Abstract

In this paper, we propose a polarization-insensitive phase modulation scheme based on frequency modulation of light waves using either one or a pair of acousto-optic modulators. A stable Sagnac quantum key distribution (QKD) system employing this technique is also proposed. The interference visibility for a 40km and a 10km fiber loop is 96% and 99% respectively, at single-photon level. We ran standard BB84 QKD protocol in a simplified Sagnac setup (40km fiber loop) continuously for one hour and the measured quantum bit error rate stayed within 2%–5% range.

© 2006 Optical Society of America

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  1. C. H. Bennett and G. Brassard, "Quantum cryptography: public key distribution and coin tossing," in Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1984), pp.175-179.
  2. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, "Quantum cryptography," Rev. Mod. Phys. 74, 145-195 (2002).
    [CrossRef]
  3. R. J. Hughes, G. L. Morgan, and C. G. Peterson, "Quantum key distribution over a 48 km optical fiber network," J. of Mod. Opt. 47, 533-547 (2000).
  4. Z. Yuan and A. Shields, "Continuous operation of a one-way quantum key distribution system over installed telecom fibre," Opt. Express 13, 660-665 (2005).
    [CrossRef] [PubMed]
  5. A. Muller, T. Herzog, B. Huttner, W. Tittel, H. Zbinden, and N. Gisin, ‘‘Plug and play’’ systems for quantum cryptography," Appl. Phys. Lett. 70, 793-795 (1997).
    [CrossRef]
  6. T. Nishioka, H. Ishizuka, T. Hasegawa, and J. Abe, "Circular type" quantum key distribution," IEEE Photon. Technol. Lett. 14, 576-578 (2002).
    [CrossRef]
  7. C. Y. Zhou and H. P. Zeng, "Time-division single-photon Sagnac interferometer for quantum key distribution," Appl. Phys. Lett. 82, 832-834 (2003).
    [CrossRef]
  8. C. Y. Zhou, G. Wu, L. E. Ding and H. P. Zeng, "Single-photon routing by time-division phase modulation in a Sagnac interferometer," Appl. Phys. Lett. 83, 15-17 (2003).
    [CrossRef]
  9. P. D. Kumavor, A. C. Beal, S. Yelin, E. Donkor, B. C. Wang, "Comparison of four multi-user quantum key distribution schemes over passive optical networks," J. Lightwave Technol. 23, 268-276 (2005).
    [CrossRef]
  10. A. Stefanov, H. Zbinden, N. Gisin, and A. Suarez, "Quantum entanglement with acousto-optic modulators: Two-photon beats and Bell experiments with moving beam splitters," Phys. Rev. A 67, 042115 (2003).
    [CrossRef]
  11. E.-B. Li, J.-Q. Yao, D.-Y. Yu, J.-T. Xi, and J. Chicharo, "Optical phase shifting with acousto-optic devices," Opt. Lett. 30, 189-191 (2005).
    [CrossRef] [PubMed]
  12. D. B. Mortimore, "Fiber loop reflectors," J. Lightwave Technol. 6, 1217-1224 (1988).
    [CrossRef]
  13. Y. Zhao, B. Qi, X.-F. Ma, H.-K. Lo, L. Qian, "Experimental quantum key distribution with decoy states," Phys. Rev. Lett. 96, 070502 (2006).
    [CrossRef] [PubMed]
  14. C.-H. F. Fung, B. Qi, K. Tamaki, and H.-K. Lo, "Phase-remapping attack in practical quantum key distribution systems," arXiv:quant-ph/0601115 (2006) http://xxx.lanl.gov/abs/quant-ph/0601115

2006 (1)

Y. Zhao, B. Qi, X.-F. Ma, H.-K. Lo, L. Qian, "Experimental quantum key distribution with decoy states," Phys. Rev. Lett. 96, 070502 (2006).
[CrossRef] [PubMed]

2005 (3)

2003 (3)

A. Stefanov, H. Zbinden, N. Gisin, and A. Suarez, "Quantum entanglement with acousto-optic modulators: Two-photon beats and Bell experiments with moving beam splitters," Phys. Rev. A 67, 042115 (2003).
[CrossRef]

C. Y. Zhou and H. P. Zeng, "Time-division single-photon Sagnac interferometer for quantum key distribution," Appl. Phys. Lett. 82, 832-834 (2003).
[CrossRef]

C. Y. Zhou, G. Wu, L. E. Ding and H. P. Zeng, "Single-photon routing by time-division phase modulation in a Sagnac interferometer," Appl. Phys. Lett. 83, 15-17 (2003).
[CrossRef]

2002 (2)

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

T. Nishioka, H. Ishizuka, T. Hasegawa, and J. Abe, "Circular type" quantum key distribution," IEEE Photon. Technol. Lett. 14, 576-578 (2002).
[CrossRef]

2000 (1)

R. J. Hughes, G. L. Morgan, and C. G. Peterson, "Quantum key distribution over a 48 km optical fiber network," J. of Mod. Opt. 47, 533-547 (2000).

1997 (1)

A. Muller, T. Herzog, B. Huttner, W. Tittel, H. Zbinden, and N. Gisin, ‘‘Plug and play’’ systems for quantum cryptography," Appl. Phys. Lett. 70, 793-795 (1997).
[CrossRef]

1988 (1)

D. B. Mortimore, "Fiber loop reflectors," J. Lightwave Technol. 6, 1217-1224 (1988).
[CrossRef]

Abe, J.

T. Nishioka, H. Ishizuka, T. Hasegawa, and J. Abe, "Circular type" quantum key distribution," IEEE Photon. Technol. Lett. 14, 576-578 (2002).
[CrossRef]

Beal, A. C.

Chicharo, J.

Ding, L. E.

C. Y. Zhou, G. Wu, L. E. Ding and H. P. Zeng, "Single-photon routing by time-division phase modulation in a Sagnac interferometer," Appl. Phys. Lett. 83, 15-17 (2003).
[CrossRef]

Donkor, E.

Gisin, N.

A. Stefanov, H. Zbinden, N. Gisin, and A. Suarez, "Quantum entanglement with acousto-optic modulators: Two-photon beats and Bell experiments with moving beam splitters," Phys. Rev. A 67, 042115 (2003).
[CrossRef]

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

A. Muller, T. Herzog, B. Huttner, W. Tittel, H. Zbinden, and N. Gisin, ‘‘Plug and play’’ systems for quantum cryptography," Appl. Phys. Lett. 70, 793-795 (1997).
[CrossRef]

Hasegawa, T.

T. Nishioka, H. Ishizuka, T. Hasegawa, and J. Abe, "Circular type" quantum key distribution," IEEE Photon. Technol. Lett. 14, 576-578 (2002).
[CrossRef]

Herzog, T.

A. Muller, T. Herzog, B. Huttner, W. Tittel, H. Zbinden, and N. Gisin, ‘‘Plug and play’’ systems for quantum cryptography," Appl. Phys. Lett. 70, 793-795 (1997).
[CrossRef]

Hughes, R. J.

R. J. Hughes, G. L. Morgan, and C. G. Peterson, "Quantum key distribution over a 48 km optical fiber network," J. of Mod. Opt. 47, 533-547 (2000).

Huttner, B.

A. Muller, T. Herzog, B. Huttner, W. Tittel, H. Zbinden, and N. Gisin, ‘‘Plug and play’’ systems for quantum cryptography," Appl. Phys. Lett. 70, 793-795 (1997).
[CrossRef]

Ishizuka, H.

T. Nishioka, H. Ishizuka, T. Hasegawa, and J. Abe, "Circular type" quantum key distribution," IEEE Photon. Technol. Lett. 14, 576-578 (2002).
[CrossRef]

Kumavor, P. D.

Li, E.-B.

Lo, H.-K.

Y. Zhao, B. Qi, X.-F. Ma, H.-K. Lo, L. Qian, "Experimental quantum key distribution with decoy states," Phys. Rev. Lett. 96, 070502 (2006).
[CrossRef] [PubMed]

Ma, X.-F.

Y. Zhao, B. Qi, X.-F. Ma, H.-K. Lo, L. Qian, "Experimental quantum key distribution with decoy states," Phys. Rev. Lett. 96, 070502 (2006).
[CrossRef] [PubMed]

Morgan, G. L.

R. J. Hughes, G. L. Morgan, and C. G. Peterson, "Quantum key distribution over a 48 km optical fiber network," J. of Mod. Opt. 47, 533-547 (2000).

Mortimore, D. B.

D. B. Mortimore, "Fiber loop reflectors," J. Lightwave Technol. 6, 1217-1224 (1988).
[CrossRef]

Muller, A.

A. Muller, T. Herzog, B. Huttner, W. Tittel, H. Zbinden, and N. Gisin, ‘‘Plug and play’’ systems for quantum cryptography," Appl. Phys. Lett. 70, 793-795 (1997).
[CrossRef]

Nishioka, T.

T. Nishioka, H. Ishizuka, T. Hasegawa, and J. Abe, "Circular type" quantum key distribution," IEEE Photon. Technol. Lett. 14, 576-578 (2002).
[CrossRef]

Peterson, C. G.

R. J. Hughes, G. L. Morgan, and C. G. Peterson, "Quantum key distribution over a 48 km optical fiber network," J. of Mod. Opt. 47, 533-547 (2000).

Qi, B.

Y. Zhao, B. Qi, X.-F. Ma, H.-K. Lo, L. Qian, "Experimental quantum key distribution with decoy states," Phys. Rev. Lett. 96, 070502 (2006).
[CrossRef] [PubMed]

Qian, L.

Y. Zhao, B. Qi, X.-F. Ma, H.-K. Lo, L. Qian, "Experimental quantum key distribution with decoy states," Phys. Rev. Lett. 96, 070502 (2006).
[CrossRef] [PubMed]

Ribordy, G.

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

Shields, A.

Stefanov, A.

A. Stefanov, H. Zbinden, N. Gisin, and A. Suarez, "Quantum entanglement with acousto-optic modulators: Two-photon beats and Bell experiments with moving beam splitters," Phys. Rev. A 67, 042115 (2003).
[CrossRef]

Suarez, A.

A. Stefanov, H. Zbinden, N. Gisin, and A. Suarez, "Quantum entanglement with acousto-optic modulators: Two-photon beats and Bell experiments with moving beam splitters," Phys. Rev. A 67, 042115 (2003).
[CrossRef]

Tittel, W.

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

A. Muller, T. Herzog, B. Huttner, W. Tittel, H. Zbinden, and N. Gisin, ‘‘Plug and play’’ systems for quantum cryptography," Appl. Phys. Lett. 70, 793-795 (1997).
[CrossRef]

Wang, B. C.

Wu, G.

C. Y. Zhou, G. Wu, L. E. Ding and H. P. Zeng, "Single-photon routing by time-division phase modulation in a Sagnac interferometer," Appl. Phys. Lett. 83, 15-17 (2003).
[CrossRef]

Xi, J.-T.

Yao, J.-Q.

Yelin, S.

Yu, D.-Y.

Yuan, Z.

Zbinden, H.

A. Stefanov, H. Zbinden, N. Gisin, and A. Suarez, "Quantum entanglement with acousto-optic modulators: Two-photon beats and Bell experiments with moving beam splitters," Phys. Rev. A 67, 042115 (2003).
[CrossRef]

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

A. Muller, T. Herzog, B. Huttner, W. Tittel, H. Zbinden, and N. Gisin, ‘‘Plug and play’’ systems for quantum cryptography," Appl. Phys. Lett. 70, 793-795 (1997).
[CrossRef]

Zeng, H. P.

C. Y. Zhou, G. Wu, L. E. Ding and H. P. Zeng, "Single-photon routing by time-division phase modulation in a Sagnac interferometer," Appl. Phys. Lett. 83, 15-17 (2003).
[CrossRef]

C. Y. Zhou and H. P. Zeng, "Time-division single-photon Sagnac interferometer for quantum key distribution," Appl. Phys. Lett. 82, 832-834 (2003).
[CrossRef]

Zhao, Y.

Y. Zhao, B. Qi, X.-F. Ma, H.-K. Lo, L. Qian, "Experimental quantum key distribution with decoy states," Phys. Rev. Lett. 96, 070502 (2006).
[CrossRef] [PubMed]

Zhou, C. Y.

C. Y. Zhou, G. Wu, L. E. Ding and H. P. Zeng, "Single-photon routing by time-division phase modulation in a Sagnac interferometer," Appl. Phys. Lett. 83, 15-17 (2003).
[CrossRef]

C. Y. Zhou and H. P. Zeng, "Time-division single-photon Sagnac interferometer for quantum key distribution," Appl. Phys. Lett. 82, 832-834 (2003).
[CrossRef]

Appl. Phys. Lett. (3)

C. Y. Zhou and H. P. Zeng, "Time-division single-photon Sagnac interferometer for quantum key distribution," Appl. Phys. Lett. 82, 832-834 (2003).
[CrossRef]

C. Y. Zhou, G. Wu, L. E. Ding and H. P. Zeng, "Single-photon routing by time-division phase modulation in a Sagnac interferometer," Appl. Phys. Lett. 83, 15-17 (2003).
[CrossRef]

A. Muller, T. Herzog, B. Huttner, W. Tittel, H. Zbinden, and N. Gisin, ‘‘Plug and play’’ systems for quantum cryptography," Appl. Phys. Lett. 70, 793-795 (1997).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

T. Nishioka, H. Ishizuka, T. Hasegawa, and J. Abe, "Circular type" quantum key distribution," IEEE Photon. Technol. Lett. 14, 576-578 (2002).
[CrossRef]

J. Lightwave Technol. (2)

J. of Mod. Opt. (1)

R. J. Hughes, G. L. Morgan, and C. G. Peterson, "Quantum key distribution over a 48 km optical fiber network," J. of Mod. Opt. 47, 533-547 (2000).

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (1)

A. Stefanov, H. Zbinden, N. Gisin, and A. Suarez, "Quantum entanglement with acousto-optic modulators: Two-photon beats and Bell experiments with moving beam splitters," Phys. Rev. A 67, 042115 (2003).
[CrossRef]

Phys. Rev. Lett. (1)

Y. Zhao, B. Qi, X.-F. Ma, H.-K. Lo, L. Qian, "Experimental quantum key distribution with decoy states," Phys. Rev. Lett. 96, 070502 (2006).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

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

Other (2)

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

C.-H. F. Fung, B. Qi, K. Tamaki, and H.-K. Lo, "Phase-remapping attack in practical quantum key distribution systems," arXiv:quant-ph/0601115 (2006) http://xxx.lanl.gov/abs/quant-ph/0601115

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Figures (6)

Fig.1.
Fig.1.

a) A phase modulator with one frequency up-shifter; (b) A phase modulator with a pair of frequency shifters. +: up-shifting AOM,-down-shifting AOM, L: fiber with length L, D: AOM driver

Fig. 2.
Fig. 2.

The experimental results at 1MHz phase modulation rate. (a) one AOM; (b) a pair of AOM.

Fig. 3.
Fig. 3.

Proposed QKD system: LD—pulsed laser diode; Cir—circulator; C—2×2 coupler; PC—polarization controller; PM1, PM2—AOM-based phase modulator (as shown in Fig. 1); SPD1, SPD2—single Photon detector

Fig. 4.
Fig. 4.

Experimental setup: L—1550nm cw laser; AM—amplitude modulator; Att—attenuator; Cir—circulator; C—2×2 coupler; PC—polarization controller; FG1, FG2—function generator; PG—pulse generator; DG—delay generator; SPD1, SPD2—single photon detector

Fig. 5.
Fig. 5.

The visibility of interference pattern is 96% for a 40km fiber loop (Dotted line—Ch1, Circular line—Ch2. Acquired at a photon level of 0.8 photon/pulse)

Fig. 6.
Fig. 6.

Measured QBER in one hour without any feedback control. The photon level is 0.8 photon/pulse (The error bars indicate the statistic fluctuation due to the finite detection events)

Equations (3)

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t 2 t 1 = n L c .
Δ ϕ = ϕ ( t 2 ) ϕ ( t 1 ) = 2 π f ( t 2 t 1 ) = 2 π n L f c .
Δ ϕ = ϕ S 2 ϕ S 1 = 4 π n L f c .

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