Abstract

Basis deviation is the reference-frame deviation between a sender and receiver caused by satellite motion in satellite-to-ground quantum communications. It increases the quantum-bit error ratio of the system and must be compensated for to guarantee reliable quantum communications. We present a new scheme for compensating for basis deviation that employs a BB84 decoding module to detect basis deviation and half-wave plate to provide compensation. Based on this detection scheme, we design a basis-deviation compensation approach and test its feasibility in a voyage experiment. Unlike other polarization-correction schemes, this compensation scheme is simple, convenient, and can be easily implemented in satellite-to-ground quantum communications without increased burden to the satellite.

© 2014 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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2013 (2)

J. Y. Wang, B. Yang, S. K. Liao, L. Zhang, Q. Shen, X. F. Hu, J. C. Wu, S. J. Yang, 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. Photonics 7(5), 387–393 (2013).
[Crossref]

M. Zhang, J. C. Wu, L. Zhang, J. J. Jia, Z. P. He, S. J. Yang, F. Qian, and J. Y. Wang, “Real time basis-deviation measurement system based on BB84 module,” Proc. SPIE 8906, 890629 (2013).
[Crossref]

2011 (1)

M. Toyoshima, H. Takenaka, Y. Shoji, Y. Takayama, M. Takeoka, M. Fujiwara, and M. Sasaki, “Polarization-Basis Tracking Scheme in Satellite Quantum Key Distribution,” Int. J. Opt. 2011, 254154 (2011).
[Crossref]

2009 (2)

2008 (1)

Y. S. Kim, Y. C. Jeong, and Y. H. Kim, “Implementation of Polarization-Coded Free-Space BB84 Quantum Key Distribution,” Laser Phys. 18(6), 810–814 (2008).
[Crossref]

2007 (1)

2006 (2)

2003 (2)

S. D. Bartlett, T. Rudolph, and R. W. Spekkens, “Classical and Quantum Communication without a Shared Reference Frame,” Phys. Rev. Lett. 91(2), 027901 (2003).
[Crossref] [PubMed]

M. Aspelmeyer, T. Jennewein, M. Pfennigbauer, W. R. Leeb, and A. Zeilinger, “Long-Distance Quantum Communication With Entangled Photons Using Satellites,” IEEE J. Sel. Top. Quantum Electron. 9(6), 1541–1551 (2003).
[Crossref]

2002 (1)

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

2000 (3)

G. Brassard, N. Lütkenhaus, T. Mor, and B. C. Sanders, “Limitations on Practical Quantum Cryptography,” Phys. Rev. Lett. 85(6), 1330–1333 (2000).
[Crossref] [PubMed]

H. Bechmann-Pasquinucci and W. Tittel, “Quantum cryptography using larger alphabets,” Phys. Rev. A 61(6), 062308 (2000).
[Crossref]

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

1999 (1)

J. W. Alexander, S. Lee, and C. C. Chen, “Pointing and tracking concepts for deep-space missions,” Proc. SPIE 3615, 230–249 (1999).
[Crossref]

1992 (1)

C. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental Quantum Cryptography,” J. Cryptol. 5, 3–28 (1992).

Alexander, J. W.

J. W. Alexander, S. Lee, and C. C. Chen, “Pointing and tracking concepts for deep-space missions,” Proc. SPIE 3615, 230–249 (1999).
[Crossref]

Aspelmeyer, M.

C. Bonato, M. Aspelmeyer, T. Jennewein, C. Pernechele, P. Villoresi, and A. Zeilinger, “Influence of satellite motion on polarization qubits in a Space-Earth quantum communication link,” Opt. Express 14(21), 10050–10059 (2006).
[Crossref] [PubMed]

M. Aspelmeyer, T. Jennewein, M. Pfennigbauer, W. R. Leeb, and A. Zeilinger, “Long-Distance Quantum Communication With Entangled Photons Using Satellites,” IEEE J. Sel. Top. Quantum Electron. 9(6), 1541–1551 (2003).
[Crossref]

Bartlett, S. D.

S. D. Bartlett, T. Rudolph, and R. W. Spekkens, “Classical and Quantum Communication without a Shared Reference Frame,” Phys. Rev. Lett. 91(2), 027901 (2003).
[Crossref] [PubMed]

Bechmann-Pasquinucci, H.

H. Bechmann-Pasquinucci and W. Tittel, “Quantum cryptography using larger alphabets,” Phys. Rev. A 61(6), 062308 (2000).
[Crossref]

Bennett, C.

C. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental Quantum Cryptography,” J. Cryptol. 5, 3–28 (1992).

Bessette, F.

C. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental Quantum Cryptography,” J. Cryptol. 5, 3–28 (1992).

Bonato, C.

Brassard, G.

G. Brassard, N. Lütkenhaus, T. Mor, and B. C. Sanders, “Limitations on Practical Quantum Cryptography,” Phys. Rev. Lett. 85(6), 1330–1333 (2000).
[Crossref] [PubMed]

C. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental Quantum Cryptography,” J. Cryptol. 5, 3–28 (1992).

Chen, C. C.

J. W. Alexander, S. Lee, and C. C. Chen, “Pointing and tracking concepts for deep-space missions,” Proc. SPIE 3615, 230–249 (1999).
[Crossref]

Chen, J.

Chen, K.

J. Y. Wang, B. Yang, S. K. Liao, L. Zhang, Q. Shen, X. F. Hu, J. C. Wu, S. J. Yang, 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. Photonics 7(5), 387–393 (2013).
[Crossref]

Chen, Y. A.

J. Y. Wang, B. Yang, S. K. Liao, L. Zhang, Q. Shen, X. F. Hu, J. C. Wu, S. J. Yang, 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. Photonics 7(5), 387–393 (2013).
[Crossref]

Deppo, V. D.

C. Bonato, A. Tomaello, V. D. Deppo, G. Naletto, and P. Villoresi, “Feasibility of satellite quantum key distribution,” New J. Phys. 11(4), 045017 (2009).
[Crossref]

Fujiwara, M.

M. Toyoshima, H. Takenaka, Y. Shoji, Y. Takayama, M. Takeoka, M. Fujiwara, and M. Sasaki, “Polarization-Basis Tracking Scheme in Satellite Quantum Key Distribution,” Int. J. Opt. 2011, 254154 (2011).
[Crossref]

Gorman, P. M.

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

He, Z. P.

M. Zhang, J. C. Wu, L. Zhang, J. J. Jia, Z. P. He, S. J. Yang, F. Qian, and J. Y. Wang, “Real time basis-deviation measurement system based on BB84 module,” Proc. SPIE 8906, 890629 (2013).
[Crossref]

Hu, X. F.

J. Y. Wang, B. Yang, S. K. Liao, L. Zhang, Q. Shen, X. F. Hu, J. C. Wu, S. J. Yang, 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. Photonics 7(5), 387–393 (2013).
[Crossref]

Jennewein, T.

C. Bonato, M. Aspelmeyer, T. Jennewein, C. Pernechele, P. Villoresi, and A. Zeilinger, “Influence of satellite motion on polarization qubits in a Space-Earth quantum communication link,” Opt. Express 14(21), 10050–10059 (2006).
[Crossref] [PubMed]

M. Aspelmeyer, T. Jennewein, M. Pfennigbauer, W. R. Leeb, and A. Zeilinger, “Long-Distance Quantum Communication With Entangled Photons Using Satellites,” IEEE J. Sel. Top. Quantum Electron. 9(6), 1541–1551 (2003).
[Crossref]

Jeong, Y. C.

Y. S. Kim, Y. C. Jeong, and Y. H. Kim, “Implementation of Polarization-Coded Free-Space BB84 Quantum Key Distribution,” Laser Phys. 18(6), 810–814 (2008).
[Crossref]

Jia, J. J.

M. Zhang, J. C. Wu, L. Zhang, J. J. Jia, Z. P. He, S. J. Yang, F. Qian, and J. Y. Wang, “Real time basis-deviation measurement system based on BB84 module,” Proc. SPIE 8906, 890629 (2013).
[Crossref]

J. Y. Wang, B. Yang, S. K. Liao, L. Zhang, Q. Shen, X. F. Hu, J. C. Wu, S. J. Yang, 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. Photonics 7(5), 387–393 (2013).
[Crossref]

Kim, Y. H.

Y. S. Kim, Y. C. Jeong, and Y. H. Kim, “Implementation of Polarization-Coded Free-Space BB84 Quantum Key Distribution,” Laser Phys. 18(6), 810–814 (2008).
[Crossref]

Kim, Y. S.

Y. S. Kim, Y. C. Jeong, and Y. H. Kim, “Implementation of Polarization-Coded Free-Space BB84 Quantum Key Distribution,” Laser Phys. 18(6), 810–814 (2008).
[Crossref]

Knight, P.

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

Koyama, Y.

Kunimori, H.

Lee, S.

J. W. Alexander, S. Lee, and C. C. Chen, “Pointing and tracking concepts for deep-space missions,” Proc. SPIE 3615, 230–249 (1999).
[Crossref]

Leeb, W. R.

M. Aspelmeyer, T. Jennewein, M. Pfennigbauer, W. R. Leeb, and A. Zeilinger, “Long-Distance Quantum Communication With Entangled Photons Using Satellites,” IEEE J. Sel. Top. Quantum Electron. 9(6), 1541–1551 (2003).
[Crossref]

M. Pfennigbauer, W. R. Leeb, and A. Zeilinger, “Free-Space Optical Quantum Key Distribution Using Inter-satellite Links,” in Proceedings of the CNES—Intersatellite Link Workshop, (2003).

Li, Y.

Liao, S. K.

J. Y. Wang, B. Yang, S. K. Liao, L. Zhang, Q. Shen, X. F. Hu, J. C. Wu, S. J. Yang, 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. Photonics 7(5), 387–393 (2013).
[Crossref]

Lütkenhaus, N.

G. Brassard, N. Lütkenhaus, T. Mor, and B. C. Sanders, “Limitations on Practical Quantum Cryptography,” Phys. Rev. Lett. 85(6), 1330–1333 (2000).
[Crossref] [PubMed]

Mor, T.

G. Brassard, N. Lütkenhaus, T. Mor, and B. C. Sanders, “Limitations on Practical Quantum Cryptography,” Phys. Rev. Lett. 85(6), 1330–1333 (2000).
[Crossref] [PubMed]

Naletto, G.

C. Bonato, A. Tomaello, V. D. Deppo, G. Naletto, and P. Villoresi, “Feasibility of satellite quantum key distribution,” New J. Phys. 11(4), 045017 (2009).
[Crossref]

Pan, J. W.

J. Y. Wang, B. Yang, S. K. Liao, L. Zhang, Q. Shen, X. F. Hu, J. C. Wu, S. J. Yang, 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. Photonics 7(5), 387–393 (2013).
[Crossref]

Peng, C. Z.

J. Y. Wang, B. Yang, S. K. Liao, L. Zhang, Q. Shen, X. F. Hu, J. C. Wu, S. J. Yang, 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. Photonics 7(5), 387–393 (2013).
[Crossref]

Pernechele, C.

Pfennigbauer, M.

M. Aspelmeyer, T. Jennewein, M. Pfennigbauer, W. R. Leeb, and A. Zeilinger, “Long-Distance Quantum Communication With Entangled Photons Using Satellites,” IEEE J. Sel. Top. Quantum Electron. 9(6), 1541–1551 (2003).
[Crossref]

M. Pfennigbauer, W. R. Leeb, and A. Zeilinger, “Free-Space Optical Quantum Key Distribution Using Inter-satellite Links,” in Proceedings of the CNES—Intersatellite Link Workshop, (2003).

Preskill, J.

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

Qian, F.

M. Zhang, J. C. Wu, L. Zhang, J. J. Jia, Z. P. He, S. J. Yang, F. Qian, and J. Y. Wang, “Real time basis-deviation measurement system based on BB84 module,” Proc. SPIE 8906, 890629 (2013).
[Crossref]

Rarity, J. G.

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

Rudolph, T.

S. D. Bartlett, T. Rudolph, and R. W. Spekkens, “Classical and Quantum Communication without a Shared Reference Frame,” Phys. Rev. Lett. 91(2), 027901 (2003).
[Crossref] [PubMed]

Salvail, L.

C. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental Quantum Cryptography,” J. Cryptol. 5, 3–28 (1992).

Sanders, B. C.

G. Brassard, N. Lütkenhaus, T. Mor, and B. C. Sanders, “Limitations on Practical Quantum Cryptography,” Phys. Rev. Lett. 85(6), 1330–1333 (2000).
[Crossref] [PubMed]

Sasaki, M.

M. Toyoshima, H. Takenaka, Y. Shoji, Y. Takayama, M. Takeoka, M. Fujiwara, and M. Sasaki, “Polarization-Basis Tracking Scheme in Satellite Quantum Key Distribution,” Int. J. Opt. 2011, 254154 (2011).
[Crossref]

Shen, Q.

J. Y. Wang, B. Yang, S. K. Liao, L. Zhang, Q. Shen, X. F. Hu, J. C. Wu, S. J. Yang, 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. Photonics 7(5), 387–393 (2013).
[Crossref]

Shoji, Y.

M. Toyoshima, H. Takenaka, Y. Shoji, Y. Takayama, M. Takeoka, M. Fujiwara, and M. Sasaki, “Polarization-Basis Tracking Scheme in Satellite Quantum Key Distribution,” Int. J. Opt. 2011, 254154 (2011).
[Crossref]

M. Toyoshima, H. Takenaka, Y. Shoji, Y. Takayama, Y. Koyama, and H. Kunimori, “Polarization measurements through space-to-ground atmospheric propagation paths by using a highly polarized laser source in space,” Opt. Express 17(25), 22333–22340 (2009).
[Crossref] [PubMed]

Shor, P. W.

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

Smolin, J.

C. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental Quantum Cryptography,” J. Cryptol. 5, 3–28 (1992).

Spedalieri, F. M.

F. M. Spedalieri, “Quantum key distribution without reference frame alignment: Exploiting photon orbital angular momentum,” Opt. Commun. 260(1), 340–346 (2006).
[Crossref]

Spekkens, R. W.

S. D. Bartlett, T. Rudolph, and R. W. Spekkens, “Classical and Quantum Communication without a Shared Reference Frame,” Phys. Rev. Lett. 91(2), 027901 (2003).
[Crossref] [PubMed]

Takayama, Y.

M. Toyoshima, H. Takenaka, Y. Shoji, Y. Takayama, M. Takeoka, M. Fujiwara, and M. Sasaki, “Polarization-Basis Tracking Scheme in Satellite Quantum Key Distribution,” Int. J. Opt. 2011, 254154 (2011).
[Crossref]

M. Toyoshima, H. Takenaka, Y. Shoji, Y. Takayama, Y. Koyama, and H. Kunimori, “Polarization measurements through space-to-ground atmospheric propagation paths by using a highly polarized laser source in space,” Opt. Express 17(25), 22333–22340 (2009).
[Crossref] [PubMed]

Takenaka, H.

M. Toyoshima, H. Takenaka, Y. Shoji, Y. Takayama, M. Takeoka, M. Fujiwara, and M. Sasaki, “Polarization-Basis Tracking Scheme in Satellite Quantum Key Distribution,” Int. J. Opt. 2011, 254154 (2011).
[Crossref]

M. Toyoshima, H. Takenaka, Y. Shoji, Y. Takayama, Y. Koyama, and H. Kunimori, “Polarization measurements through space-to-ground atmospheric propagation paths by using a highly polarized laser source in space,” Opt. Express 17(25), 22333–22340 (2009).
[Crossref] [PubMed]

Takeoka, M.

M. Toyoshima, H. Takenaka, Y. Shoji, Y. Takayama, M. Takeoka, M. Fujiwara, and M. Sasaki, “Polarization-Basis Tracking Scheme in Satellite Quantum Key Distribution,” Int. J. Opt. 2011, 254154 (2011).
[Crossref]

Tapster, P. R.

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

Tittel, W.

H. Bechmann-Pasquinucci and W. Tittel, “Quantum cryptography using larger alphabets,” Phys. Rev. A 61(6), 062308 (2000).
[Crossref]

Tomaello, A.

C. Bonato, A. Tomaello, V. D. Deppo, G. Naletto, and P. Villoresi, “Feasibility of satellite quantum key distribution,” New J. Phys. 11(4), 045017 (2009).
[Crossref]

Toyoshima, M.

M. Toyoshima, H. Takenaka, Y. Shoji, Y. Takayama, M. Takeoka, M. Fujiwara, and M. Sasaki, “Polarization-Basis Tracking Scheme in Satellite Quantum Key Distribution,” Int. J. Opt. 2011, 254154 (2011).
[Crossref]

M. Toyoshima, H. Takenaka, Y. Shoji, Y. Takayama, Y. Koyama, and H. Kunimori, “Polarization measurements through space-to-ground atmospheric propagation paths by using a highly polarized laser source in space,” Opt. Express 17(25), 22333–22340 (2009).
[Crossref] [PubMed]

Villoresi, P.

Wang, J. Y.

M. Zhang, J. C. Wu, L. Zhang, J. J. Jia, Z. P. He, S. J. Yang, F. Qian, and J. Y. Wang, “Real time basis-deviation measurement system based on BB84 module,” Proc. SPIE 8906, 890629 (2013).
[Crossref]

J. Y. Wang, B. Yang, S. K. Liao, L. Zhang, Q. Shen, X. F. Hu, J. C. Wu, S. J. Yang, 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. Photonics 7(5), 387–393 (2013).
[Crossref]

Wu, E.

Wu, G.

Wu, J. C.

J. Y. Wang, B. Yang, S. K. Liao, L. Zhang, Q. Shen, X. F. Hu, J. C. Wu, S. J. Yang, 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. Photonics 7(5), 387–393 (2013).
[Crossref]

M. Zhang, J. C. Wu, L. Zhang, J. J. Jia, Z. P. He, S. J. Yang, F. Qian, and J. Y. Wang, “Real time basis-deviation measurement system based on BB84 module,” Proc. SPIE 8906, 890629 (2013).
[Crossref]

Yang, B.

J. Y. Wang, B. Yang, S. K. Liao, L. Zhang, Q. Shen, X. F. Hu, J. C. Wu, S. J. Yang, 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. Photonics 7(5), 387–393 (2013).
[Crossref]

Yang, S. J.

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M. Zhang, J. C. Wu, L. Zhang, J. J. Jia, Z. P. He, S. J. Yang, F. Qian, and J. Y. Wang, “Real time basis-deviation measurement system based on BB84 module,” Proc. SPIE 8906, 890629 (2013).
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C. Bonato, M. Aspelmeyer, T. Jennewein, C. Pernechele, P. Villoresi, and A. Zeilinger, “Influence of satellite motion on polarization qubits in a Space-Earth quantum communication link,” Opt. Express 14(21), 10050–10059 (2006).
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M. Zhang, J. C. Wu, L. Zhang, J. J. Jia, Z. P. He, S. J. Yang, F. Qian, and J. Y. Wang, “Real time basis-deviation measurement system based on BB84 module,” Proc. SPIE 8906, 890629 (2013).
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M. Zhang, J. C. Wu, L. Zhang, J. J. Jia, Z. P. He, S. J. Yang, F. Qian, and J. Y. Wang, “Real time basis-deviation measurement system based on BB84 module,” Proc. SPIE 8906, 890629 (2013).
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M. Aspelmeyer, T. Jennewein, M. Pfennigbauer, W. R. Leeb, and A. Zeilinger, “Long-Distance Quantum Communication With Entangled Photons Using Satellites,” IEEE J. Sel. Top. Quantum Electron. 9(6), 1541–1551 (2003).
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Figures (11)

Fig. 1
Fig. 1 Influence of satellite motion on basis vectors in a satellite-to-ground quantum communications link. (a) The ATP process for a satellite communicating with the OGS while the satellite executes its orbit. Points A and B are two specific points on the orbit. (b) The basis vectors of the satellite and the OGS change with the rotation of the telescope. H1A and H2A represent the basis vectors of the satellite and OGS, respectively, at Point A, and H1B and H2B represent the deflected basis vectors of the satellite and OGS, respectively, at Point B.
Fig. 2
Fig. 2 The ER of elliptic-polarized light: (a) the profile of elliptic-polarized light detected by the H/V base and (b) the profile of elliptic-polarized light with a basis deviation of θ detected by the H/V base.
Fig. 3
Fig. 3 The results for (a) the fraction of QBER caused by polarization error N ' and (b) the fraction caused by a basis deviation of Δ N as functions of basis deviation and ER.
Fig. 4
Fig. 4 The standard BB84 decoding module. IS: incident signal; BS: beam splitter; HWP: half-wave plate; PBS: polarization beam splitter; P: polarizer; FL: focusing lens; APD: avalanche-diode photo-detector.
Fig. 5
Fig. 5 The tabletop detection system with the BB84 decoding module.
Fig. 6
Fig. 6 (a) The relationship between calculation error and signal polarization angle. (b) Calculation angle as a function of q and k when the signal polarization angle is 45°.
Fig. 7
Fig. 7 The results for (a) the calculated polarization and (b) the detection accuracy as functions of basis deviation.
Fig. 8
Fig. 8 The light-rotation characteristics of the HWP, showing (a) the incident light and (b) the output light.
Fig. 9
Fig. 9 The basis-deviation compensation system in Bob’s terminal.
Fig. 10
Fig. 10 The Zhoushan voyage experiment. The sender (Alice) is mounted on a helicopter while the receiver (Bob) is mounted on the top floor of a building in an airport. Here, H, V, + , and −: pulse lasers with polarizations of H, V, + , and −, respectively; ATP: the acquisition, tracking, and pointing system; CCU: the central control unit; CCS: the classic communication system; HWP: the half-wave plate; and MS: motor stage.
Fig. 11
Fig. 11 The total counts of the four APDs ((a) and (c)) and the polarization detected by the receiver module ((b) and (d)) after basis-deviation compensation. The two sets of data ((a)-(b) and (c)-(d)) were acquired in the 10-km route.

Equations (17)

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θ= θ 1 + θ 2 .
E R = ( a b ) 2 = 1 tan 2 α .
N= 1 ER+1 .
R= |PP' | 2 |QQ' | 2 = ER cos 2 θ+ sin 2 θ cos 2 θ+ER sin 2 θ ,
N'= 1 R+1 = (ER+1)(ER1)cos2θ 2(ER+1) = N+ ER1 ER+1 sin 2 θ.
Δ N = N ' N = E R 1 E R + 1 sin 2 θ .
θ=arctan( n( nsin δ 2 +cos δ 2 1 m 2 n 2 )sin δ 2 mcos δ 2 )/2 +a π 2 ,
{ m=cos2αcos2θ= E H /( R H τ 1 ) E V /( R V τ 2 ) E H /( R H τ 1 )+ E V /( R V τ 2 ) n=cos δ 2 cos2αsin2θ+sin δ 2 sin2α= E + /( τ 3 ) E /( τ 4 ) E + /( τ 3 )+ E /( τ 4 ) × ( T H + T V )+( T H T V )m 2 T H T V
Δθ= θ c θ r .
η= η r 2 + η h 2 +2 η p 2 + η c 2 ,
ΔP= C d C + P v .
P E (1 ΔP 2 )P P E (1+ ΔP 2 ).
θ ' = arc tan ( n m ) / 2 = arc tan ( ( q y 1 q y + 1 ) / ( k x 1 k x + 1 ) ) / 2 + a π 2 .
{ x = E H E V = E R + 1 + ( E R - 1 ) cos 2 θ E R + 1 ( E R - 1 ) cos 2 θ y = E + E = E R + 1 + ( E R - 1 ) cos 2 ( θ 45 ° ) E R + 1 ( E R - 1 ) cos 2 ( θ 45 ° ) = E R + 1 + ( E R - 1 ) sin 2 θ E R + 1 ( E R - 1 ) sin 2 θ .
η c =arctan( ( q max y1 q max y+1 )/( k min x1 k min x+1 ) )/2+aa π 2 -arctan( ( q min y1 q min y+1 )/( k max x1 k max x+1 ) )/2bb π 2 ,
J H W P = [ cos 2 β , sin 2 β sin 2 β , cos 2 β ] .
S o u t = J H W P · S i n = [ cos 2 β , sin 2 β sin 2 β , cos 2 β ] [ cos α sin α ] = [ cos ( 2 β α ) sin ( 2 β α ) ] .

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