Abstract

We report a free-space entanglement-based quantum key distribution experiment, implementing the biased basis protocol between two sites which are 15.3 km apart. Photon pairs from a polarization-entangled source are distributed through two 7.8-km free-space optical links. An optimal bias 20:80 between the X and Z basis is used. A post-processing scheme with finite-key analysis is applied to extract the final secure key. After three-hour continuous operation at night, a 4293-bit secure key is obtained, with a final key rate of 0.124 bit per raw key bit which increases the final key rate by 14.8% comparing to the standard BB84 case. Our results experimentally demonstrate that the efficient BB84 protocol, which increases key generation efficiency by biasing Alice and Bob’s basis choices, is potentially useful for the ground-satellite quantum communication.

© 2013 OSA

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  4. C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bell’s theorem,” Phys. Rev. Lett.68, 557–559 (1992).
    [CrossRef] [PubMed]
  5. C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” Journal of Cryptology ( 5), 3–28 (1992).
    [CrossRef]
  6. In fact, commercial QKD systems have already been available in the market, for example, www.magiqtech.com ; www.idquantique.com ; www.quantum-info.com .
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    [CrossRef]
  8. Z. L. Yuan, A. R. Dixon, J. F. Dynes, A. W. Sharpe, and A. J. Shields, “Practical gigahertz quantum key distribution based on avalanche photodiodes,” New J. Phys.11, 045019 (2009).
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  9. Y. Liu, T.-Y. Chen, J. Wang, W.-Q. Cai, X. Wan, L.-K. Chen, J.-H. Wang, S.-B. Liu, H. Liang, L. Yang, C.-Z. Peng, K. Chen, Z.-B. Chen, and J.-W. Pan, “Decoy-state quantum key distribution with polarized photons over 200 km,” Opt. Express18, 8587–8594 (2010).
    [CrossRef] [PubMed]
  10. M. Aspelmeyer, T. Jennewein, M. Pfennigbauer, W. Leeb, and A. Zeilinger, “Long-distance quantum communication with entangled photons using satellites,” IEEE J. Sel. Top. Quantum Electron.9, 1514–1551 (2003).
  11. T. Schmitt-Manderbach, H. Weier, M. Furst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, 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, 010504 (2007).
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    [CrossRef]
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    [CrossRef]
  20. C. Erven, X. Ma, R. Laflamme, and G. Weihs, “Entangled quantum key distribution with a biased basis choice,” New J. Phys.11, 045025 (2009).
    [CrossRef]
  21. X. Ma, C.-H. F. Fung, J.-C. Boileau, and H.F. Chau, “Universally composable and customizable post-processing for practical quantum key distribution,” Computers & Security30, 172–177 (2011).
    [CrossRef]
  22. C.-H. F. Fung, X. Ma, and H. F. Chau, “Practical issues in quantum-key-distribution postprocessing,” Phys. Rev. A81, 012318 (2010).
    [CrossRef]
  23. X.-Y. Hu, E. Eleftheriou, and D. M. Arnold, “Regular and irregular progressive edge-growth tanner graphs,” Information Theory, IEEE Transactions on51, 386 (2005).
    [CrossRef]
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    [CrossRef] [PubMed]
  25. This can be simply calculated by comparing the basis-sift factor of 0.22+ 0.82= 0.68 to 1/2.
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  29. C. Bonato, A. Tomaello, V. D. Deppo, G. Naletto, and P. Villoresi, “Feasibility of satellite quantum key distribution,” New J. Phys.11, 045017 (2005).
    [CrossRef]
  30. 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. Express2120032–20040 (2013)
    [CrossRef] [PubMed]
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  33. Y. Zhao, C.-H. F. Fung, B. Qi, C. Chen, and H.-K. Lo, “Quantum hacking: Experimental demonstration of time-shift attack against practical quantum-key-distribution systems,” Phys. Rev. A78, 042333 (2008).
    [CrossRef]
  34. V. Makarov, A. Anisimov, and J. Skaar, “Effects of detector efficiency mismatch on security of quantum cryptosystems,” Phys. Rev. A74, 022313 (2006).
    [CrossRef]
  35. N. Jain, C. Wittmann, L. Lydersen, C. Wiechers, D. Elser, C. Marquardt, V. Makarov, and G. Leuchs, “Device calibration impacts security of quantum key distribution,” Phys. Rev. Lett.107, 110501 (2011).
    [CrossRef] [PubMed]
  36. J. Yin, Y. Cao, H.-L. Yong, J.-G. Ren, H. Liang, S.-K. Liao, F. Zhou, C. Liu, Y.-P. Wu, G.-S. Pan, L. Li, N.-L. Liu, Q. Zhang, C.-Z. Peng, and J.-W. Pan, “Lower bound on the speed of nonlocal correlations without locality and measurement choice loopholes,” Phys. Rev. Lett.110, 260407 (2013).
    [CrossRef] [PubMed]

2013

S. Nauerth, F. Moll, M. Rau, J. Horwath, S. Frick, C. Fuchs, and H. Weinfurter, “Air-to-ground quantum communication,” Nat. Photonics7, 382–386 (2013).
[CrossRef]

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. Photonics7, 387–393 (2013).
[CrossRef]

J. Yin, Y. Cao, H.-L. Yong, J.-G. Ren, H. Liang, S.-K. Liao, F. Zhou, C. Liu, Y.-P. Wu, G.-S. Pan, L. Li, N.-L. Liu, Q. Zhang, C.-Z. Peng, and J.-W. Pan, “Lower bound on the speed of nonlocal correlations without locality and measurement choice loopholes,” Phys. Rev. Lett.110, 260407 (2013).
[CrossRef] [PubMed]

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. Express2120032–20040 (2013)
[CrossRef] [PubMed]

2012

F. Steinlechner, P. Trojek, M. Jofre, H. Weier, D. Perez, T. Jennewein, R. Ursin, J. Rarity, M. W. Mitchell, J. P. Torres, H. Weinfurter, and V. Pruneri, “A high-brightness source of polarization-entangled photons optimized for applications in free space,” Opt. Express20, 9640–9649 (2012).
[CrossRef] [PubMed]

R. Stone, “Entangled Secret Messages From Space,” Science336, 1632 (2012).
[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,” Nature488, 185–188 (2012).
[CrossRef] [PubMed]

X.-S. Ma, T. Herbst, T. Scheidl, D. Wang, S. Kropatschek, W. Naylor, B. Wittmann, A. Mech, J. Kofler, E. Anisimova, V. Makarov, T. Jennewein, R. Ursin, and A. Zeilinger, “Quantum teleportation over 143 kilometres using active feed-forward,” Nature489, 269–273 (2012).
[CrossRef] [PubMed]

2011

X. Ma, C.-H. F. Fung, J.-C. Boileau, and H.F. Chau, “Universally composable and customizable post-processing for practical quantum key distribution,” Computers & Security30, 172–177 (2011).
[CrossRef]

H. Xin, “Chinese academy takes space under its wing,” Science332, 904 (2011).
[CrossRef]

N. Jain, C. Wittmann, L. Lydersen, C. Wiechers, D. Elser, C. Marquardt, V. Makarov, and G. Leuchs, “Device calibration impacts security of quantum key distribution,” Phys. Rev. Lett.107, 110501 (2011).
[CrossRef] [PubMed]

2010

2009

C. Erven, X. Ma, R. Laflamme, and G. Weihs, “Entangled quantum key distribution with a biased basis choice,” New J. Phys.11, 045025 (2009).
[CrossRef]

Z. L. Yuan, A. R. Dixon, J. F. Dynes, A. W. Sharpe, and A. J. Shields, “Practical gigahertz quantum key distribution based on avalanche photodiodes,” New J. Phys.11, 045019 (2009).
[CrossRef]

2008

2007

B. Qi, C.-H. F. Fung, H.-K. Lo, and X. Ma, “Time-shift attack in practical quantum cryptosystems,” Quantum Inf. Comput.7, 073 (2007).

T. Schmitt-Manderbach, H. Weier, M. Furst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, 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, 010504 (2007).
[CrossRef] [PubMed]

R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Omer, M. Frst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Entanglement-based quantum communication over 144 km,” Nat. Phys.3, 481–486 (2007).
[CrossRef]

2006

V. Makarov, A. Anisimov, and J. Skaar, “Effects of detector efficiency mismatch on security of quantum cryptosystems,” Phys. Rev. A74, 022313 (2006).
[CrossRef]

2005

C. Bonato, A. Tomaello, V. D. Deppo, G. Naletto, and P. Villoresi, “Feasibility of satellite quantum key distribution,” New J. Phys.11, 045017 (2005).
[CrossRef]

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, 150501 (2005).
[CrossRef] [PubMed]

X.-Y. Hu, E. Eleftheriou, and D. M. Arnold, “Regular and irregular progressive edge-growth tanner graphs,” Information Theory, IEEE Transactions on51, 386 (2005).
[CrossRef]

H.-K. Lo, H. F. Chau, and M. Ardehali, “Efficient quantum key distribution scheme and a proof of its unconditional security,” Journal of Cryptology18, 133–165 (2005).
[CrossRef]

2003

M. Koashi and J. Preskill, “Secure quantum key distribution with an uncharacterized source,” Phys. Rev. Lett.90, 057902 (2003).
[CrossRef] [PubMed]

M. Aspelmeyer, T. Jennewein, M. Pfennigbauer, W. Leeb, and A. Zeilinger, “Long-distance quantum communication with entangled photons using satellites,” IEEE J. Sel. Top. Quantum Electron.9, 1514–1551 (2003).

1992

C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett.68, 3121–3124 (1992).
[CrossRef] [PubMed]

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bell’s theorem,” Phys. Rev. Lett.68, 557–559 (1992).
[CrossRef] [PubMed]

C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” Journal of Cryptology ( 5), 3–28 (1992).
[CrossRef]

1991

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett.67, 661–663 (1991).
[CrossRef] [PubMed]

Anisimov, A.

V. Makarov, A. Anisimov, and J. Skaar, “Effects of detector efficiency mismatch on security of quantum cryptosystems,” Phys. Rev. A74, 022313 (2006).
[CrossRef]

Anisimova, E.

X.-S. Ma, T. Herbst, T. Scheidl, D. Wang, S. Kropatschek, W. Naylor, B. Wittmann, A. Mech, J. Kofler, E. Anisimova, V. Makarov, T. Jennewein, R. Ursin, and A. Zeilinger, “Quantum teleportation over 143 kilometres using active feed-forward,” Nature489, 269–273 (2012).
[CrossRef] [PubMed]

Ardehali, M.

H.-K. Lo, H. F. Chau, and M. Ardehali, “Efficient quantum key distribution scheme and a proof of its unconditional security,” Journal of Cryptology18, 133–165 (2005).
[CrossRef]

Arnold, D. M.

X.-Y. Hu, E. Eleftheriou, and D. M. Arnold, “Regular and irregular progressive edge-growth tanner graphs,” Information Theory, IEEE Transactions on51, 386 (2005).
[CrossRef]

Aspelmeyer, M.

M. Aspelmeyer, T. Jennewein, M. Pfennigbauer, W. Leeb, and A. Zeilinger, “Long-distance quantum communication with entangled photons using satellites,” IEEE J. Sel. Top. Quantum Electron.9, 1514–1551 (2003).

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, 150501 (2005).
[CrossRef] [PubMed]

Barbieri, C.

R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Omer, M. Frst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Entanglement-based quantum communication over 144 km,” Nat. Phys.3, 481–486 (2007).
[CrossRef]

Bennett, C. H.

C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” Journal of Cryptology ( 5), 3–28 (1992).
[CrossRef]

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bell’s theorem,” Phys. Rev. Lett.68, 557–559 (1992).
[CrossRef] [PubMed]

C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett.68, 3121–3124 (1992).
[CrossRef] [PubMed]

C. H. Bennett and G. Brassard, “Quantum Cryptography: Public Key Distribution and Coin Tossing,” in Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing (New York, 1985) p.175.

Bessette, F.

C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” Journal of Cryptology ( 5), 3–28 (1992).
[CrossRef]

Blauensteiner, B.

R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Omer, M. Frst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Entanglement-based quantum communication over 144 km,” Nat. Phys.3, 481–486 (2007).
[CrossRef]

Boileau, J.-C.

X. Ma, C.-H. F. Fung, J.-C. Boileau, and H.F. Chau, “Universally composable and customizable post-processing for practical quantum key distribution,” Computers & Security30, 172–177 (2011).
[CrossRef]

Bonato, C.

C. Bonato, A. Tomaello, V. D. Deppo, G. Naletto, and P. Villoresi, “Feasibility of satellite quantum key distribution,” New J. Phys.11, 045017 (2005).
[CrossRef]

Brassard, G.

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bell’s theorem,” Phys. Rev. Lett.68, 557–559 (1992).
[CrossRef] [PubMed]

C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” Journal of Cryptology ( 5), 3–28 (1992).
[CrossRef]

C. H. Bennett and G. Brassard, “Quantum Cryptography: Public Key Distribution and Coin Tossing,” in Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing (New York, 1985) p.175.

Cai, W.-Q.

Cai, X.-D.

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,” Nature488, 185–188 (2012).
[CrossRef] [PubMed]

Cao, Y.

J. Yin, Y. Cao, H.-L. Yong, J.-G. Ren, H. Liang, S.-K. Liao, F. Zhou, C. Liu, Y.-P. Wu, G.-S. Pan, L. Li, N.-L. Liu, Q. Zhang, C.-Z. Peng, and J.-W. Pan, “Lower bound on the speed of nonlocal correlations without locality and measurement choice loopholes,” Phys. Rev. Lett.110, 260407 (2013).
[CrossRef] [PubMed]

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. Express2120032–20040 (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,” Nature488, 185–188 (2012).
[CrossRef] [PubMed]

Chau, H. F.

C.-H. F. Fung, X. Ma, and H. F. Chau, “Practical issues in quantum-key-distribution postprocessing,” Phys. Rev. A81, 012318 (2010).
[CrossRef]

H.-K. Lo, H. F. Chau, and M. Ardehali, “Efficient quantum key distribution scheme and a proof of its unconditional security,” Journal of Cryptology18, 133–165 (2005).
[CrossRef]

Chau, H.F.

X. Ma, C.-H. F. Fung, J.-C. Boileau, and H.F. Chau, “Universally composable and customizable post-processing for practical quantum key distribution,” Computers & Security30, 172–177 (2011).
[CrossRef]

Chen, C.

Y. Zhao, C.-H. F. Fung, B. Qi, C. Chen, and H.-K. Lo, “Quantum hacking: Experimental demonstration of time-shift attack against practical quantum-key-distribution systems,” Phys. Rev. A78, 042333 (2008).
[CrossRef]

Chen, K.

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. Photonics7, 387–393 (2013).
[CrossRef]

Y. Liu, T.-Y. Chen, J. Wang, W.-Q. Cai, X. Wan, L.-K. Chen, J.-H. Wang, S.-B. Liu, H. Liang, L. Yang, C.-Z. Peng, K. Chen, Z.-B. Chen, and J.-W. Pan, “Decoy-state quantum key distribution with polarized photons over 200 km,” Opt. Express18, 8587–8594 (2010).
[CrossRef] [PubMed]

Chen, L.-K.

Chen, T.-Y.

Chen, Y.-A.

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. Express2120032–20040 (2013)
[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. Photonics7, 387–393 (2013).
[CrossRef]

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Mitchell, M. W.

Moll, F.

S. Nauerth, F. Moll, M. Rau, J. Horwath, S. Frick, C. Fuchs, and H. Weinfurter, “Air-to-ground quantum communication,” Nat. Photonics7, 382–386 (2013).
[CrossRef]

Naletto, G.

C. Bonato, A. Tomaello, V. D. Deppo, G. Naletto, and P. Villoresi, “Feasibility of satellite quantum key distribution,” New J. Phys.11, 045017 (2005).
[CrossRef]

Nauerth, S.

S. Nauerth, F. Moll, M. Rau, J. Horwath, S. Frick, C. Fuchs, and H. Weinfurter, “Air-to-ground quantum communication,” Nat. Photonics7, 382–386 (2013).
[CrossRef]

Naylor, W.

X.-S. Ma, T. Herbst, T. Scheidl, D. Wang, S. Kropatschek, W. Naylor, B. Wittmann, A. Mech, J. Kofler, E. Anisimova, V. Makarov, T. Jennewein, R. Ursin, and A. Zeilinger, “Quantum teleportation over 143 kilometres using active feed-forward,” Nature489, 269–273 (2012).
[CrossRef] [PubMed]

Omer, B.

R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Omer, M. Frst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Entanglement-based quantum communication over 144 km,” Nat. Phys.3, 481–486 (2007).
[CrossRef]

Pan, G.-S.

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. Photonics7, 387–393 (2013).
[CrossRef]

J. Yin, Y. Cao, H.-L. Yong, J.-G. Ren, H. Liang, S.-K. Liao, F. Zhou, C. Liu, Y.-P. Wu, G.-S. Pan, L. Li, N.-L. Liu, Q. Zhang, C.-Z. Peng, and J.-W. Pan, “Lower bound on the speed of nonlocal correlations without locality and measurement choice loopholes,” Phys. Rev. Lett.110, 260407 (2013).
[CrossRef] [PubMed]

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. Express2120032–20040 (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,” Nature488, 185–188 (2012).
[CrossRef] [PubMed]

Pan, J.-W

Pan, J.-W.

J. Yin, Y. Cao, H.-L. Yong, J.-G. Ren, H. Liang, S.-K. Liao, F. Zhou, C. Liu, Y.-P. Wu, G.-S. Pan, L. Li, N.-L. Liu, Q. Zhang, C.-Z. Peng, and J.-W. Pan, “Lower bound on the speed of nonlocal correlations without locality and measurement choice loopholes,” Phys. Rev. Lett.110, 260407 (2013).
[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. Photonics7, 387–393 (2013).
[CrossRef]

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,” Nature488, 185–188 (2012).
[CrossRef] [PubMed]

Y. Liu, T.-Y. Chen, J. Wang, W.-Q. Cai, X. Wan, L.-K. Chen, J.-H. Wang, S.-B. Liu, H. Liang, L. Yang, C.-Z. Peng, K. Chen, Z.-B. Chen, and J.-W. Pan, “Decoy-state quantum key distribution with polarized photons over 200 km,” Opt. Express18, 8587–8594 (2010).
[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, 150501 (2005).
[CrossRef] [PubMed]

Peng, C.-Z.

J. Yin, Y. Cao, H.-L. Yong, J.-G. Ren, H. Liang, S.-K. Liao, F. Zhou, C. Liu, Y.-P. Wu, G.-S. Pan, L. Li, N.-L. Liu, Q. Zhang, C.-Z. Peng, and J.-W. Pan, “Lower bound on the speed of nonlocal correlations without locality and measurement choice loopholes,” Phys. Rev. Lett.110, 260407 (2013).
[CrossRef] [PubMed]

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. Express2120032–20040 (2013)
[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. Photonics7, 387–393 (2013).
[CrossRef]

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,” Nature488, 185–188 (2012).
[CrossRef] [PubMed]

Y. Liu, T.-Y. Chen, J. Wang, W.-Q. Cai, X. Wan, L.-K. Chen, J.-H. Wang, S.-B. Liu, H. Liang, L. Yang, C.-Z. Peng, K. Chen, Z.-B. Chen, and J.-W. Pan, “Decoy-state quantum key distribution with polarized photons over 200 km,” Opt. Express18, 8587–8594 (2010).
[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, 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. Omer, M. Frst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Entanglement-based quantum communication over 144 km,” Nat. Phys.3, 481–486 (2007).
[CrossRef]

T. Schmitt-Manderbach, H. Weier, M. Furst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, 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, 010504 (2007).
[CrossRef] [PubMed]

Perez, D.

Pfennigbauer, M.

M. Aspelmeyer, T. Jennewein, M. Pfennigbauer, W. Leeb, and A. Zeilinger, “Long-distance quantum communication with entangled photons using satellites,” IEEE J. Sel. Top. Quantum Electron.9, 1514–1551 (2003).

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M. Koashi and J. Preskill, “Secure quantum key distribution with an uncharacterized source,” Phys. Rev. Lett.90, 057902 (2003).
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Pruneri, V.

Qi, B.

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. Photonics7, 387–393 (2013).
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Y. Zhao, C.-H. F. Fung, B. Qi, C. Chen, and H.-K. Lo, “Quantum hacking: Experimental demonstration of time-shift attack against practical quantum-key-distribution systems,” Phys. Rev. A78, 042333 (2008).
[CrossRef]

B. Qi, C.-H. F. Fung, H.-K. Lo, and X. Ma, “Time-shift attack in practical quantum cryptosystems,” Quantum Inf. Comput.7, 073 (2007).

Rarity, J.

F. Steinlechner, P. Trojek, M. Jofre, H. Weier, D. Perez, T. Jennewein, R. Ursin, J. Rarity, M. W. Mitchell, J. P. Torres, H. Weinfurter, and V. Pruneri, “A high-brightness source of polarization-entangled photons optimized for applications in free space,” Opt. Express20, 9640–9649 (2012).
[CrossRef] [PubMed]

R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Omer, M. Frst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Entanglement-based quantum communication over 144 km,” Nat. Phys.3, 481–486 (2007).
[CrossRef]

Rarity, J. G.

T. Schmitt-Manderbach, H. Weier, M. Furst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, 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, 010504 (2007).
[CrossRef] [PubMed]

Rau, M.

S. Nauerth, F. Moll, M. Rau, J. Horwath, S. Frick, C. Fuchs, and H. Weinfurter, “Air-to-ground quantum communication,” Nat. Photonics7, 382–386 (2013).
[CrossRef]

Ren, J.-G.

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. Photonics7, 387–393 (2013).
[CrossRef]

J. Yin, Y. Cao, H.-L. Yong, J.-G. Ren, H. Liang, S.-K. Liao, F. Zhou, C. Liu, Y.-P. Wu, G.-S. Pan, L. Li, N.-L. Liu, Q. Zhang, C.-Z. Peng, and J.-W. Pan, “Lower bound on the speed of nonlocal correlations without locality and measurement choice loopholes,” Phys. Rev. Lett.110, 260407 (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,” Nature488, 185–188 (2012).
[CrossRef] [PubMed]

Salvail, L.

C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” Journal of Cryptology ( 5), 3–28 (1992).
[CrossRef]

Scheidl, T.

X.-S. Ma, T. Herbst, T. Scheidl, D. Wang, S. Kropatschek, W. Naylor, B. Wittmann, A. Mech, J. Kofler, E. Anisimova, V. Makarov, T. Jennewein, R. Ursin, and A. Zeilinger, “Quantum teleportation over 143 kilometres using active feed-forward,” Nature489, 269–273 (2012).
[CrossRef] [PubMed]

R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Omer, M. Frst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Entanglement-based quantum communication over 144 km,” Nat. Phys.3, 481–486 (2007).
[CrossRef]

T. Schmitt-Manderbach, H. Weier, M. Furst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, 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, 010504 (2007).
[CrossRef] [PubMed]

Schmitt-Manderbach, T.

T. Schmitt-Manderbach, H. Weier, M. Furst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, 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, 010504 (2007).
[CrossRef] [PubMed]

R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Omer, M. Frst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Entanglement-based quantum communication over 144 km,” Nat. Phys.3, 481–486 (2007).
[CrossRef]

Sharpe, A. W.

Z. L. Yuan, A. R. Dixon, J. F. Dynes, A. W. Sharpe, and A. J. Shields, “Practical gigahertz quantum key distribution based on avalanche photodiodes,” New J. Phys.11, 045019 (2009).
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A. R. Dixon, Z. L. Yuan, J. F. Dynes, A. W. Sharpe, and A. J. Shields, “Gigahertz decoy quantum key distribution with 1 Mbit/s secure key rate,” Opt. Express16, 18790–18979 (2008).
[CrossRef]

Shen, Q.

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. Photonics7, 387–393 (2013).
[CrossRef]

Shields, A. J.

Z. L. Yuan, A. R. Dixon, J. F. Dynes, A. W. Sharpe, and A. J. Shields, “Practical gigahertz quantum key distribution based on avalanche photodiodes,” New J. Phys.11, 045019 (2009).
[CrossRef]

A. R. Dixon, Z. L. Yuan, J. F. Dynes, A. W. Sharpe, and A. J. Shields, “Gigahertz decoy quantum key distribution with 1 Mbit/s secure key rate,” Opt. Express16, 18790–18979 (2008).
[CrossRef]

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V. Makarov, A. Anisimov, and J. Skaar, “Effects of detector efficiency mismatch on security of quantum cryptosystems,” Phys. Rev. A74, 022313 (2006).
[CrossRef]

Smolin, J.

C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” Journal of Cryptology ( 5), 3–28 (1992).
[CrossRef]

Sodnik, Z.

R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Omer, M. Frst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Entanglement-based quantum communication over 144 km,” Nat. Phys.3, 481–486 (2007).
[CrossRef]

T. Schmitt-Manderbach, H. Weier, M. Furst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, 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, 010504 (2007).
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Stone, R.

R. Stone, “Entangled Secret Messages From Space,” Science336, 1632 (2012).
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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. Photonics7, 387–393 (2013).
[CrossRef]

Tian, B.-L.

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, 150501 (2005).
[CrossRef] [PubMed]

Tiefenbacher, F.

R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Omer, M. Frst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Entanglement-based quantum communication over 144 km,” Nat. Phys.3, 481–486 (2007).
[CrossRef]

T. Schmitt-Manderbach, H. Weier, M. Furst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, 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, 010504 (2007).
[CrossRef] [PubMed]

Tomaello, A.

C. Bonato, A. Tomaello, V. D. Deppo, G. Naletto, and P. Villoresi, “Feasibility of satellite quantum key distribution,” New J. Phys.11, 045017 (2005).
[CrossRef]

Torres, J. P.

Trojek, P.

F. Steinlechner, P. Trojek, M. Jofre, H. Weier, D. Perez, T. Jennewein, R. Ursin, J. Rarity, M. W. Mitchell, J. P. Torres, H. Weinfurter, and V. Pruneri, “A high-brightness source of polarization-entangled photons optimized for applications in free space,” Opt. Express20, 9640–9649 (2012).
[CrossRef] [PubMed]

R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Omer, M. Frst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Entanglement-based quantum communication over 144 km,” Nat. Phys.3, 481–486 (2007).
[CrossRef]

Ursin, R.

X.-S. Ma, T. Herbst, T. Scheidl, D. Wang, S. Kropatschek, W. Naylor, B. Wittmann, A. Mech, J. Kofler, E. Anisimova, V. Makarov, T. Jennewein, R. Ursin, and A. Zeilinger, “Quantum teleportation over 143 kilometres using active feed-forward,” Nature489, 269–273 (2012).
[CrossRef] [PubMed]

F. Steinlechner, P. Trojek, M. Jofre, H. Weier, D. Perez, T. Jennewein, R. Ursin, J. Rarity, M. W. Mitchell, J. P. Torres, H. Weinfurter, and V. Pruneri, “A high-brightness source of polarization-entangled photons optimized for applications in free space,” Opt. Express20, 9640–9649 (2012).
[CrossRef] [PubMed]

T. Schmitt-Manderbach, H. Weier, M. Furst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, 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, 010504 (2007).
[CrossRef] [PubMed]

R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Omer, M. Frst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Entanglement-based quantum communication over 144 km,” Nat. Phys.3, 481–486 (2007).
[CrossRef]

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C. Bonato, A. Tomaello, V. D. Deppo, G. Naletto, and P. Villoresi, “Feasibility of satellite quantum key distribution,” New J. Phys.11, 045017 (2005).
[CrossRef]

Wan, X.

Wang, D.

X.-S. Ma, T. Herbst, T. Scheidl, D. Wang, S. Kropatschek, W. Naylor, B. Wittmann, A. Mech, J. Kofler, E. Anisimova, V. Makarov, T. Jennewein, R. Ursin, and A. Zeilinger, “Quantum teleportation over 143 kilometres using active feed-forward,” Nature489, 269–273 (2012).
[CrossRef] [PubMed]

Wang, J.

Wang, J.-H.

Wang, J.-Y.

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. Photonics7, 387–393 (2013).
[CrossRef]

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,” Nature488, 185–188 (2012).
[CrossRef] [PubMed]

Weier, H.

F. Steinlechner, P. Trojek, M. Jofre, H. Weier, D. Perez, T. Jennewein, R. Ursin, J. Rarity, M. W. Mitchell, J. P. Torres, H. Weinfurter, and V. Pruneri, “A high-brightness source of polarization-entangled photons optimized for applications in free space,” Opt. Express20, 9640–9649 (2012).
[CrossRef] [PubMed]

T. Schmitt-Manderbach, H. Weier, M. Furst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, 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, 010504 (2007).
[CrossRef] [PubMed]

R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Omer, M. Frst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Entanglement-based quantum communication over 144 km,” Nat. Phys.3, 481–486 (2007).
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C. Erven, X. Ma, R. Laflamme, and G. Weihs, “Entangled quantum key distribution with a biased basis choice,” New J. Phys.11, 045025 (2009).
[CrossRef]

C. Erven, C. Couteau, R. Laflamme, and G. Weihs, “Entangled quantum key distribution over two free-space optical links,” Opt. Express16, 16840–16853 (2008).
[CrossRef] [PubMed]

Weinfurter, H.

S. Nauerth, F. Moll, M. Rau, J. Horwath, S. Frick, C. Fuchs, and H. Weinfurter, “Air-to-ground quantum communication,” Nat. Photonics7, 382–386 (2013).
[CrossRef]

F. Steinlechner, P. Trojek, M. Jofre, H. Weier, D. Perez, T. Jennewein, R. Ursin, J. Rarity, M. W. Mitchell, J. P. Torres, H. Weinfurter, and V. Pruneri, “A high-brightness source of polarization-entangled photons optimized for applications in free space,” Opt. Express20, 9640–9649 (2012).
[CrossRef] [PubMed]

T. Schmitt-Manderbach, H. Weier, M. Furst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, 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, 010504 (2007).
[CrossRef] [PubMed]

R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Omer, M. Frst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Entanglement-based quantum communication over 144 km,” Nat. Phys.3, 481–486 (2007).
[CrossRef]

Wiechers, C.

N. Jain, C. Wittmann, L. Lydersen, C. Wiechers, D. Elser, C. Marquardt, V. Makarov, and G. Leuchs, “Device calibration impacts security of quantum key distribution,” Phys. Rev. Lett.107, 110501 (2011).
[CrossRef] [PubMed]

Wittmann, B.

X.-S. Ma, T. Herbst, T. Scheidl, D. Wang, S. Kropatschek, W. Naylor, B. Wittmann, A. Mech, J. Kofler, E. Anisimova, V. Makarov, T. Jennewein, R. Ursin, and A. Zeilinger, “Quantum teleportation over 143 kilometres using active feed-forward,” Nature489, 269–273 (2012).
[CrossRef] [PubMed]

Wittmann, C.

N. Jain, C. Wittmann, L. Lydersen, C. Wiechers, D. Elser, C. Marquardt, V. Makarov, and G. Leuchs, “Device calibration impacts security of quantum key distribution,” Phys. Rev. Lett.107, 110501 (2011).
[CrossRef] [PubMed]

Wu, J.-C.

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. Photonics7, 387–393 (2013).
[CrossRef]

Wu, Y.-P.

J. Yin, Y. Cao, H.-L. Yong, J.-G. Ren, H. Liang, S.-K. Liao, F. Zhou, C. Liu, Y.-P. Wu, G.-S. Pan, L. Li, N.-L. Liu, Q. Zhang, C.-Z. Peng, and J.-W. Pan, “Lower bound on the speed of nonlocal correlations without locality and measurement choice loopholes,” Phys. Rev. Lett.110, 260407 (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,” Nature488, 185–188 (2012).
[CrossRef] [PubMed]

Xin, H.

H. Xin, “Chinese academy takes space under its wing,” Science332, 904 (2011).
[CrossRef]

Xu, P.

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,” Nature488, 185–188 (2012).
[CrossRef] [PubMed]

Yang, B.

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. Photonics7, 387–393 (2013).
[CrossRef]

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, 150501 (2005).
[CrossRef] [PubMed]

Yang, F.-M.

Yang, J.

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, 150501 (2005).
[CrossRef] [PubMed]

Yang, L.

Yang, S.-J.

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. Photonics7, 387–393 (2013).
[CrossRef]

Yang, T.

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. Express2120032–20040 (2013)
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Yin, H.

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,” Nature488, 185–188 (2012).
[CrossRef] [PubMed]

Yin, J.

J. Yin, Y. Cao, H.-L. Yong, J.-G. Ren, H. Liang, S.-K. Liao, F. Zhou, C. Liu, Y.-P. Wu, G.-S. Pan, L. Li, N.-L. Liu, Q. Zhang, C.-Z. Peng, and J.-W. Pan, “Lower bound on the speed of nonlocal correlations without locality and measurement choice loopholes,” Phys. Rev. Lett.110, 260407 (2013).
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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. Express2120032–20040 (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. Photonics7, 387–393 (2013).
[CrossRef]

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,” Nature488, 185–188 (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, 150501 (2005).
[CrossRef] [PubMed]

Yong, H.-L.

J. Yin, Y. Cao, H.-L. Yong, J.-G. Ren, H. Liang, S.-K. Liao, F. Zhou, C. Liu, Y.-P. Wu, G.-S. Pan, L. Li, N.-L. Liu, Q. Zhang, C.-Z. Peng, and J.-W. Pan, “Lower bound on the speed of nonlocal correlations without locality and measurement choice loopholes,” Phys. Rev. Lett.110, 260407 (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,” Nature488, 185–188 (2012).
[CrossRef] [PubMed]

Yuan, Z. L.

Z. L. Yuan, A. R. Dixon, J. F. Dynes, A. W. Sharpe, and A. J. Shields, “Practical gigahertz quantum key distribution based on avalanche photodiodes,” New J. Phys.11, 045019 (2009).
[CrossRef]

A. R. Dixon, Z. L. Yuan, J. F. Dynes, A. W. Sharpe, and A. J. Shields, “Gigahertz decoy quantum key distribution with 1 Mbit/s secure key rate,” Opt. Express16, 18790–18979 (2008).
[CrossRef]

Zeilinger, A.

X.-S. Ma, T. Herbst, T. Scheidl, D. Wang, S. Kropatschek, W. Naylor, B. Wittmann, A. Mech, J. Kofler, E. Anisimova, V. Makarov, T. Jennewein, R. Ursin, and A. Zeilinger, “Quantum teleportation over 143 kilometres using active feed-forward,” Nature489, 269–273 (2012).
[CrossRef] [PubMed]

R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Omer, M. Frst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Entanglement-based quantum communication over 144 km,” Nat. Phys.3, 481–486 (2007).
[CrossRef]

T. Schmitt-Manderbach, H. Weier, M. Furst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, 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, 010504 (2007).
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M. Aspelmeyer, T. Jennewein, M. Pfennigbauer, W. Leeb, and A. Zeilinger, “Long-distance quantum communication with entangled photons using satellites,” IEEE J. Sel. Top. Quantum Electron.9, 1514–1551 (2003).

Zhang, J.

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, 150501 (2005).
[CrossRef] [PubMed]

Zhang, L.

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. Photonics7, 387–393 (2013).
[CrossRef]

Zhang, Q.

J. Yin, Y. Cao, H.-L. Yong, J.-G. Ren, H. Liang, S.-K. Liao, F. Zhou, C. Liu, Y.-P. Wu, G.-S. Pan, L. Li, N.-L. Liu, Q. Zhang, C.-Z. Peng, and J.-W. Pan, “Lower bound on the speed of nonlocal correlations without locality and measurement choice loopholes,” Phys. Rev. Lett.110, 260407 (2013).
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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, 150501 (2005).
[CrossRef] [PubMed]

Zhang, Z.-P.

Zhao, Y.

Y. Zhao, C.-H. F. Fung, B. Qi, C. Chen, and H.-K. Lo, “Quantum hacking: Experimental demonstration of time-shift attack against practical quantum-key-distribution systems,” Phys. Rev. A78, 042333 (2008).
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Zhong, B.

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. Photonics7, 387–393 (2013).
[CrossRef]

Zhou, F.

J. Yin, Y. Cao, H.-L. Yong, J.-G. Ren, H. Liang, S.-K. Liao, F. Zhou, C. Liu, Y.-P. Wu, G.-S. Pan, L. Li, N.-L. Liu, Q. Zhang, C.-Z. Peng, and J.-W. Pan, “Lower bound on the speed of nonlocal correlations without locality and measurement choice loopholes,” Phys. Rev. Lett.110, 260407 (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,” Nature488, 185–188 (2012).
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Nat. Photonics

S. Nauerth, F. Moll, M. Rau, J. Horwath, S. Frick, C. Fuchs, and H. Weinfurter, “Air-to-ground quantum communication,” Nat. Photonics7, 382–386 (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. Photonics7, 387–393 (2013).
[CrossRef]

Nat. Phys.

R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Omer, M. Frst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Entanglement-based quantum communication over 144 km,” Nat. Phys.3, 481–486 (2007).
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Nature

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,” Nature488, 185–188 (2012).
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X.-S. Ma, T. Herbst, T. Scheidl, D. Wang, S. Kropatschek, W. Naylor, B. Wittmann, A. Mech, J. Kofler, E. Anisimova, V. Makarov, T. Jennewein, R. Ursin, and A. Zeilinger, “Quantum teleportation over 143 kilometres using active feed-forward,” Nature489, 269–273 (2012).
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New J. Phys.

C. Erven, X. Ma, R. Laflamme, and G. Weihs, “Entangled quantum key distribution with a biased basis choice,” New J. Phys.11, 045025 (2009).
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Opt. Express

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[CrossRef] [PubMed]

J. Yin, Y. Cao, H.-L. Yong, J.-G. Ren, H. Liang, S.-K. Liao, F. Zhou, C. Liu, Y.-P. Wu, G.-S. Pan, L. Li, N.-L. Liu, Q. Zhang, C.-Z. Peng, and J.-W. Pan, “Lower bound on the speed of nonlocal correlations without locality and measurement choice loopholes,” Phys. Rev. Lett.110, 260407 (2013).
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This can be simply calculated by comparing the basis-sift factor of 0.22+ 0.82= 0.68 to 1/2.

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In fact, commercial QKD systems have already been available in the market, for example, www.magiqtech.com ; www.idquantique.com ; www.quantum-info.com .

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Figures (3)

Fig. 1
Fig. 1

A schematic diagram of the entanglement-based QKD setup. At the transmitter, a Sagnac PDC source generates entangled photon pairs. Two 80-mm-diameter telescopes are used to transmit photon pairs to two receiver sites, 7.8 km away from the transmitter each. The detector modules, employed in both receivers, consist of a Pockels Cell (PoC), a polarization beam splitter cube (PBS) with two collimators placed in the transmitted and the reflected output port of PBS.

Fig. 2
Fig. 2

A Logic Module is applied for controlling the Pockels Cells, switching polarization bases and outputting measurement results. Commercial QRNGs are applied to choosing measurement basis. The logical operation and the human-computer interface are realized via a CPLD (Complex programmable logic device) chip and a Single-Chip Microcomputer.

Fig. 3
Fig. 3

The coincident detection events between Alice and Bob in a 25-min continuous sampling test. After balancing the number of coincident events and the source visibility, we set the gate width to be 2.5 ns in our experiment.

Tables (1)

Tables Icon

Table 1 List of measurement and post-processing results. After taking into account of error correction and privacy amplification, we evaluate the final secure key length. The sifted key length are nx and nz in the X and Z bases, respectively. The error correction efficiencies, febx and febz, are evaluated by considering the low-density parity-check (LDPC) codes and progressive edge-growth (PEG) algorithm [23]. The failure probability εph in phase error rate estimation processing is defined in [21]. The bit error rates in the X and Z bases are ebx and ebz, respectively. Denote qact to be the experimental value of basis bias and qopt to be the optimal value given by theoretical calculation.

Equations (6)

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

Prob ( a k = 1 ) = N 0 × 2 10 .
δ px = e b z , δ pz = e b x .
N R N sift k e c k p r ,
n sift = n x + n z , k e c = n x f ( e b x ) H ( e b x ) + n z f ( e b z ) H ( e b z ) , k p r = n x H ( e b z + θ z ) + n z H ( e b x + θ x ) ,
P θ x < n x + n z n x n z e b x ( 1 e b x ) 2 ( n x + n z ) ξ x ( θ x )
ε p h P θ x + P θ z

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