Abstract

Free space optical (FSO) communications are enabling high-speed global wireless networks. Thanks to the highly directional nature of laser beam, they also yield a greater security advantage over radio frequency counterparts. When combined with a scheme of secret key agreement (SKA), FSO-SKA can establish at high speed a symmetric secret key which cannot be decrypted even by unbounded computer resources. Although there have been many theoretical studies on SKA, experimental investigations have been quite lacking, especially on quantifying eavesdropping risks and secret key rates in realistic environment. Here, we report the first full-field implementations of FSO-SKA in a 7.8-km terrestrial link with a probing station, enabling the estimation of eavesdropping risks. We attain the final key rates from 100 kbps to 7.77 Mbps under various atmospheric and beaming conditions even with total losses of 55dB or higher, in which known quantum key distribution schemes attain impractically low key rates.

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

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S.-K. Liao, W.-Q. Cai, J. Handsteiner, B. Liu, J. Yin, L. Zhang, D. Rauch, M. Fink, J.-G. Ren, W.-Y. Liu, Y. Li, Q. Shen, Y. Cao, F.-Z. Li, J.-F. Wang, Y.-M. Huang, L. Deng, T. Xi, L. Ma, T. Hu, L. Li, N.-L. Liu, F. Koidl, P. Wang, Y.-A. Chen, X.-B. Wang, M. Steindorfer, G. Kirchner, C.-Y. Lu, R. Shu, R. Ursin, T. Scheidl, C.-Z. Peng, J.-Y. Wang, A. Zeilinger, and J.-W. Pan, “Satellite-relayed intercontinental quantum network,” Phys. Rev. Lett. 120(3), 030501 (2018).
[Crossref] [PubMed]

C. Chen, A. Grier, M. Malfa, E. Booen, H. Harding, C. Xia, M. Hunwardsen, J. Demers, K. Kudinov, G. Mak, B. Smith, A. Sahasrabudhe, F. Patawaran, T. Wang, A. Wang, C. Zhao, D. Leang, J. Gin, M. Lewis, B. Zhang, D. Nguyen, D. Jandrain, F. Haque, and K. Quirk, “Demonstration of a bidirectional coherent air-to-ground optical link,” Proc. SPIE 10524, 105240G (2018).

K. Suzuki, D. Kolev, A. C. Casado, and M. Toyoshima, “Environmental-data collection system for satellite-to-ground optical communications,” Trans. JSASS Aerosp. Tech. Jpn. 16(1), 35–39 (2018). The data from OBSOC are available on http://sstg.nict.go.jp/OBSOC/?lang=e .
[Crossref]

M. Fujiwara, T. Ito, M. Kitamura, H. Endo, O. Tsuzuki, M. Toyoshima, H. Takenaka, Y. Takayama, R. Shimizu, M. Takeoka, R. Matsumoto, and M. Sasaki, “Free-space optical wiretap channel and experimental secret key agreement in 7.8 km terrestrial link,” Opt. Express 26(15), 19513–19523 (2018).
[Crossref]

2017 (10)

K. Günthner, I. Khan, D. Elser, B. Stiller, Ömer Bayraktar, C. R. Müller, K. Saucke, D. Tröndle, F. Heine, S. Seel, P. Greulich, H. Zech, B. Gütlich, S. Philipp-May, C. Marquardt, and G. Leuchs, “Quantum-limited measurements of optical signals from a geostationary satellite,” Optica 4(6), 611–616 (2017).
[Crossref]

M. Sasaki, H. Endo, M. Fujiwara, M. Kitamura, T. Ito, R. Shimizu, and M. Toyoshima, “Quantum photonic network and physical layer security,” Philos. Trans. R. Soc. Lond. A 375(2099), 20160243 (2017).
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H. Takenaka, A. Carrasco-Casado, M. Fujiwara, M. Kitamura, M. Sasaki, and M. Toyoshima, “Satellite-to-ground quantum-limited communication using a 50-kg-class microsatellite,” Nat. Photon. 11502 (2017).
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S. Pirandola, R. Laurenza, C. Ottaviani, and L. Banchi, “Fundamental limits of repeaterless quantum communications,” Nat. Commun. 8, 15043 (2017).
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C. J. Pugh, S. Kaiser, J.-P. Bourgoin, J. Jin, N. Sultana, S. Agne, E. Anisimova, V. Makarov, E. Choi, B. L. Higgins, and T. Jennewein, “Airborne demonstration of a quantum key distribution receiver payload,” Quantum Sci. Technol. 2(2), 024009 (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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S.-K. Liao, H.-L. Yong, C. Liu, G.-L. Shentu, D.-D. Li, J. Lin, H. Dai, S.-Q. Zhao, B. Li, J.-Y. Guan, W. Chen, Y.-H. Gong, Y. Li, Z.-H. Lin, G.-S. Pan, J. S. Pelc, M. M. Fejer, W.-Z. Zhang, W.-Y. Liu, J. Yin, J.-G. Ren, X.-B. Wang, Q. Zhang, C.-Z. Peng, and J.-W. Pan, “Long-distance free-space quantum key distribution in daylight towards inter-satellite communication,” Nat. Photon. 11, 509 (2017).
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J. Yin, Y. Cao, Y.-H. Li, J.-G. Ren, S.-K. Liao, L. Zhang, W.-Q. Cai, W.-Y. Liu, B. Li, H. Dai, M. Li, Y.-M. Huang, L. Deng, L. Li, Q. Zhang, N.-L. Liu, Y.-A. Chen, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground entanglement-based quantum key distribution,” Phys. Rev. Lett. 119(20), 200501 (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, 43 (2017).
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2016 (5)

R. Courtland, “China’s 2,000-km quantum link is almost complete [news],” IEEE Spectr. 53(11), 11–12 (2016).

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J. Zhang, R. Woods, T. Q. Duong, A. Marshall, Y. Ding, Y. Huang, and Q. Xu, “Experimental study on key generation for physical layer security in wireless communications,” IEEE Access 4, 4464–4477 (2016).
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H. Endo, M. Fujiwara, M. Kitamura, T. Ito, M. Toyoshima, Y. Takayama, H. Takenaka, R. Shimizu, N. Laurenti, G. Vallone, P. Villoresi, T. Aoki, and M. Sasaki, “Free-space optical channel estimation for physical layer security,” Opt. Express 24(8), 8940–8955 (2016).
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2015 (6)

W. S. Rabinovich, C. I. Moore, R. Mahon, P. G. Goetz, H. R. Burris, M. S. Ferraro, J. L. Murphy, L. M. Thomas, G. C. Gilbreath, M. Vilcheck, and M. R. Suite, “Free-space optical communications research and demonstrations at the U.S Naval Research Laboratory,” Appl. Opt. 54(31), F189–F200 (2015).
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J.-P. Bourgoin, B. L. Higgins, N. Gigov, C. Holloway, C. J. Pugh, S. Kaiser, M. Cranmer, and T. Jennewein, “Free-space quantum key distribution to a moving receiver,” Opt. Express 23(26), 33437–33447 (2015).
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H. Endo, T. S. Han, T. Aoki, and M. Sasaki, “Numerical study on secrecy capacity and code length dependence of the performances in optical wiretap channels,” IEEE Photon. J. 7(5), 7903418 (2015).
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F. J. Lopez-Martinez, G. Gomez, and J. M. Garrido-Balsells, “Physical-layer security in free-space optical communications,” IEEE Photon. J. 7(2), 7901014 (2015).
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K. Zeng, “Physical layer key generation in wireless networks: challenges and opportunities,” IEEE Commun. Mag. 53(6), 33–39 (2015).
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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).
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2014 (1)

M. Takeoka, S. Guha, and M. M. Wilde, “Fundamental rate-loss tradeoff for optical quantum key distribution,” Nat. Commun. 5, 5235 (2014).
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2013 (4)

J. Yin, Y. Cao, S.-B. Liu, G.-S. Pan, J.-H. Wang, T. Yang, Z.-P. Zhang, F.-M. Yang, Y.-A. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental quasi-single-photon transmission from satellite to earth,” Opt. Express 21(17), 20032–20040 (2013).
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S. N. Premnath, S. Jana, J. Croft, P. L. Gowda, M. Clark, S. K. Kasera, N. Patwari, and S. V. Krishnamurthy, “Secret key extraction from wireless signal strength in real environments,” IEEE Trans. Mob. Comput. 12(5), 917–930 (2013).
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J.-Y. Wang, B. Yang, S.-K. Liao, L. Zhang, Q. Shen, X.-F. Hu, J.-C. Wu, S.-J. Yang, H. Jiang, Y.-L. Tang, B. Zhong, H. Liang, W.-Y. Liu, Y.-H. Hu, Y.-M. Huang, B. Qi, J.-G. Ren, G.-S. Pan, J. Yin, J.-J. Jia, Y.-A. Chen, K. Chen, C.-Z. Peng, and J.-W. Pan, “Direct and full-scale experimental verifications towards ground-satellite quantum key distribution,” Nat. Photon. 7, 387 (2013).
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S. Nauerth, F. Moll, M. Rau, C. Fuchs, J. Horwath, S. Frick, and H. Weinfurter, “Air-to-ground quantum communication,” Nat. Photon. 7, 382 (2013).
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2012 (2)

M. Toyoshima, H. Takenaka, Y. Shoji, Y. Takayama, Y. Koyama, and H. Kunimori, “Results of Kirari optical communication demonstration experiments with NICT optical ground station (KODEN) aiming for future classical and quantum communications in space,” Acta. Astronaut. 74, 40–49 (2012).
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J. Yin, J.-G. Ren, H. Lu, Y. Cao, H.-L. Yong, Y.-P. Wu, C. Liu, S.-K. Liao, F. Zhou, Y. Jiang, X.-D. Cai, P. Xu, G.-S. Pan, J.-J. Jia, Y.-M. Huang, H. Yin, J.-Y. Wang, Y.-A. Chen, C.-Z. Peng, and J.-W. Pan, “Quantum teleportation and entanglement distribution over 100-kilometre free-space channels,” Nature 488, 185 (2012).
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2011 (1)

2009 (1)

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys. 11, 075001 (2009).
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2008 (1)

P. Villoresi, T. Jennewein, F. Tamburini, M. Aspelmeyer, C. Bonato, R. Ursin, C. Pernechele, V. Luceri, G. Bianco, A. Zeilinger, and C. Barbieri, “Experimental verification of the feasibility of a quantum channel between space and earth,” New J. Phys. 10(3), 033038 (2008).
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2007 (3)

R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Ömer, M. Fürst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Entanglement-based quantum communication over 144 km,” Nat. Phys. 3, 481 (2007).
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T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurtsiefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98(1), 010504 (2007).
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T. Jono, Y. Takayama, K. Shiratama, I. Mase, B. Demelenne, Z. Sodnik, A. Bird, M. Toyoshima, H. Kunimori, D. Giggenbach, N. Perlot, M. Knapek, and K. Arai, “Overview of the inter-orbit and the orbit-to-ground laser communication demonstration by OICETS,” Proc. SPIE 6457, 645702 (2007).
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2005 (2)

T. Aono, K. Higuchi, T. Ohira, B. Komiyama, and H. Sasaoka, “Wireless secret key generation exploiting reactance-domain scalar response of multipath fading channels,” IEEE Trans. Antennas Propag. 53(11), 3776–3784 (2005).
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C.-Z. Peng, T. Yang, X.-H. Bao, J. Zhang, X.-M. Jin, F.-Y. Feng, B. Yang, J. Yang, J. Yin, Q. Zhang, N. Li, B.-L. Tian, and J.-W. Pan, “Experimental free-space distribution of entangled photon pairs over 13 km: Towards satellite-based global quantum communication,” Phys. Rev. Lett. 94(15), 150501 (2005).
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2003 (1)

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using gaussian-modulated coherent states,” Nature 421, 238–242 (2003).
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2002 (5)

V. Ramasarma, “Free space optics: A viable last-mile solution,” Bechtel Telecommun. Tech. J. 1, 22–30 (2002).

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J. E. Nordholt, R. J. Hughes, G. L. Morgan, C. G. Peterson, and C. C. Wipf, “Present and future free-space quantum key distribution,” Proc. SPIE 4635, 116–126 (2002).
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R. J. Hughes, J. E. Nordholt, D. Derkacs, and C. G. Peterson, “Practical free-space quantum key distribution over 10 km in daylight and at night,” New J. Phys. 4, 43 (2002).
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A. Acampora, “Last mile by laser,” Sci. Am. 287(1), 32–37 (2002).
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1998 (1)

R. Sridharan and A. F. Pa, “U. S. space surveillance network capabilities,” Proc. SPIE 3434, 88–100 (1998).
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1995 (1)

C. H. Bennett, G. Brassard, C. Crepeau, and U. M. Maurer, “Generalized privacy amplification,” IEEE Trans. Inf. Theory 41(6), 1915–1923 (1995).
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1994 (1)

G. Brassard and L. Salvail, “Secret key reconciliation by public discussion,” Lect. Notes Comput. Sci. 765, 410–423 (1994).
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1993 (2)

U. M. Maurer, “Secret key agreement by public discussion from common information,” IEEE Trans. Inf. Theory 39(3), 733–742 (1993).
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1991 (1)

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67(6), 661–663 (1991).
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1988 (1)

C. H. Bennett, G. Brassard, and J. M. Robert, “Privacy amplification by public discussion,” SIAM J. Comput. 17(2), 210–229 (1988).
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1979 (1)

J. L. Carter and M. N. Wegman, “Universal classes of hash functions,” J. Comput. Syst. Sci. 18(2), 143–154 (1979).
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1978 (1)

I. Csiszár and J. Körner, “Broadcast channels with confidential messages,” IEEE Trans. Inf. Theory 24(3), 339–348 (1978).
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1975 (1)

A. D. Shannon, “The wire-tap channel,” Bell Syst. Tech. J. 54(8), 1355–1387 (1975).
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1949 (1)

C. E. Shannon, “Communication theory of secrecy systems,” Bell Labs Tech. J. 28(4), 656–715 (1949).
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1926 (1)

G. S. Vernam, “Cipher printing telegraph systems for secret wire and radio telegraphic communications,” Trans. Am. Inst. Electr. Eng XLV, 295–301 (1926).
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Acampora, A.

A. Acampora, “Last mile by laser,” Sci. Am. 287(1), 32–37 (2002).
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Agne, S.

C. J. Pugh, S. Kaiser, J.-P. Bourgoin, J. Jin, N. Sultana, S. Agne, E. Anisimova, V. Makarov, E. Choi, B. L. Higgins, and T. Jennewein, “Airborne demonstration of a quantum key distribution receiver payload,” Quantum Sci. Technol. 2(2), 024009 (2017).
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Ahlswede, R.

R. Ahlswede and I. Csiszar, “Common randomness in information theory and cryptography. I. secret sharing,” IEEE Trans. Inf. Theory 39(4), 1121–1132 (1993).
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Allacher, A.

Alléaume, R.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys. 11, 075001 (2009).
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Anisimova, E.

C. J. Pugh, S. Kaiser, J.-P. Bourgoin, J. Jin, N. Sultana, S. Agne, E. Anisimova, V. Makarov, E. Choi, B. L. Higgins, and T. Jennewein, “Airborne demonstration of a quantum key distribution receiver payload,” Quantum Sci. Technol. 2(2), 024009 (2017).
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Aoki, T.

H. Endo, M. Fujiwara, M. Kitamura, T. Ito, M. Toyoshima, Y. Takayama, H. Takenaka, R. Shimizu, N. Laurenti, G. Vallone, P. Villoresi, T. Aoki, and M. Sasaki, “Free-space optical channel estimation for physical layer security,” Opt. Express 24(8), 8940–8955 (2016).
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H. Endo, T. S. Han, T. Aoki, and M. Sasaki, “Numerical study on secrecy capacity and code length dependence of the performances in optical wiretap channels,” IEEE Photon. J. 7(5), 7903418 (2015).
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Aono, T.

T. Aono, K. Higuchi, T. Ohira, B. Komiyama, and H. Sasaoka, “Wireless secret key generation exploiting reactance-domain scalar response of multipath fading channels,” IEEE Trans. Antennas Propag. 53(11), 3776–3784 (2005).
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Arai, K.

T. Jono, Y. Takayama, K. Shiratama, I. Mase, B. Demelenne, Z. Sodnik, A. Bird, M. Toyoshima, H. Kunimori, D. Giggenbach, N. Perlot, M. Knapek, and K. Arai, “Overview of the inter-orbit and the orbit-to-ground laser communication demonstration by OICETS,” Proc. SPIE 6457, 645702 (2007).
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Asai, T.

Aspelmeyer, M.

P. Villoresi, T. Jennewein, F. Tamburini, M. Aspelmeyer, C. Bonato, R. Ursin, C. Pernechele, V. Luceri, G. Bianco, A. Zeilinger, and C. Barbieri, “Experimental verification of the feasibility of a quantum channel between space and earth,” New J. Phys. 10(3), 033038 (2008).
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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).
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Banchi, L.

S. Pirandola, R. Laurenza, C. Ottaviani, and L. Banchi, “Fundamental limits of repeaterless quantum communications,” Nat. Commun. 8, 15043 (2017).
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Banks, D. L.

L. E. Bassham, A. L. Rukhin, J. Soto, J. R. Nechvatal, M. E. Smid, S. D. Leigh, M. Levenson, M. Vangel, N. A. Heckert, and D. L. Banks, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Special Publication 800-22 Rev. 1a.

Bao, X.-H.

C.-Z. Peng, T. Yang, X.-H. Bao, J. Zhang, X.-M. Jin, F.-Y. Feng, B. Yang, J. Yang, J. Yin, Q. Zhang, N. Li, B.-L. Tian, and J.-W. Pan, “Experimental free-space distribution of entangled photon pairs over 13 km: Towards satellite-based global quantum communication,” Phys. Rev. Lett. 94(15), 150501 (2005).
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Barbieri, C.

P. Villoresi, T. Jennewein, F. Tamburini, M. Aspelmeyer, C. Bonato, R. Ursin, C. Pernechele, V. Luceri, G. Bianco, A. Zeilinger, and C. Barbieri, “Experimental verification of the feasibility of a quantum channel between space and earth,” New J. Phys. 10(3), 033038 (2008).
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R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Ömer, M. Fürst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Entanglement-based quantum communication over 144 km,” Nat. Phys. 3, 481 (2007).
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Barreiro, C.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys. 11, 075001 (2009).
[Crossref]

Barros, J.

M. Bloch and J. Barros, Physical-Layer Security: From Information Theory to Security Engineering (Cambridge University, 2011).
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Bassham, L. E.

L. E. Bassham, A. L. Rukhin, J. Soto, J. R. Nechvatal, M. E. Smid, S. D. Leigh, M. Levenson, M. Vangel, N. A. Heckert, and D. L. Banks, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Special Publication 800-22 Rev. 1a.

Bayraktar, Ömer

Bennett, C. H.

C. H. Bennett, G. Brassard, C. Crepeau, and U. M. Maurer, “Generalized privacy amplification,” IEEE Trans. Inf. Theory 41(6), 1915–1923 (1995).
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C. H. Bennett, G. Brassard, and J. M. Robert, “Privacy amplification by public discussion,” SIAM J. Comput. 17(2), 210–229 (1988).
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C. H. Bennett and G. Brassard, “Quantum cryptography: public-key distribution and coin tossing,” in Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, (IEEE, 1984), pp. 175–179.

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]

P. Villoresi, T. Jennewein, F. Tamburini, M. Aspelmeyer, C. Bonato, R. Ursin, C. Pernechele, V. Luceri, G. Bianco, A. Zeilinger, and C. Barbieri, “Experimental verification of the feasibility of a quantum channel between space and earth,” New J. Phys. 10(3), 033038 (2008).
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Bird, A.

T. Jono, Y. Takayama, K. Shiratama, I. Mase, B. Demelenne, Z. Sodnik, A. Bird, M. Toyoshima, H. Kunimori, D. Giggenbach, N. Perlot, M. Knapek, and K. Arai, “Overview of the inter-orbit and the orbit-to-ground laser communication demonstration by OICETS,” Proc. SPIE 6457, 645702 (2007).
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Blauensteiner, B.

R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Ömer, M. Fürst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Entanglement-based quantum communication over 144 km,” Nat. Phys. 3, 481 (2007).
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Bloch, M.

M. Bloch and J. Barros, Physical-Layer Security: From Information Theory to Security Engineering (Cambridge University, 2011).
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Bock, R.

L. Li, R. Zhang, Z. Zhao, G. Xie, P. Liao, K. Pang, H. Song, C. Liu, Y. Ren, G. Labroille, P. Jian, D. Starodubov, B. Lynn, R. Bock, M. Tur, and A. E. Willner, “High-capacity free-space optical communications between a ground transmitter and a ground receiver via a UAV using multiplexing of multiple orbital-angular-momentum beams,” Sci. Rep. 7(1), 17427 (2017).
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Li, L.

S.-K. Liao, W.-Q. Cai, J. Handsteiner, B. Liu, J. Yin, L. Zhang, D. Rauch, M. Fink, J.-G. Ren, W.-Y. Liu, Y. Li, Q. Shen, Y. Cao, F.-Z. Li, J.-F. Wang, Y.-M. Huang, L. Deng, T. Xi, L. Ma, T. Hu, L. Li, N.-L. Liu, F. Koidl, P. Wang, Y.-A. Chen, X.-B. Wang, M. Steindorfer, G. Kirchner, C.-Y. Lu, R. Shu, R. Ursin, T. Scheidl, C.-Z. Peng, J.-Y. Wang, A. Zeilinger, and J.-W. Pan, “Satellite-relayed intercontinental quantum network,” Phys. Rev. Lett. 120(3), 030501 (2018).
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R. J. Hughes, J. E. Nordholt, D. Derkacs, and C. G. Peterson, “Practical free-space quantum key distribution over 10 km in daylight and at night,” New J. Phys. 4, 43 (2002).
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Ogata, W.

M. Fujiwara, A. Waseda, R. Nojima, S. Moriai, W. Ogata, and M. Sasaki, “Unbreakable distributed storage with quantum key distribution network and password-authenticated secret sharing,” Sci. Rep. 6, 28988 (2016).
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R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Ömer, M. Fürst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Entanglement-based quantum communication over 144 km,” Nat. Phys. 3, 481 (2007).
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Ottaviani, C.

S. Pirandola, R. Laurenza, C. Ottaviani, and L. Banchi, “Fundamental limits of repeaterless quantum communications,” Nat. Commun. 8, 15043 (2017).
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R. Sridharan and A. F. Pa, “U. S. space surveillance network capabilities,” Proc. SPIE 3434, 88–100 (1998).
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M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys. 11, 075001 (2009).
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Page, J.-B.

M. Sasaki, M. Fujiwara, H. Ishizuka, W. Klaus, K. Wakui, M. Takeoka, S. Miki, T. Yamashita, Z. Wang, A. Tanaka, K. Yoshino, Y. Nambu, S. Takahashi, A. Tajima, A. Tomita, T. Domeki, T. Hasegawa, Y. Sakai, H. Kobayashi, T. Asai, K. Shimizu, T. Tokura, T. Tsurumaru, M. Matsui, T. Honjo, K. Tamaki, H. Takesue, Y. Tokura, J. F. Dynes, A. R. Dixon, A. W. Sharpe, Z. L. Yuan, A. J. Shields, S. Uchikoga, M. Legré, S. Robyr, P. Trinkler, L. Monat, J.-B. Page, G. Ribordy, A. Poppe, A. Allacher, O. Maurhart, T. Länger, M. Peev, and A. Zeilinger, “Field test of quantum key distribution in the Tokyo QKD Network,” Opt. Express 19(11), 10387–10409 (2011).
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Pan, G.-S.

S.-K. Liao, H.-L. Yong, C. Liu, G.-L. Shentu, D.-D. Li, J. Lin, H. Dai, S.-Q. Zhao, B. Li, J.-Y. Guan, W. Chen, Y.-H. Gong, Y. Li, Z.-H. Lin, G.-S. Pan, J. S. Pelc, M. M. Fejer, W.-Z. Zhang, W.-Y. Liu, J. Yin, J.-G. Ren, X.-B. Wang, Q. Zhang, C.-Z. Peng, and J.-W. Pan, “Long-distance free-space quantum key distribution in daylight towards inter-satellite communication,” Nat. Photon. 11, 509 (2017).
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J. Yin, Y. Cao, S.-B. Liu, G.-S. Pan, J.-H. Wang, T. Yang, Z.-P. Zhang, F.-M. Yang, Y.-A. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental quasi-single-photon transmission from satellite to earth,” Opt. Express 21(17), 20032–20040 (2013).
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J.-Y. Wang, B. Yang, S.-K. Liao, L. Zhang, Q. Shen, X.-F. Hu, J.-C. Wu, S.-J. Yang, H. Jiang, Y.-L. Tang, B. Zhong, H. Liang, W.-Y. Liu, Y.-H. Hu, Y.-M. Huang, B. Qi, J.-G. Ren, G.-S. Pan, J. Yin, J.-J. Jia, Y.-A. Chen, K. Chen, C.-Z. Peng, and J.-W. Pan, “Direct and full-scale experimental verifications towards ground-satellite quantum key distribution,” Nat. Photon. 7, 387 (2013).
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J. Yin, J.-G. Ren, H. Lu, Y. Cao, H.-L. Yong, Y.-P. Wu, C. Liu, S.-K. Liao, F. Zhou, Y. Jiang, X.-D. Cai, P. Xu, G.-S. Pan, J.-J. Jia, Y.-M. Huang, H. Yin, J.-Y. Wang, Y.-A. Chen, C.-Z. Peng, and J.-W. Pan, “Quantum teleportation and entanglement distribution over 100-kilometre free-space channels,” Nature 488, 185 (2012).
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Pan, J.-W.

S.-K. Liao, W.-Q. Cai, J. Handsteiner, B. Liu, J. Yin, L. Zhang, D. Rauch, M. Fink, J.-G. Ren, W.-Y. Liu, Y. Li, Q. Shen, Y. Cao, F.-Z. Li, J.-F. Wang, Y.-M. Huang, L. Deng, T. Xi, L. Ma, T. Hu, L. Li, N.-L. Liu, F. Koidl, P. Wang, Y.-A. Chen, X.-B. Wang, M. Steindorfer, G. Kirchner, C.-Y. Lu, R. Shu, R. Ursin, T. Scheidl, C.-Z. Peng, J.-Y. Wang, A. Zeilinger, and J.-W. Pan, “Satellite-relayed intercontinental quantum network,” Phys. Rev. Lett. 120(3), 030501 (2018).
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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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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, 43 (2017).
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J. Yin, Y. Cao, Y.-H. Li, J.-G. Ren, S.-K. Liao, L. Zhang, W.-Q. Cai, W.-Y. Liu, B. Li, H. Dai, M. Li, Y.-M. Huang, L. Deng, L. Li, Q. Zhang, N.-L. Liu, Y.-A. Chen, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground entanglement-based quantum key distribution,” Phys. Rev. Lett. 119(20), 200501 (2017).
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S.-K. Liao, H.-L. Yong, C. Liu, G.-L. Shentu, D.-D. Li, J. Lin, H. Dai, S.-Q. Zhao, B. Li, J.-Y. Guan, W. Chen, Y.-H. Gong, Y. Li, Z.-H. Lin, G.-S. Pan, J. S. Pelc, M. M. Fejer, W.-Z. Zhang, W.-Y. Liu, J. Yin, J.-G. Ren, X.-B. Wang, Q. Zhang, C.-Z. Peng, and J.-W. Pan, “Long-distance free-space quantum key distribution in daylight towards inter-satellite communication,” Nat. Photon. 11, 509 (2017).
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J.-Y. Wang, B. Yang, S.-K. Liao, L. Zhang, Q. Shen, X.-F. Hu, J.-C. Wu, S.-J. Yang, H. Jiang, Y.-L. Tang, B. Zhong, H. Liang, W.-Y. Liu, Y.-H. Hu, Y.-M. Huang, B. Qi, J.-G. Ren, G.-S. Pan, J. Yin, J.-J. Jia, Y.-A. Chen, K. Chen, C.-Z. Peng, and J.-W. Pan, “Direct and full-scale experimental verifications towards ground-satellite quantum key distribution,” Nat. Photon. 7, 387 (2013).
[Crossref]

J. Yin, Y. Cao, S.-B. Liu, G.-S. Pan, J.-H. Wang, T. Yang, Z.-P. Zhang, F.-M. Yang, Y.-A. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental quasi-single-photon transmission from satellite to earth,” Opt. Express 21(17), 20032–20040 (2013).
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J. Yin, J.-G. Ren, H. Lu, Y. Cao, H.-L. Yong, Y.-P. Wu, C. Liu, S.-K. Liao, F. Zhou, Y. Jiang, X.-D. Cai, P. Xu, G.-S. Pan, J.-J. Jia, Y.-M. Huang, H. Yin, J.-Y. Wang, Y.-A. Chen, C.-Z. Peng, and J.-W. Pan, “Quantum teleportation and entanglement distribution over 100-kilometre free-space channels,” Nature 488, 185 (2012).
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C.-Z. Peng, T. Yang, X.-H. Bao, J. Zhang, X.-M. Jin, F.-Y. Feng, B. Yang, J. Yang, J. Yin, Q. Zhang, N. Li, B.-L. Tian, and J.-W. Pan, “Experimental free-space distribution of entangled photon pairs over 13 km: Towards satellite-based global quantum communication,” Phys. Rev. Lett. 94(15), 150501 (2005).
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Pang, K.

L. Li, R. Zhang, Z. Zhao, G. Xie, P. Liao, K. Pang, H. Song, C. Liu, Y. Ren, G. Labroille, P. Jian, D. Starodubov, B. Lynn, R. Bock, M. Tur, and A. E. Willner, “High-capacity free-space optical communications between a ground transmitter and a ground receiver via a UAV using multiplexing of multiple orbital-angular-momentum beams,” Sci. Rep. 7(1), 17427 (2017).
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Patwari, N.

S. N. Premnath, S. Jana, J. Croft, P. L. Gowda, M. Clark, S. K. Kasera, N. Patwari, and S. V. Krishnamurthy, “Secret key extraction from wireless signal strength in real environments,” IEEE Trans. Mob. Comput. 12(5), 917–930 (2013).
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Peev, M.

M. Sasaki, M. Fujiwara, H. Ishizuka, W. Klaus, K. Wakui, M. Takeoka, S. Miki, T. Yamashita, Z. Wang, A. Tanaka, K. Yoshino, Y. Nambu, S. Takahashi, A. Tajima, A. Tomita, T. Domeki, T. Hasegawa, Y. Sakai, H. Kobayashi, T. Asai, K. Shimizu, T. Tokura, T. Tsurumaru, M. Matsui, T. Honjo, K. Tamaki, H. Takesue, Y. Tokura, J. F. Dynes, A. R. Dixon, A. W. Sharpe, Z. L. Yuan, A. J. Shields, S. Uchikoga, M. Legré, S. Robyr, P. Trinkler, L. Monat, J.-B. Page, G. Ribordy, A. Poppe, A. Allacher, O. Maurhart, T. Länger, M. Peev, and A. Zeilinger, “Field test of quantum key distribution in the Tokyo QKD Network,” Opt. Express 19(11), 10387–10409 (2011).
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M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys. 11, 075001 (2009).
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Pelc, J. S.

S.-K. Liao, H.-L. Yong, C. Liu, G.-L. Shentu, D.-D. Li, J. Lin, H. Dai, S.-Q. Zhao, B. Li, J.-Y. Guan, W. Chen, Y.-H. Gong, Y. Li, Z.-H. Lin, G.-S. Pan, J. S. Pelc, M. M. Fejer, W.-Z. Zhang, W.-Y. Liu, J. Yin, J.-G. Ren, X.-B. Wang, Q. Zhang, C.-Z. Peng, and J.-W. Pan, “Long-distance free-space quantum key distribution in daylight towards inter-satellite communication,” Nat. Photon. 11, 509 (2017).
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Peng, C.-Z.

S.-K. Liao, W.-Q. Cai, J. Handsteiner, B. Liu, J. Yin, L. Zhang, D. Rauch, M. Fink, J.-G. Ren, W.-Y. Liu, Y. Li, Q. Shen, Y. Cao, F.-Z. Li, J.-F. Wang, Y.-M. Huang, L. Deng, T. Xi, L. Ma, T. Hu, L. Li, N.-L. Liu, F. Koidl, P. Wang, Y.-A. Chen, X.-B. Wang, M. Steindorfer, G. Kirchner, C.-Y. Lu, R. Shu, R. Ursin, T. Scheidl, C.-Z. Peng, J.-Y. Wang, A. Zeilinger, and J.-W. Pan, “Satellite-relayed intercontinental quantum network,” Phys. Rev. Lett. 120(3), 030501 (2018).
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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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S.-K. Liao, H.-L. Yong, C. Liu, G.-L. Shentu, D.-D. Li, J. Lin, H. Dai, S.-Q. Zhao, B. Li, J.-Y. Guan, W. Chen, Y.-H. Gong, Y. Li, Z.-H. Lin, G.-S. Pan, J. S. Pelc, M. M. Fejer, W.-Z. Zhang, W.-Y. Liu, J. Yin, J.-G. Ren, X.-B. Wang, Q. Zhang, C.-Z. Peng, and J.-W. Pan, “Long-distance free-space quantum key distribution in daylight towards inter-satellite communication,” Nat. Photon. 11, 509 (2017).
[Crossref]

J. Yin, Y. Cao, Y.-H. Li, J.-G. Ren, S.-K. Liao, L. Zhang, W.-Q. Cai, W.-Y. Liu, B. Li, H. Dai, M. Li, Y.-M. Huang, L. Deng, L. Li, Q. Zhang, N.-L. Liu, Y.-A. Chen, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground entanglement-based quantum key distribution,” Phys. Rev. Lett. 119(20), 200501 (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, 43 (2017).
[Crossref] [PubMed]

J.-Y. Wang, B. Yang, S.-K. Liao, L. Zhang, Q. Shen, X.-F. Hu, J.-C. Wu, S.-J. Yang, H. Jiang, Y.-L. Tang, B. Zhong, H. Liang, W.-Y. Liu, Y.-H. Hu, Y.-M. Huang, B. Qi, J.-G. Ren, G.-S. Pan, J. Yin, J.-J. Jia, Y.-A. Chen, K. Chen, C.-Z. Peng, and J.-W. Pan, “Direct and full-scale experimental verifications towards ground-satellite quantum key distribution,” Nat. Photon. 7, 387 (2013).
[Crossref]

J. Yin, Y. Cao, S.-B. Liu, G.-S. Pan, J.-H. Wang, T. Yang, Z.-P. Zhang, F.-M. Yang, Y.-A. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental quasi-single-photon transmission from satellite to earth,” Opt. Express 21(17), 20032–20040 (2013).
[Crossref] [PubMed]

J. Yin, J.-G. Ren, H. Lu, Y. Cao, H.-L. Yong, Y.-P. Wu, C. Liu, S.-K. Liao, F. Zhou, Y. Jiang, X.-D. Cai, P. Xu, G.-S. Pan, J.-J. Jia, Y.-M. Huang, H. Yin, J.-Y. Wang, Y.-A. Chen, C.-Z. Peng, and J.-W. Pan, “Quantum teleportation and entanglement distribution over 100-kilometre free-space channels,” Nature 488, 185 (2012).
[Crossref] [PubMed]

C.-Z. Peng, T. Yang, X.-H. Bao, J. Zhang, X.-M. Jin, F.-Y. Feng, B. Yang, J. Yang, J. Yin, Q. Zhang, N. Li, B.-L. Tian, and J.-W. Pan, “Experimental free-space distribution of entangled photon pairs over 13 km: Towards satellite-based global quantum communication,” Phys. Rev. Lett. 94(15), 150501 (2005).
[Crossref] [PubMed]

Perdigues, J.

R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Ömer, M. Fürst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Entanglement-based quantum communication over 144 km,” Nat. Phys. 3, 481 (2007).
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T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurtsiefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98(1), 010504 (2007).
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Perlot, N.

T. Jono, Y. Takayama, K. Shiratama, I. Mase, B. Demelenne, Z. Sodnik, A. Bird, M. Toyoshima, H. Kunimori, D. Giggenbach, N. Perlot, M. Knapek, and K. Arai, “Overview of the inter-orbit and the orbit-to-ground laser communication demonstration by OICETS,” Proc. SPIE 6457, 645702 (2007).
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Pernechele, C.

P. Villoresi, T. Jennewein, F. Tamburini, M. Aspelmeyer, C. Bonato, R. Ursin, C. Pernechele, V. Luceri, G. Bianco, A. Zeilinger, and C. Barbieri, “Experimental verification of the feasibility of a quantum channel between space and earth,” New J. Phys. 10(3), 033038 (2008).
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Peterson, C. G.

R. J. Hughes, J. E. Nordholt, D. Derkacs, and C. G. Peterson, “Practical free-space quantum key distribution over 10 km in daylight and at night,” New J. Phys. 4, 43 (2002).
[Crossref]

J. E. Nordholt, R. J. Hughes, G. L. Morgan, C. G. Peterson, and C. C. Wipf, “Present and future free-space quantum key distribution,” Proc. SPIE 4635, 116–126 (2002).
[Crossref]

Philipp-May, S.

Pirandola, S.

S. Pirandola, R. Laurenza, C. Ottaviani, and L. Banchi, “Fundamental limits of repeaterless quantum communications,” Nat. Commun. 8, 15043 (2017).
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Poppe, A.

M. Sasaki, M. Fujiwara, H. Ishizuka, W. Klaus, K. Wakui, M. Takeoka, S. Miki, T. Yamashita, Z. Wang, A. Tanaka, K. Yoshino, Y. Nambu, S. Takahashi, A. Tajima, A. Tomita, T. Domeki, T. Hasegawa, Y. Sakai, H. Kobayashi, T. Asai, K. Shimizu, T. Tokura, T. Tsurumaru, M. Matsui, T. Honjo, K. Tamaki, H. Takesue, Y. Tokura, J. F. Dynes, A. R. Dixon, A. W. Sharpe, Z. L. Yuan, A. J. Shields, S. Uchikoga, M. Legré, S. Robyr, P. Trinkler, L. Monat, J.-B. Page, G. Ribordy, A. Poppe, A. Allacher, O. Maurhart, T. Länger, M. Peev, and A. Zeilinger, “Field test of quantum key distribution in the Tokyo QKD Network,” Opt. Express 19(11), 10387–10409 (2011).
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Supplementary Material (2)

NameDescription
» Data File 1       This zip contains the data sets of free space optical transmission conducted from 10:00 on 7 Jun. 2017 to 10:35 on 13 Jun. 2017.
» Visualization 1       This movie presents the variations of experimental final key rate and the histograms of the demodulated sequences during 27 hours from 18:00 on 11 June.

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Figures (14)

Fig. 1
Fig. 1 (a) Schematic diagram of the configuration of FSO-SKA. (b) Key-distillation processing conducted over the public channel.
Fig. 2
Fig. 2 (a) Geographical configuration of Tokyo FSO Testbed. (b) Beam footprint at Bob’s site (the NICT building). (c) Photographs of Skytower West Tokyo at 4.5-km distance from NICT. The right picture is the enlarged view for the antenna and its supporting poles located on the Skytower West Tokyo. (d) Photographs of Alice’s site taken from NICT at 7.8-km distance from NICT.
Fig. 3
Fig. 3 Channel characterization for the data acquired at 14:50 on 23 May 2017. (a) Demodulated sequence ay(i) at Bob, where the index i runs from 1 to 2300000 to over at least one frame in the sequence. Also shown is the threshold based on the two-sided moving average. (b) Diagram of the main channel. Edges represent the conditional probabilities PAB(y|x). (c) Experimentally characterized PAB(y|x) of the main channel. (d) Demodulated sequence a(i) at v-Eve. (e) Diagram of the probing channel. Edges represent the conditional probabilities PAE(|x). (f) Experimentally characterized PAE(|x). For soft decision, bin width Δ is chosen so that the leaked information is appropriately estimated with finite-size data in practical experiment (see Appendix B). In this figure, the total bin number K is taken to be 763.
Fig. 4
Fig. 4 Theoretical calculations of mutual information (a) I(X; Y), (b) I(X; ), and (c) I(Y; ). The repetition rate and the laser wave length are assumed to be 10 MHz and 1550 nm, respectively. The detailed description of the calculation is given in Appendix C.
Fig. 5
Fig. 5 (a) Theoretical curve of the asymptotic key rate R K A. (b) Plot of the experimental R K A. The data points of outage, for which R K A 0, are indicated by x-marks. (c) Contour plot of the theoretical and experimental R K A.
Fig. 6
Fig. 6 Histograms of the demodulated sequences for cases A to E. These cases are shown in the upper left inset of Fig. 5(c). For each case, ARPSs B and E, wind velocity (w.v.), and experimental R K A are shown as well as the time and date.
Fig. 7
Fig. 7 Histograms of the demodulated sequences for cases F to J. These cases are shown in the upper right inset of Fig. 5(c). For each case, ARPSs B and E, wind velocity (w.v.), and experimental R K A are shown as well as the time and date.
Fig. 8
Fig. 8 Flow chart of the key-distillation processing.
Fig. 9
Fig. 9 (a) Theoretical characteristics of the final key rate R K F. (b) Plot of the experimental R K F. The data points of outage, for which R K F 0, are indicated by x-marks. (c) Contour plot of the theoretical and experimental R K F.
Fig. 10
Fig. 10 Summary of Campaign No. 3. (a) Variations of the one-hour averaged final key rate R K F (blue solid line) and the failure rate (red chain line). During experiment, 10 frames were recorded every 5 minutes. Thus, 120 frames were transmitted in each one hour. Gray shades indicate the night time between sunset and sunrise and dashed lines show the 00:00 AM in JST. (b) Variations of the one-hour averaged B (solid line) and E (chain line). (c) Variations of the one-hour averaged solar radiation and cloud ceiling. These meteorological data were provided by OBSOC [67], the compound meteorological sensor at NICT premises. For the interested reader, we provide Data File 1 [68] which includes the original data sets for this figure ( R K F, B, and E) as well as the histograms of the demodulated sequences. In Visualization 1, we present a movie of the variations of R K F and the histograms of the demodulated sequences during 27 hours from 18:00 on 11 June.
Fig. 11
Fig. 11 Summary of the NIST randomness test suites [69] for keys generated on 9 June 2017. We applied the tests on 1000 instances with a length of 106 bits. The acceptable uniformity should be larger than 10−4. As shown by the black dotted lines, the acceptable success rate range for excluding Random Excursions (Variant) test is 0.99 ± 0.00943: The acceptable success rate range is 0.99 ± 0.0121 for Random Excursions (Variant) test. For the items with multiple tests (Cumulative Sums, Non Overlapping Template, Random Excursions, and Random Excursions Variant), we show the range of the lowest and highest scores by the black solid lines.
Fig. 12
Fig. 12 (a) Comparison between I(X; ) and I(Y; ). The color of each point corresponds to the BER in the main channel. (b) Comparison between I(X; Y)−I(X; ) and I(X; Y)−I(Y; ). The color of each point corresponds to the BER in the probing channel.
Fig. 13
Fig. 13 (a) Average E[Pe,lPe,n] for 10000 trials. (b) Standard deviation var [ P e , l P e , n ] for 10000 trials. (c) Histogram of Pe,lPe,n for l = 10000 bits. The solid line represents the PDF of the Gaussian distribution with an average of 4.79 × 10−5% and a standard deviation of 0.0964%. (d) Histogram of Pe,lPe,n for l = 64000 bits. The solid line is the PDF of the Gaussian distribution with an average of 1.39 × 10−4% and a standard deviation of 0.0392%.
Fig. 14
Fig. 14 (a) Bin-width dependence of Il(Y; ) when test-sample length l is 64000 bits. (b) Average E[Il(Y; )−In(Y; )] for 10000 trials. (c) Standard deviation var [ I l ( Y ; Z ^ ) I n ( Y ; Z ^ ) ] for 10000 trials. (d) Histogram of Il(Y; ) − In(Y; ) for 10000 test samples. The solid line represents the PDF of the Gaussian distribution with an average of 2.78 × 10−2 bits/symbol and a standard deviation of 6.61 × 10−3 bits/symbol. (e) Histogram of Il(Y; ) − In(Y; ) for 64000 test samples. The solid line represents the PDF of the Gaussian distribution with an average of 6.57 × 10−3 bits/symbol and a standard deviation of 2.86 × 10−3 bits/symbol. For these two histograms, the bin width Δ is 0.08 mV.

Tables (1)

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Table 1 Summary of experimental configurations of FSO transmission campaigns

Equations (25)

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C K R K = I ( X ; Y ) min [ I ( X ; Z ) , I ( Y ; Z ) ] ,
I ( X ; Y ) = x y P A ( x ) P AB ( y | x ) log 2 [ P AB ( y | x ) x P A ( x ) P AB ( y | x ) ] ,
I ( X ; Z ) = x z P A ( x ) P AE ( z | x ) log 2 [ P AE ( z | x ) x P A ( x ) P AE ( z | x ) ] ,
I ( Y ; Z ) = y z P B ( y ) P BE ( z | y ) log 2 [ P BE ( z | y ) y P B ( y ) P BE ( z | y ) ] ,
θ IFoV = 2 tan 1 ( d pix 2 f tele ) .
a ¯ y ( i ) = 1 3001 j = i 1500 i + 1500 a y ( j ) .
P AB ( y | x ) = N AB ( y | x ) N A ( x )
R LDPC = { 0.85 ( 0 % P e < 0.7 % ) 0.80 ( 0.7 % P e < 1.7 % ) 0.75 ( 1.7 % P e < 2.7 % ) 0.70 ( 2.7 % P e < 3.7 % ) 0.65 ( 3.7 % P e < 4.7 % ) 0.60 ( 4.7 % P e < 5.7 % ) 0.55 ( 5.7 % P e < 6.7 % ) 0.50 ( otherwise ) .
I ( X ; Z ) I ( Y ; Z ) , I ( X ; Y ) I ( Y ; Z )
I ( X ; Y ) I ( Y ; Z ) max [ I ( X ; Y ) I ( X ; Z ) , 0 ] ,
I ( X ; Y ) = x = 0 , 1 y = 0 , 1 P A ( x ) P AB ( y | x ) log 2 [ P AB ( y | x ) x P A ( x ) P AB ( y | x ) ] .
P AB ( y = 1 | x ) = v th 0 Q AB ( v B | x ) d v B , P AB ( y = 0 | x ) = v th Q AB ( v B | x ) d v B ,
σ B 2 ( S ) = 1.57 × 10 2 S 2 + 7.75 × 10 19 S + 1.44 × 10 2 ,
Q AB ( v B | x ) = 1 2 π σ B 2 ( 2 x S ¯ B ) exp ( ( v B 2 x S ¯ B ) 2 σ B 2 ( 2 x S ¯ B ) ) .
P AB ( 1 | 0 ) = S ¯ B Q AB ( v B | 0 ) d v B = 1 2 erfc ( S ¯ B 2 σ B 2 ( 0 ) ) ,
P AB ( 0 | 1 ) = S ¯ B Q AB ( v B | 1 ) d v B = 1 2 erfc ( S ¯ B 2 σ B 2 ( 2 S ¯ B ) ) ,
I ( X ; Z ^ ) = x = 0 , 1 P A ( x ) Q AE ( v ^ E | x ) log 2 [ Q AE ( v ^ E | x ) x P A ( x ) Q AE ( v ^ E | x ) ] d v ^ E ,
Q AE ( v ^ E | x ) = 1 2 π σ E 2 ( 2 x S ¯ E ) exp ( ( v ^ E 2 x S ¯ E ) 2 σ E 2 ( 2 x S ¯ E ) ) ,
σ E 2 ( S ) = 1.92 × 10 2 S 2 + 1.65 × 10 19 S + 2.68 × 10 1 .
I ( Y ; Z ^ ) = x = 0 , 1 P B ( y ) Q BE ( v ^ E | y ) log 2 [ Q BE ( v ^ E | y ) y P B ( y ) Q BE ( v ^ E | y ) ] d v ^ B ,
P B ( y ) = x = 0 , 1 P A ( x ) P AB ( y | x ) = 1 2 x = 0 , 1 P AB ( y | x ) .
Q BE ( v ^ E | y ) = x = 0 , 1 Q AE ( v ^ E | x ) P BA ( x | y )
= x = 0 , 1 Q AE ( v ^ E | x ) P AB ( y | x ) P A ( x ) P B ( y )
= P AB ( y | 0 ) Q AE ( v ^ E | 0 ) + P AB ( y | 1 ) Q AE ( v ^ E | 1 ) 2 P B ( y ) ,
P BA ( x | y ) P B ( y ) = P AB ( y | x ) P A ( x ) .

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