, T., Perdigues, J., Trojek, P., et al.: Entanglement-based quantum communication over 144 km. Nat. Phys. 3(7), 481–486 (2007)CrossRefGoogle Scholar
  61. 61.
    Villoresi, P., Jennewein, T., Tamburini, F., Aspelmeyer, M., Bonato, C., Ursin, R., Pernechele, C., Luceri, V., Bianco, G., Zeilinger, A., et al.: Experimental verification of the feasibility of a quantum channel between space and Earth. New J. Phys. 10(3), 033038 (2008)ADSCrossRefGoogle Scholar
  62. 62.
    Wang, J.-Y., Yang, B., Liao, S.-K., Zhang, L., Shen, Q., Hu, X.-F., Wu, J.-C., Yang, S.-J., Jiang, H., Tang, Y.-L., et al.: Direct and full-scale experimental verifications towards ground-satellite quantum key distribution. Nat. Photon. 7(5), 387 (2013)ADSCrossRefGoogle Scholar
  63. 63.
    Hughes, R.J., Buttler, W.T., Kwiat, P.G., Lamoreuax, S.K., Morgan, G.L., Nordholt, J.E., Peterson, C.G.: Quantum cryptography for secure satellite communications. In: Aerospace Conference Proceedings, 2000 IEEE, vol. 1, pp. 191–200 (2000)Google Scholar
  64. 64.
    Hughes, R.J., Buttler, W.T., Lamoreaux, S.K., Morgan, G.L., Nordholt, J.E., Peterson, C.G., Kwiat, P.G.: Method and apparatus for free-space quantum key distribution in daylight. US Patent 6,748,083, Google Patents (2004)Google Scholar
  65. 65.
    Bourgoin, J.P., Meyer-Scott, E., Higgins, B.L., Helou, B., Erven, C., Huebel, H., Kumar, B., Hudson, D., D’Souza, I., Girard, R., et al.: A comprehensive design and performance analysis of low Earth orbit satellite quantum communication. New J. Phys. 15(2), 023006 (2013)ADSCrossRefGoogle Scholar
  66. 66.
    Hughes, R.J., Buttler, W.T., Kwiat, P.G., Luther, G.G., Morgan, G.L., Nordholt, J.E., Peterson, C.G., Simmons, C.M.: Secure communications with low-orbit spacecraft using quantum cryptography. US Patent 5,966,224, Google Patents (1999)Google Scholar
  67. 67.
    Nelson, E.A., O’meara, M.B.: System and method for communication between airborne and ground-based entities. US Patent 6,760,778, Google Patents (2004)Google Scholar
  68. 68.
    Peloso, M.P., Gerhardt, I., Ho, C., Lamas-Linares, A., Kurtsiefer, C.: Daylight operation of a free space, entanglement-based quantum key distribution system. New J. Phys. 11(4), 045007 (2009)ADSCrossRefGoogle Scholar
  69. 69.
    Teich, M.C., Saleh, B.: Fundamentals of Photonics, vol. 3. Wiley, Hoboken (1991)Google Scholar
  70. 70.
    Alda, J.: Laser and gaussian beam propagation and transformation. Encycl. Opt. Eng. 2013, 999–1013 (2003)Google Scholar
  71. 71.
    Klein, B.J., Degnan, J.J.: Optical antenna gain. 1: Transmitting antennas. Appl. Opt. 13(9), 2134–2141 (1974)ADSCrossRefGoogle Scholar
  72. 72.
    Degnan, J.J., Klein, B.J.: Optical antenna gain. 2: Receiving antennas. Appl. Opt. 13(10), 2397–2401 (1974)ADSCrossRefGoogle Scholar
  73. 73.
    Bloom, S., Korevaar, E., Schuster, J., Willebrand, H.: Understanding the performance of free-space optics. J. Opt. Netw. 2(6), 178–200 (2003)Google Scholar
  74. 74.
    Arnon, S.: Effects of atmospheric turbulence and building sway on optical wireless-communication systems. Opt. Lett. 28(2), 129–131 (2003)ADSCrossRefGoogle Scholar
  75. 75.
    Gabay, M., Arnon, S.: Quantum key distribution by a free-space mimo system. J. Lightwave Technol. 24(8), 3114–3120 (2006)ADSCrossRefGoogle Scholar
  76. 76.
    Hosseinidehaj, N., Malaney, R., Ng, S.X., Hanzo, L.: Satellite-based continuous-variable quantum communications: state-of-the-art and a predictive outlook. ArXiv preprint arXiv:1712.09722 (2017)
  77. 77.
    Gatenby, P.V., Grant, M.A.: Optical intersatellite links. Electron. Commun. Eng. J. 3(6), 280–288 (1991)CrossRefGoogle Scholar
  78. 78.
    Elterman, L.: Parameters for attenuation in the atmospheric windows for fifteen wavelengths. Appl. Opt. 3(6), 745–749 (1964)ADSCrossRefGoogle Scholar
  79. 79.
    Fuchs, C.A., Gisin, N., Griffiths, R.B., Niu, C.-S., Peres, A.: Optimal eavesdropping in quantum cryptography. I. Information bound and optimal strategy. Phys. Rev. A 56(2), 1163 (1997)ADSMathSciNetCrossRefGoogle Scholar
  80. 80.
    Bruß, D., Lütkenhaus, N.: Quantum key distribution: from principles to practicalities. Appl. Algebra Eng. Commun. Comput. 10(4), 383–399 (2000)MathSciNetzbMATHGoogle Scholar
  81. 81.
    Loudon, R.: The Quantum Theory of Light. Oxford University Press, Oxford (2000)zbMATHGoogle Scholar
  82. 82.
    Sharma, V., Shukla, C., Banerjee, S., Pathak, A.: Controlled bidirectional remote state preparation in noisy environment: a generalized view. Quantum Inf. Process. 14(9), 3441–3464 (2015)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  83. 83.
    Sharma, V., Thapliyal, K., Pathak, A., Banerjee, S.: A comparative study of protocols for secure quantum communication under noisy environment: single-qubit-based protocols versus entangled-state-based protocols. Quantum Inf. Process. 15(11), 4681–4710 (2016)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  84. 84.
    Cover, T.M., Thomas, J.A.: Elements of Information Theory, 2nd edn. Wiley, Hoboken (2006)zbMATHGoogle Scholar
  85. 85.
    Brassard, G., Crépeau, C.: Quantum cryptography. In: Encyclopedia of Cryptography and Security, pp. 495–500. Springer (2005)Google Scholar
  86. 86.
    Scarani, V., Acin, A., Ribordy, G., Gisin, N.: Quantum cryptography protocols robust against photon number splitting attacks for weak laser pulse implementations. Phys. Rev. Lett. 92(5), 057901 (2004)ADSCrossRefGoogle Scholar
  87. 87.
    Chefles, A.: Unambiguous discrimination between linearly independent quantum states. Phys. Lett. A 239(6), 339–347 (1998)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  88. 88.
    Acin, A., Gisin, N., Scarani, V.: Coherent-pulse implementations of quantum cryptography protocols resistant to photon-number-splitting attacks. Phys. Rev. A 69(1), 012309 (2004)ADSCrossRefGoogle Scholar
  89. 89.
    Tamaki, K., Lo, H.-K.: Unconditionally secure key distillation from multiphotons. Phys. Rev. A 73(1), 010302 (2006)ADSCrossRefGoogle Scholar
  90. 90.
    Hwang, W.-Y.: Quantum key distribution with high loss: toward global secure communication. Phys. Rev. Lett. 91(5), 057901 (2003)ADSCrossRefGoogle Scholar
  91. 91.
    Horikiri, T., Kobayashi, T.: Decoy state quantum key distribution with a photon number resolved heralded single photon source. Phys. Rev. A 73(3), 032331 (2006)ADSCrossRefGoogle Scholar
  92. 92.
    Meyer-Scott, E., Yan, Z., MacDonald, A., Bourgoin, J.-P., Hübel, H., Jennewein, T.: How to implement decoy-state quantum key distribution for a satellite uplink with 50-dB channel loss. Phys. Rev. A 84(6), 062326 (2011)ADSCrossRefGoogle Scholar
  93. 93.
    Gottesman, D., Lo, H.-K., Lutkenhaus, N., Preskill, J.: Security of quantum key distribution with imperfect devices. In: Information Theory, 2004. ISIT 2004. Proceedings. International Symposium on, p. 136. IEEE (2004)Google Scholar
  94. 94.
    Fung, C.-H.F., Tamaki, K., Lo, H.-K.: Performance of two quantum-key-distribution protocols. Phys. Rev. A 73(1), 012337 (2006)ADSCrossRefGoogle Scholar
  95. 95.
    Er-long, M., Zheng-fu, H., Shun-sheng, G., Tao, Z., Da-Sheng, Diao, Guang-Can, Guo: Background noise of satellite-to-ground quantum key distribution. New J. Phys. 7(1), 215 (2005)ADSCrossRefGoogle Scholar
  96. 96.
    Aviv, D.G.: Laser Space Communications. Artech House Publishers, Norwood (2006)Google Scholar
  97. 97.
    Ma, X., Fung, C.-H.F., Lo, H.-K.: Quantum key distribution with entangled photon sources. Phys. Rev. A 76(1), 012307 (2007)ADSCrossRefGoogle Scholar
  98. 98.
    Jeong, Y.-C., Kim, Y.-S., Kim, Y.-H.: Effects of depolarizing quantum channels on BB84 and SARG04 quantum cryptography protocols. Laser Phys. 21(8), 1438–1442 (2011)ADSCrossRefGoogle Scholar
  99. 99.
    Ali, S., Wahiddin, M.R.B.: Fiber and free-space practical decoy state QKD for both BB84 and SARG04 protocols. Eur. Phys. J. D 60(2), 405–410 (2010)ADSCrossRefGoogle Scholar
  100. 100.
    Zadok, A., Scheuer, J., Sendowski, J., Yariv, A.: Secure key generation using an ultra-long fiber laser: transient analysis and experiment. Opt. Express 16(21), 16680–16690 (2008)ADSCrossRefGoogle Scholar
  101. 101.
    Pelton, J.N.: The Basics of Satellite Communications. Intl Engineering Consortium, Chicago (2006)Google Scholar
  102. 102.
    Manning, T.: Microwave radio transmission design guide. Artech House, Norwood (2009)Google Scholar
  103. 103.
    Rappaport, T.S., MacCartney, G.R., Samimi, M.K., Sun, S.: Wideband millimeter-wave propagation measurements and channel models for future wireless communication system design. IEEE Trans. Commun. 63(9), 3029–3056 (2015)CrossRefGoogle Scholar
  104. 104.
    Rosen, HA: Satellite communications system employing frequency reuse. Google Patents, US Patent, 4,879,711, (1989)Google Scholar
  105. 105.
    Gilhousen, K.S., Jacobs, I.M., Weaver. Jr., L.A.: Spread spectrum multiple access communication system using satellite or terrestrial repeaters, Google Patents, US Patent, 4,901,307, (1990)Google Scholar
  106. 106.
    Wang, A.W.: Method and apparatus for providing wideband services using medium and low earth orbit satellites. Google Patents, US Patent, 7,627,284 (2009)Google Scholar
  107. 107.
    Pearson, J.E.: Atmospheric turbulence compensation using coherent optical adaptive techniques. Appl. Opt. 15(3), 622–631 (1976)ADSCrossRefGoogle Scholar
  108. 108.
    Kedar, D., Arnon, S.: Urban optical wireless communication networks: the main challenges and possible solutions. IEEE Commun. Mag. 42(5), S2–S7 (2004)CrossRefGoogle Scholar
  109. 109.
    Ricklin, J.C., Davidson, F.M.: Atmospheric turbulence effects on a partially coherent Gaussian beam: implications for free-space laser communication. JOSA A 19(9), 1794–1802 (2002)ADSCrossRefGoogle Scholar
  110. 110.
    Ellerbroek, B.L.: First-order performance evaluation of adaptive-optics systems for atmospheric-turbulence compensation in extended-field-of-view astronomical telescopes. JOSA A 11(2), 783–805 (1994)ADSCrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.IIT JodhpurJodhpurIndia

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