Abstract

A new technique for phase tracking in quantum cryptography systems is proposed that adjusts phase in an optimal way, using only as many photon counts as necessary. We derive an upper bound on the number of photons that need to be registered during phase adjustment to achieve a given phase accuracy. It turns out that most quantum cryptosystems can successfully track phase on a single-photon level, entirely with software, without any additional hardware components or extensive phase-stabilization measures. The technique is tested experimentally on a quantum cryptosystem.

© 2004 Optical Society of America

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References

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  1. C. Marand, P. Townsend, “Quantum key distribution over distances as long as 30 km,” Opt. Lett. 20, 1695–1697 (1995).
    [CrossRef] [PubMed]
  2. The threshold value of QBER is still being discussed. Most recent strict security analyses, however, put it at 11%. For a review, see for example Refs. 3 and 4 and references therein.
  3. N. Gisin, G. Ribordy, W. Tittel, H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
    [CrossRef]
  4. M. Bourenanne, A. Karlsson, G. Bjork, N. Gisin, N. J. Cerf, “Quantum key distribution using multilevel encoding: security analysis,” J. Phys. A Math. Gen. 35, 10,065–10,076 (2002).
    [CrossRef]
  5. M. Martinelli, “A universal compensator for polarization changes induced by birefringence on a retracting beam,” Opt. Commun. 72, 341–344 (1989).
    [CrossRef]
  6. M. Martinelli, “Time reversal for the polarization state in optical systems,” J. Mod. Opt. 39, 451–455 (1992).
    [CrossRef]
  7. H. Zbinden, J. D. Gautier, N. Gisin, B. Huttner, A. Muller, W. Tittel, “Interferometry with Faraday mirrors for quantum cryptography,” Electron. Lett. 33, 586–588 (1997).
    [CrossRef]
  8. D. Stucki, N. Gisin, O. Guinnard, G. Ribordy, H. Zbinden, “Quantum key distribution over 67 km with a plug play system,” New J. Phys. 4, 41.1–41.8 (2002).
    [CrossRef]
  9. As of March 2004, one could place an order for a complete quantum cryptosystem with a plug and play type of optical scheme with two companies: id Quantique (Geneva, Switzerland, http://www.idquantique.com/ ) and MagiQ Technologies (Boston, Mass., http://www.magiqtech.com/ ).
  10. A. Vakhitov, V. Makarov, D. R. Hjelme, “Large pulse attack as a method of conventional optical eavesdropping in quantum cryptography,” J. Mod. Opt. 48, 2023–2038 (2001).
  11. G. Ribordy, J.-D. Gautier, N. Gisin, O. Guinnard, H. Zbinden, “Automated plug play quantum key distribution,” Electron. Lett. 34, 2116–2117 (1998).
    [CrossRef]
  12. W. Tittel, J. Brendel, H. Zbinden, N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84, 4737–4740 (2000).
    [CrossRef] [PubMed]
  13. W. Tittel, J. Brendel, N. Gisin, H. Zbinden, “Long-distance Bell-type tests using energy-time entangled photons,” Phys. Rev. A 59, 4150–4163 (1999).
    [CrossRef]
  14. G. Ribordy, J. Brendel, J.-D. Gautier, N. Gisin, H. Zbinden, “Long-distance entanglement-based quantum key distribution,” Phys. Rev. A 63, 012309 (2001).
    [CrossRef]
  15. Hugo. Zbinden, Group of Applied Physics—Optique, Université de Genève, Rue de l’École-de-Médecine 20, CH-1211 Geneva 4, Switzerland (personal communication, 2001).
  16. S. Pellegrini, “EQUIS project,” http://www.phy.hw.ac.uk/resrev/EQUIS/ ; see p. WP4, “Integrated Mach-Zehnder/Michelson interferometer.”
  17. G. Bonfrate, “Integrated optics for practical quantum cryptography systems,” presented at the Second Quantum Information Processing and Communications Workshop, Turin, Italy, 28–31 October 2001.
  18. R. Hughes, G. Morgan, C. Peterson, “Practical quantum key distribution over a 48-km optical fiber network,” J. Mod. Opt. 47, 533–547 (2000).
  19. P. Townsend, J. Rarity, P. Tapster, “Enhanced single photon fringe visibility in a 10 km-long prototype quantum cryptography channel,” Electron. Letters 29, 1291–1293 (1993).
    [CrossRef]
  20. A. Brylevski, “Quantum key distribution: real-time compensation of interferometer phase drift,” M.S. thesis [written at the Department of Physical Electronics, Norwegian University of Science and Technology (NTNU) and defended at the Department of Radiophysics, St. Petersburg State Technical University, St. Petersburg, Russia, 2002], http://www.vad1.com/qcr/alexey/ .
  21. C. H. Bennett, G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1984), pp. 175–179.
  22. K. Vylegjanine, “High-speed single photon detector for quantum cryptosystems,” M.S. thesis [written at the Department of Physical Electronics, Norwegian University of Science and Technology (NTNU) and defended at the Department of Radiophysics, St. Petersburg State Technical University, St. Petersburg, Russia, 2000], http://www.vad1.com/qcr/kirill/ .

2002 (3)

N. Gisin, G. Ribordy, W. Tittel, H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

M. Bourenanne, A. Karlsson, G. Bjork, N. Gisin, N. J. Cerf, “Quantum key distribution using multilevel encoding: security analysis,” J. Phys. A Math. Gen. 35, 10,065–10,076 (2002).
[CrossRef]

D. Stucki, N. Gisin, O. Guinnard, G. Ribordy, H. Zbinden, “Quantum key distribution over 67 km with a plug play system,” New J. Phys. 4, 41.1–41.8 (2002).
[CrossRef]

2001 (2)

A. Vakhitov, V. Makarov, D. R. Hjelme, “Large pulse attack as a method of conventional optical eavesdropping in quantum cryptography,” J. Mod. Opt. 48, 2023–2038 (2001).

G. Ribordy, J. Brendel, J.-D. Gautier, N. Gisin, H. Zbinden, “Long-distance entanglement-based quantum key distribution,” Phys. Rev. A 63, 012309 (2001).
[CrossRef]

2000 (2)

R. Hughes, G. Morgan, C. Peterson, “Practical quantum key distribution over a 48-km optical fiber network,” J. Mod. Opt. 47, 533–547 (2000).

W. Tittel, J. Brendel, H. Zbinden, N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84, 4737–4740 (2000).
[CrossRef] [PubMed]

1999 (1)

W. Tittel, J. Brendel, N. Gisin, H. Zbinden, “Long-distance Bell-type tests using energy-time entangled photons,” Phys. Rev. A 59, 4150–4163 (1999).
[CrossRef]

1998 (1)

G. Ribordy, J.-D. Gautier, N. Gisin, O. Guinnard, H. Zbinden, “Automated plug play quantum key distribution,” Electron. Lett. 34, 2116–2117 (1998).
[CrossRef]

1997 (1)

H. Zbinden, J. D. Gautier, N. Gisin, B. Huttner, A. Muller, W. Tittel, “Interferometry with Faraday mirrors for quantum cryptography,” Electron. Lett. 33, 586–588 (1997).
[CrossRef]

1995 (1)

1993 (1)

P. Townsend, J. Rarity, P. Tapster, “Enhanced single photon fringe visibility in a 10 km-long prototype quantum cryptography channel,” Electron. Letters 29, 1291–1293 (1993).
[CrossRef]

1992 (1)

M. Martinelli, “Time reversal for the polarization state in optical systems,” J. Mod. Opt. 39, 451–455 (1992).
[CrossRef]

1989 (1)

M. Martinelli, “A universal compensator for polarization changes induced by birefringence on a retracting beam,” Opt. Commun. 72, 341–344 (1989).
[CrossRef]

Bennett, C. H.

C. H. Bennett, G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1984), pp. 175–179.

Bjork, G.

M. Bourenanne, A. Karlsson, G. Bjork, N. Gisin, N. J. Cerf, “Quantum key distribution using multilevel encoding: security analysis,” J. Phys. A Math. Gen. 35, 10,065–10,076 (2002).
[CrossRef]

Bonfrate, G.

G. Bonfrate, “Integrated optics for practical quantum cryptography systems,” presented at the Second Quantum Information Processing and Communications Workshop, Turin, Italy, 28–31 October 2001.

Bourenanne, M.

M. Bourenanne, A. Karlsson, G. Bjork, N. Gisin, N. J. Cerf, “Quantum key distribution using multilevel encoding: security analysis,” J. Phys. A Math. Gen. 35, 10,065–10,076 (2002).
[CrossRef]

Brassard, G.

C. H. Bennett, G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1984), pp. 175–179.

Brendel, J.

G. Ribordy, J. Brendel, J.-D. Gautier, N. Gisin, H. Zbinden, “Long-distance entanglement-based quantum key distribution,” Phys. Rev. A 63, 012309 (2001).
[CrossRef]

W. Tittel, J. Brendel, H. Zbinden, N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84, 4737–4740 (2000).
[CrossRef] [PubMed]

W. Tittel, J. Brendel, N. Gisin, H. Zbinden, “Long-distance Bell-type tests using energy-time entangled photons,” Phys. Rev. A 59, 4150–4163 (1999).
[CrossRef]

Cerf, N. J.

M. Bourenanne, A. Karlsson, G. Bjork, N. Gisin, N. J. Cerf, “Quantum key distribution using multilevel encoding: security analysis,” J. Phys. A Math. Gen. 35, 10,065–10,076 (2002).
[CrossRef]

Gautier, J. D.

H. Zbinden, J. D. Gautier, N. Gisin, B. Huttner, A. Muller, W. Tittel, “Interferometry with Faraday mirrors for quantum cryptography,” Electron. Lett. 33, 586–588 (1997).
[CrossRef]

Gautier, J.-D.

G. Ribordy, J. Brendel, J.-D. Gautier, N. Gisin, H. Zbinden, “Long-distance entanglement-based quantum key distribution,” Phys. Rev. A 63, 012309 (2001).
[CrossRef]

G. Ribordy, J.-D. Gautier, N. Gisin, O. Guinnard, H. Zbinden, “Automated plug play quantum key distribution,” Electron. Lett. 34, 2116–2117 (1998).
[CrossRef]

Gisin, N.

D. Stucki, N. Gisin, O. Guinnard, G. Ribordy, H. Zbinden, “Quantum key distribution over 67 km with a plug play system,” New J. Phys. 4, 41.1–41.8 (2002).
[CrossRef]

M. Bourenanne, A. Karlsson, G. Bjork, N. Gisin, N. J. Cerf, “Quantum key distribution using multilevel encoding: security analysis,” J. Phys. A Math. Gen. 35, 10,065–10,076 (2002).
[CrossRef]

N. Gisin, G. Ribordy, W. Tittel, H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

G. Ribordy, J. Brendel, J.-D. Gautier, N. Gisin, H. Zbinden, “Long-distance entanglement-based quantum key distribution,” Phys. Rev. A 63, 012309 (2001).
[CrossRef]

W. Tittel, J. Brendel, H. Zbinden, N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84, 4737–4740 (2000).
[CrossRef] [PubMed]

W. Tittel, J. Brendel, N. Gisin, H. Zbinden, “Long-distance Bell-type tests using energy-time entangled photons,” Phys. Rev. A 59, 4150–4163 (1999).
[CrossRef]

G. Ribordy, J.-D. Gautier, N. Gisin, O. Guinnard, H. Zbinden, “Automated plug play quantum key distribution,” Electron. Lett. 34, 2116–2117 (1998).
[CrossRef]

H. Zbinden, J. D. Gautier, N. Gisin, B. Huttner, A. Muller, W. Tittel, “Interferometry with Faraday mirrors for quantum cryptography,” Electron. Lett. 33, 586–588 (1997).
[CrossRef]

Guinnard, O.

D. Stucki, N. Gisin, O. Guinnard, G. Ribordy, H. Zbinden, “Quantum key distribution over 67 km with a plug play system,” New J. Phys. 4, 41.1–41.8 (2002).
[CrossRef]

G. Ribordy, J.-D. Gautier, N. Gisin, O. Guinnard, H. Zbinden, “Automated plug play quantum key distribution,” Electron. Lett. 34, 2116–2117 (1998).
[CrossRef]

Hjelme, D. R.

A. Vakhitov, V. Makarov, D. R. Hjelme, “Large pulse attack as a method of conventional optical eavesdropping in quantum cryptography,” J. Mod. Opt. 48, 2023–2038 (2001).

Hughes, R.

R. Hughes, G. Morgan, C. Peterson, “Practical quantum key distribution over a 48-km optical fiber network,” J. Mod. Opt. 47, 533–547 (2000).

Huttner, B.

H. Zbinden, J. D. Gautier, N. Gisin, B. Huttner, A. Muller, W. Tittel, “Interferometry with Faraday mirrors for quantum cryptography,” Electron. Lett. 33, 586–588 (1997).
[CrossRef]

Karlsson, A.

M. Bourenanne, A. Karlsson, G. Bjork, N. Gisin, N. J. Cerf, “Quantum key distribution using multilevel encoding: security analysis,” J. Phys. A Math. Gen. 35, 10,065–10,076 (2002).
[CrossRef]

Makarov, V.

A. Vakhitov, V. Makarov, D. R. Hjelme, “Large pulse attack as a method of conventional optical eavesdropping in quantum cryptography,” J. Mod. Opt. 48, 2023–2038 (2001).

Marand, C.

Martinelli, M.

M. Martinelli, “Time reversal for the polarization state in optical systems,” J. Mod. Opt. 39, 451–455 (1992).
[CrossRef]

M. Martinelli, “A universal compensator for polarization changes induced by birefringence on a retracting beam,” Opt. Commun. 72, 341–344 (1989).
[CrossRef]

Morgan, G.

R. Hughes, G. Morgan, C. Peterson, “Practical quantum key distribution over a 48-km optical fiber network,” J. Mod. Opt. 47, 533–547 (2000).

Muller, A.

H. Zbinden, J. D. Gautier, N. Gisin, B. Huttner, A. Muller, W. Tittel, “Interferometry with Faraday mirrors for quantum cryptography,” Electron. Lett. 33, 586–588 (1997).
[CrossRef]

Peterson, C.

R. Hughes, G. Morgan, C. Peterson, “Practical quantum key distribution over a 48-km optical fiber network,” J. Mod. Opt. 47, 533–547 (2000).

Rarity, J.

P. Townsend, J. Rarity, P. Tapster, “Enhanced single photon fringe visibility in a 10 km-long prototype quantum cryptography channel,” Electron. Letters 29, 1291–1293 (1993).
[CrossRef]

Ribordy, G.

N. Gisin, G. Ribordy, W. Tittel, H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

D. Stucki, N. Gisin, O. Guinnard, G. Ribordy, H. Zbinden, “Quantum key distribution over 67 km with a plug play system,” New J. Phys. 4, 41.1–41.8 (2002).
[CrossRef]

G. Ribordy, J. Brendel, J.-D. Gautier, N. Gisin, H. Zbinden, “Long-distance entanglement-based quantum key distribution,” Phys. Rev. A 63, 012309 (2001).
[CrossRef]

G. Ribordy, J.-D. Gautier, N. Gisin, O. Guinnard, H. Zbinden, “Automated plug play quantum key distribution,” Electron. Lett. 34, 2116–2117 (1998).
[CrossRef]

Stucki, D.

D. Stucki, N. Gisin, O. Guinnard, G. Ribordy, H. Zbinden, “Quantum key distribution over 67 km with a plug play system,” New J. Phys. 4, 41.1–41.8 (2002).
[CrossRef]

Tapster, P.

P. Townsend, J. Rarity, P. Tapster, “Enhanced single photon fringe visibility in a 10 km-long prototype quantum cryptography channel,” Electron. Letters 29, 1291–1293 (1993).
[CrossRef]

Tittel, W.

N. Gisin, G. Ribordy, W. Tittel, H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

W. Tittel, J. Brendel, H. Zbinden, N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84, 4737–4740 (2000).
[CrossRef] [PubMed]

W. Tittel, J. Brendel, N. Gisin, H. Zbinden, “Long-distance Bell-type tests using energy-time entangled photons,” Phys. Rev. A 59, 4150–4163 (1999).
[CrossRef]

H. Zbinden, J. D. Gautier, N. Gisin, B. Huttner, A. Muller, W. Tittel, “Interferometry with Faraday mirrors for quantum cryptography,” Electron. Lett. 33, 586–588 (1997).
[CrossRef]

Townsend, P.

C. Marand, P. Townsend, “Quantum key distribution over distances as long as 30 km,” Opt. Lett. 20, 1695–1697 (1995).
[CrossRef] [PubMed]

P. Townsend, J. Rarity, P. Tapster, “Enhanced single photon fringe visibility in a 10 km-long prototype quantum cryptography channel,” Electron. Letters 29, 1291–1293 (1993).
[CrossRef]

Vakhitov, A.

A. Vakhitov, V. Makarov, D. R. Hjelme, “Large pulse attack as a method of conventional optical eavesdropping in quantum cryptography,” J. Mod. Opt. 48, 2023–2038 (2001).

Zbinden, H.

D. Stucki, N. Gisin, O. Guinnard, G. Ribordy, H. Zbinden, “Quantum key distribution over 67 km with a plug play system,” New J. Phys. 4, 41.1–41.8 (2002).
[CrossRef]

N. Gisin, G. Ribordy, W. Tittel, H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

G. Ribordy, J. Brendel, J.-D. Gautier, N. Gisin, H. Zbinden, “Long-distance entanglement-based quantum key distribution,” Phys. Rev. A 63, 012309 (2001).
[CrossRef]

W. Tittel, J. Brendel, H. Zbinden, N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84, 4737–4740 (2000).
[CrossRef] [PubMed]

W. Tittel, J. Brendel, N. Gisin, H. Zbinden, “Long-distance Bell-type tests using energy-time entangled photons,” Phys. Rev. A 59, 4150–4163 (1999).
[CrossRef]

G. Ribordy, J.-D. Gautier, N. Gisin, O. Guinnard, H. Zbinden, “Automated plug play quantum key distribution,” Electron. Lett. 34, 2116–2117 (1998).
[CrossRef]

H. Zbinden, J. D. Gautier, N. Gisin, B. Huttner, A. Muller, W. Tittel, “Interferometry with Faraday mirrors for quantum cryptography,” Electron. Lett. 33, 586–588 (1997).
[CrossRef]

Zbinden, Hugo.

Hugo. Zbinden, Group of Applied Physics—Optique, Université de Genève, Rue de l’École-de-Médecine 20, CH-1211 Geneva 4, Switzerland (personal communication, 2001).

Electron. Lett. (2)

H. Zbinden, J. D. Gautier, N. Gisin, B. Huttner, A. Muller, W. Tittel, “Interferometry with Faraday mirrors for quantum cryptography,” Electron. Lett. 33, 586–588 (1997).
[CrossRef]

G. Ribordy, J.-D. Gautier, N. Gisin, O. Guinnard, H. Zbinden, “Automated plug play quantum key distribution,” Electron. Lett. 34, 2116–2117 (1998).
[CrossRef]

Electron. Letters (1)

P. Townsend, J. Rarity, P. Tapster, “Enhanced single photon fringe visibility in a 10 km-long prototype quantum cryptography channel,” Electron. Letters 29, 1291–1293 (1993).
[CrossRef]

J. Mod. Opt. (3)

A. Vakhitov, V. Makarov, D. R. Hjelme, “Large pulse attack as a method of conventional optical eavesdropping in quantum cryptography,” J. Mod. Opt. 48, 2023–2038 (2001).

R. Hughes, G. Morgan, C. Peterson, “Practical quantum key distribution over a 48-km optical fiber network,” J. Mod. Opt. 47, 533–547 (2000).

M. Martinelli, “Time reversal for the polarization state in optical systems,” J. Mod. Opt. 39, 451–455 (1992).
[CrossRef]

J. Phys. A Math. Gen. (1)

M. Bourenanne, A. Karlsson, G. Bjork, N. Gisin, N. J. Cerf, “Quantum key distribution using multilevel encoding: security analysis,” J. Phys. A Math. Gen. 35, 10,065–10,076 (2002).
[CrossRef]

New J. Phys. (1)

D. Stucki, N. Gisin, O. Guinnard, G. Ribordy, H. Zbinden, “Quantum key distribution over 67 km with a plug play system,” New J. Phys. 4, 41.1–41.8 (2002).
[CrossRef]

Opt. Commun. (1)

M. Martinelli, “A universal compensator for polarization changes induced by birefringence on a retracting beam,” Opt. Commun. 72, 341–344 (1989).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (2)

W. Tittel, J. Brendel, N. Gisin, H. Zbinden, “Long-distance Bell-type tests using energy-time entangled photons,” Phys. Rev. A 59, 4150–4163 (1999).
[CrossRef]

G. Ribordy, J. Brendel, J.-D. Gautier, N. Gisin, H. Zbinden, “Long-distance entanglement-based quantum key distribution,” Phys. Rev. A 63, 012309 (2001).
[CrossRef]

Phys. Rev. Lett. (1)

W. Tittel, J. Brendel, H. Zbinden, N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84, 4737–4740 (2000).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

N. Gisin, G. Ribordy, W. Tittel, H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

Other (8)

As of March 2004, one could place an order for a complete quantum cryptosystem with a plug and play type of optical scheme with two companies: id Quantique (Geneva, Switzerland, http://www.idquantique.com/ ) and MagiQ Technologies (Boston, Mass., http://www.magiqtech.com/ ).

The threshold value of QBER is still being discussed. Most recent strict security analyses, however, put it at 11%. For a review, see for example Refs. 3 and 4 and references therein.

Hugo. Zbinden, Group of Applied Physics—Optique, Université de Genève, Rue de l’École-de-Médecine 20, CH-1211 Geneva 4, Switzerland (personal communication, 2001).

S. Pellegrini, “EQUIS project,” http://www.phy.hw.ac.uk/resrev/EQUIS/ ; see p. WP4, “Integrated Mach-Zehnder/Michelson interferometer.”

G. Bonfrate, “Integrated optics for practical quantum cryptography systems,” presented at the Second Quantum Information Processing and Communications Workshop, Turin, Italy, 28–31 October 2001.

A. Brylevski, “Quantum key distribution: real-time compensation of interferometer phase drift,” M.S. thesis [written at the Department of Physical Electronics, Norwegian University of Science and Technology (NTNU) and defended at the Department of Radiophysics, St. Petersburg State Technical University, St. Petersburg, Russia, 2002], http://www.vad1.com/qcr/alexey/ .

C. H. Bennett, G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1984), pp. 175–179.

K. Vylegjanine, “High-speed single photon detector for quantum cryptosystems,” M.S. thesis [written at the Department of Physical Electronics, Norwegian University of Science and Technology (NTNU) and defended at the Department of Radiophysics, St. Petersburg State Technical University, St. Petersburg, Russia, 2000], http://www.vad1.com/qcr/kirill/ .

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Figures (7)

Fig. 1
Fig. 1

QBER versus interferometer phase mismatch in the absence of other sources of error.

Fig. 2
Fig. 2

Illustration of phase adjustment at stage 2. Only the interference curve for the 0 time slot is shown.

Fig. 3
Fig. 3

QKD setup: SM, single-mode; other abbreviations defined in text.

Fig. 4
Fig. 4

Bob’s interferometer. All components are mounted on a 400 mm × 400 mm × 6 mm aluminum plate, and their fiber pigtails are affixed to the plate surface with pieces of adhesive tape. Everything is covered by custom-cut pieces of foam insulation (not shown in the photo) and mounted inside a box. Alice’s interferometer is similar.

Fig. 5
Fig. 5

Interference curves for the 0 (filled squares) and 1 (open squares) time slots, plotted from data measured in a single run of stage 1 phase adjustment. The 2π phase range was scanned in 16 steps, and on average 150 counts were collected in stage 1.

Fig. 6
Fig. 6

Voltage in Bob’s phase modulator, scaled to the equivalent phase shift. A 1-h fragment of phase tracking data from a test run with both stage 1 and stage 2 phase adjustment performed each time. Phase adjustment is run every 3 s; the average number of counts collected in stage 1 is 150 and in stage 2 is 230. Vertical hops in the figures do not represent any phase discontinuity (the phase is cyclic over 2π) but do represent jumps in phase modulator voltage, because we had to stay within the voltage range of our phase modulators limited to just over ±V π. If we neglected jumps in phase modulator voltage and printed cylindrically shaped graphs for phase, there would be no hops on them.

Fig. 7
Fig. 7

Voltage of Bob’s phase modulator, scaled to the equivalent phase shift. A 1-h fragment of phase tracking data from a test run with only stage 2 of the phase adjustment performed each time. Phase compensation from previous phase adjustment is used as input to stage 2. Phase adjustment is run every 3 s, and the average number of counts is 230 for each adjustment.

Equations (11)

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

QBERopt Δφ=sin2Δφ/2,
Function 0 N=Nmax-Nminsin2φ-φ02+NminFunction 1 N=Nmax-Nminsin2φ-φ0+δ2+Nmin, δ=φ1-φ0.
δ=14arccos2 Nmin 0-N0+Nmax 0-Nmin 0+1-arccos2 Nmin 0-N0-Nmax 0-Nmin 0+1+arccos2 Nmin 1-N1-Nmax 1-Nmin 1+1-arccos2 Nmin 1-N1+Nmax 1-Nmin 1+1.
N=Nmax-Nminsin2φ-φ12+Nmin,
dNdφ=12Nmax-Nminsinφ-φ1.
ΔNΔφ=12Nmax-Nmin.
ΔN=kσ=kNmax/2,
Nmax=2k2/Δφ2.
N0++N0-=2k2/Δφ2.
N0++N0-+N1++N1-=2k2/Δφ2.
N0++N0-+N1++N1-=2 2210°/180°π2=262 counts

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