Abstract

We report the first Sagnac quantum secret sharing (in three-and four-party implementations) over 1550 nm single mode fiber (SMF) networks, using a single qubit protocol with phase encoding. Our secret sharing experiment has been based on a single qubit protocol, which has opened the door to practical secret sharing implementation over fiber telecom channels and in free-space. The previous quantum secret sharing proposals were based on multiparticle entangled states, difficult in the practical implementation and not scalable. Our experimental data in the three-party implementation show stable (in regards to birefringence drift) quantum secret sharing transmissions at the total Sagnac transmission loop distances of 55-75 km with the quantum bit error rates (QBER) of 2.3-2.4% for the mean photon number μ = 0.1 and 1.7-2.1% for μ = 0.3. In the four-party case we have achieved quantum secret sharing transmissions at the total Sagnac transmission loop distances of 45-55 km with the quantum bit error rates (QBER) of 3.0-3.7% for the mean photon number μ = 0.1 and 1.8-3.0% for μ = 0.3. The stability of quantum transmission has been achieved thanks to our new concept for compensation of SMF birefringence effects in Sagnac, based on a polarization control system and a polarization insensitive phase modulator. The measurement results have showed feasibility of quantum secret sharing over telecom fiber networks in Sagnac configuration, using standard fiber telecom components.

© 2009 Optical Society of America

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References

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  1. B. Schneier, Applied Cryptography (John Wiley & Sons, Inc. 1996).
  2. M. Hillery, V. Buzek, and A. Berthiaume, "Quantum secret sharing," Phys. Rev. A 59, 1829-1834 (1999).
    [CrossRef]
  3. R. Cleve, D. Gottesmann, and H.-K. Lo, "How to Share a Quantum Secret," Phys. Rev. Lett. 83, 648-651 (1999).
    [CrossRef]
  4. W. Tittel, H. Zbinden, and N. Gisin, "Experimental demonstration of quantum secret sharing," Phys. Rev. A 63, 042301-042306 (2001).
    [CrossRef]
  5. Y. A. Chen, A. N. Zhang, Z. Zhao, X. Q. Zhou, C. Y. Lu, C. Z. Peng, T. Yang, and J. W. Pan, "Experimental quantum secret sharing and third-man quantum cryptography," Phys. Rev. Lett.  95, 200502.1-200502.4 (2005).
    [CrossRef]
  6. S. Gaertner, C. Kurtsiefer, M. Bourennane, and H. Weinfurter, "Experimental demonstration of four-party quantum secret sharing," Phys. Rev. Lett.  98, 020503.1-020503.4 (2007).
    [CrossRef]
  7. C. Schmid, P. Trojek, H. Weinfurter, M. Bourennane, M. Zukowski, and C. Kurtsiefer, "Experimental single qubit quantum secret sharing," Phys. Rev. Lett.  95, 230505.1-230505.4 (2005).
    [CrossRef]
  8. C. Schmid, P. Trojek, M . Bourennane, C . Kurtsiefer, M . Zukowski, and H . Weinfurter, "Comment on experimental single qubit quantum secret sharing," Phys. Rev. Lett.  98, 028901.1 (2007).
  9. A. Kuzin, H. Cerecedo Nez, and N. Korneev, "Alignment of a birefringent fiber Sagnac interferometer by fiber twist," Opt. Commun. 160, 37-41 (1999).
    [CrossRef]
  10. B. Ibarra-Escamilla, E. A. Kuzin, O. Pottiez, J. W. Haus, F. Gutierrez-Zainos, R. Grajales-Coutin, and P. Zaca-Moran, "Fiber optical loop mirror with a symmetrical coupler nand a quarter-wave retarder plate in the loop," Opt. Commun. 242, 191-197 (2004).
    [CrossRef]
  11. D. B. Mortimore, "Fiber loop reflectors," Opt. Commun. 6, 1217-1224 (1988).
  12. C. Tsao, Optical fibre waveguide analysis, (Oxford Science Publ. 1992).
  13. D. Stucki, N. Gisin, O. Guinnard, G. Ribordy, and H. Zibiden, "Quantum key distribution over 67 km with a plug and play system," New J. Phys.  4,41.1-41.8 (2002).
    [CrossRef]
  14. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, "Quantum cryptography," Rev. Mod. Phys. 74, 145-195 (2002).
    [CrossRef]
  15. G. Ribordy, J. D. Gautier, N. Gisin, O. Guinnard, and H. Zbinden, "Fast and user-friendly quantum key distribution," J. Mod. Opt. 47, 517-531 (2000).
  16. H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, "Quantum key distribution over a 40-dB channel loss using superconducting single-photon detectors," Nat. Photonics 1, 343-348 (2007)
    [CrossRef]
  17. E. Udd, "Sensing and instrumentation applications of the Sagnac fiber optic interferometer," Proc. SPIE 2341, 52-59 (1994).
    [CrossRef]

2007 (1)

H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, "Quantum key distribution over a 40-dB channel loss using superconducting single-photon detectors," Nat. Photonics 1, 343-348 (2007)
[CrossRef]

2004 (1)

B. Ibarra-Escamilla, E. A. Kuzin, O. Pottiez, J. W. Haus, F. Gutierrez-Zainos, R. Grajales-Coutin, and P. Zaca-Moran, "Fiber optical loop mirror with a symmetrical coupler nand a quarter-wave retarder plate in the loop," Opt. Commun. 242, 191-197 (2004).
[CrossRef]

2002 (1)

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

2001 (1)

W. Tittel, H. Zbinden, and N. Gisin, "Experimental demonstration of quantum secret sharing," Phys. Rev. A 63, 042301-042306 (2001).
[CrossRef]

2000 (1)

G. Ribordy, J. D. Gautier, N. Gisin, O. Guinnard, and H. Zbinden, "Fast and user-friendly quantum key distribution," J. Mod. Opt. 47, 517-531 (2000).

1999 (3)

A. Kuzin, H. Cerecedo Nez, and N. Korneev, "Alignment of a birefringent fiber Sagnac interferometer by fiber twist," Opt. Commun. 160, 37-41 (1999).
[CrossRef]

M. Hillery, V. Buzek, and A. Berthiaume, "Quantum secret sharing," Phys. Rev. A 59, 1829-1834 (1999).
[CrossRef]

R. Cleve, D. Gottesmann, and H.-K. Lo, "How to Share a Quantum Secret," Phys. Rev. Lett. 83, 648-651 (1999).
[CrossRef]

1994 (1)

E. Udd, "Sensing and instrumentation applications of the Sagnac fiber optic interferometer," Proc. SPIE 2341, 52-59 (1994).
[CrossRef]

1988 (1)

D. B. Mortimore, "Fiber loop reflectors," Opt. Commun. 6, 1217-1224 (1988).

Berthiaume, A.

M. Hillery, V. Buzek, and A. Berthiaume, "Quantum secret sharing," Phys. Rev. A 59, 1829-1834 (1999).
[CrossRef]

Buzek, V.

M. Hillery, V. Buzek, and A. Berthiaume, "Quantum secret sharing," Phys. Rev. A 59, 1829-1834 (1999).
[CrossRef]

Cerecedo Nez, H.

A. Kuzin, H. Cerecedo Nez, and N. Korneev, "Alignment of a birefringent fiber Sagnac interferometer by fiber twist," Opt. Commun. 160, 37-41 (1999).
[CrossRef]

Cleve, R.

R. Cleve, D. Gottesmann, and H.-K. Lo, "How to Share a Quantum Secret," Phys. Rev. Lett. 83, 648-651 (1999).
[CrossRef]

Gautier, J. D.

G. Ribordy, J. D. Gautier, N. Gisin, O. Guinnard, and H. Zbinden, "Fast and user-friendly quantum key distribution," J. Mod. Opt. 47, 517-531 (2000).

Gisin, N.

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

W. Tittel, H. Zbinden, and N. Gisin, "Experimental demonstration of quantum secret sharing," Phys. Rev. A 63, 042301-042306 (2001).
[CrossRef]

G. Ribordy, J. D. Gautier, N. Gisin, O. Guinnard, and H. Zbinden, "Fast and user-friendly quantum key distribution," J. Mod. Opt. 47, 517-531 (2000).

Gottesmann, D.

R. Cleve, D. Gottesmann, and H.-K. Lo, "How to Share a Quantum Secret," Phys. Rev. Lett. 83, 648-651 (1999).
[CrossRef]

Grajales-Coutin, R.

B. Ibarra-Escamilla, E. A. Kuzin, O. Pottiez, J. W. Haus, F. Gutierrez-Zainos, R. Grajales-Coutin, and P. Zaca-Moran, "Fiber optical loop mirror with a symmetrical coupler nand a quarter-wave retarder plate in the loop," Opt. Commun. 242, 191-197 (2004).
[CrossRef]

Guinnard, O.

G. Ribordy, J. D. Gautier, N. Gisin, O. Guinnard, and H. Zbinden, "Fast and user-friendly quantum key distribution," J. Mod. Opt. 47, 517-531 (2000).

Gutierrez-Zainos, F.

B. Ibarra-Escamilla, E. A. Kuzin, O. Pottiez, J. W. Haus, F. Gutierrez-Zainos, R. Grajales-Coutin, and P. Zaca-Moran, "Fiber optical loop mirror with a symmetrical coupler nand a quarter-wave retarder plate in the loop," Opt. Commun. 242, 191-197 (2004).
[CrossRef]

Hadfield, R. H.

H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, "Quantum key distribution over a 40-dB channel loss using superconducting single-photon detectors," Nat. Photonics 1, 343-348 (2007)
[CrossRef]

Haus, J. W.

B. Ibarra-Escamilla, E. A. Kuzin, O. Pottiez, J. W. Haus, F. Gutierrez-Zainos, R. Grajales-Coutin, and P. Zaca-Moran, "Fiber optical loop mirror with a symmetrical coupler nand a quarter-wave retarder plate in the loop," Opt. Commun. 242, 191-197 (2004).
[CrossRef]

Hillery, M.

M. Hillery, V. Buzek, and A. Berthiaume, "Quantum secret sharing," Phys. Rev. A 59, 1829-1834 (1999).
[CrossRef]

Honjo, T.

H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, "Quantum key distribution over a 40-dB channel loss using superconducting single-photon detectors," Nat. Photonics 1, 343-348 (2007)
[CrossRef]

Ibarra-Escamilla, B.

B. Ibarra-Escamilla, E. A. Kuzin, O. Pottiez, J. W. Haus, F. Gutierrez-Zainos, R. Grajales-Coutin, and P. Zaca-Moran, "Fiber optical loop mirror with a symmetrical coupler nand a quarter-wave retarder plate in the loop," Opt. Commun. 242, 191-197 (2004).
[CrossRef]

Korneev, N.

A. Kuzin, H. Cerecedo Nez, and N. Korneev, "Alignment of a birefringent fiber Sagnac interferometer by fiber twist," Opt. Commun. 160, 37-41 (1999).
[CrossRef]

Kuzin, A.

A. Kuzin, H. Cerecedo Nez, and N. Korneev, "Alignment of a birefringent fiber Sagnac interferometer by fiber twist," Opt. Commun. 160, 37-41 (1999).
[CrossRef]

Kuzin, E. A.

B. Ibarra-Escamilla, E. A. Kuzin, O. Pottiez, J. W. Haus, F. Gutierrez-Zainos, R. Grajales-Coutin, and P. Zaca-Moran, "Fiber optical loop mirror with a symmetrical coupler nand a quarter-wave retarder plate in the loop," Opt. Commun. 242, 191-197 (2004).
[CrossRef]

Lo, H.-K.

R. Cleve, D. Gottesmann, and H.-K. Lo, "How to Share a Quantum Secret," Phys. Rev. Lett. 83, 648-651 (1999).
[CrossRef]

Mortimore, D. B.

D. B. Mortimore, "Fiber loop reflectors," Opt. Commun. 6, 1217-1224 (1988).

Nam, S. W.

H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, "Quantum key distribution over a 40-dB channel loss using superconducting single-photon detectors," Nat. Photonics 1, 343-348 (2007)
[CrossRef]

Pottiez, O.

B. Ibarra-Escamilla, E. A. Kuzin, O. Pottiez, J. W. Haus, F. Gutierrez-Zainos, R. Grajales-Coutin, and P. Zaca-Moran, "Fiber optical loop mirror with a symmetrical coupler nand a quarter-wave retarder plate in the loop," Opt. Commun. 242, 191-197 (2004).
[CrossRef]

Ribordy, G.

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

G. Ribordy, J. D. Gautier, N. Gisin, O. Guinnard, and H. Zbinden, "Fast and user-friendly quantum key distribution," J. Mod. Opt. 47, 517-531 (2000).

Takesue, H.

H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, "Quantum key distribution over a 40-dB channel loss using superconducting single-photon detectors," Nat. Photonics 1, 343-348 (2007)
[CrossRef]

Tamaki, K.

H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, "Quantum key distribution over a 40-dB channel loss using superconducting single-photon detectors," Nat. Photonics 1, 343-348 (2007)
[CrossRef]

Tittel, W.

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

W. Tittel, H. Zbinden, and N. Gisin, "Experimental demonstration of quantum secret sharing," Phys. Rev. A 63, 042301-042306 (2001).
[CrossRef]

Udd, E.

E. Udd, "Sensing and instrumentation applications of the Sagnac fiber optic interferometer," Proc. SPIE 2341, 52-59 (1994).
[CrossRef]

Yamamoto, Y.

H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, "Quantum key distribution over a 40-dB channel loss using superconducting single-photon detectors," Nat. Photonics 1, 343-348 (2007)
[CrossRef]

Zaca-Moran, P.

B. Ibarra-Escamilla, E. A. Kuzin, O. Pottiez, J. W. Haus, F. Gutierrez-Zainos, R. Grajales-Coutin, and P. Zaca-Moran, "Fiber optical loop mirror with a symmetrical coupler nand a quarter-wave retarder plate in the loop," Opt. Commun. 242, 191-197 (2004).
[CrossRef]

Zbinden, H.

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

W. Tittel, H. Zbinden, and N. Gisin, "Experimental demonstration of quantum secret sharing," Phys. Rev. A 63, 042301-042306 (2001).
[CrossRef]

G. Ribordy, J. D. Gautier, N. Gisin, O. Guinnard, and H. Zbinden, "Fast and user-friendly quantum key distribution," J. Mod. Opt. 47, 517-531 (2000).

Zhang, Q.

H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, "Quantum key distribution over a 40-dB channel loss using superconducting single-photon detectors," Nat. Photonics 1, 343-348 (2007)
[CrossRef]

J. Mod. Opt. (1)

G. Ribordy, J. D. Gautier, N. Gisin, O. Guinnard, and H. Zbinden, "Fast and user-friendly quantum key distribution," J. Mod. Opt. 47, 517-531 (2000).

Nat. Photonics (1)

H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, "Quantum key distribution over a 40-dB channel loss using superconducting single-photon detectors," Nat. Photonics 1, 343-348 (2007)
[CrossRef]

Opt. Commun. (3)

A. Kuzin, H. Cerecedo Nez, and N. Korneev, "Alignment of a birefringent fiber Sagnac interferometer by fiber twist," Opt. Commun. 160, 37-41 (1999).
[CrossRef]

B. Ibarra-Escamilla, E. A. Kuzin, O. Pottiez, J. W. Haus, F. Gutierrez-Zainos, R. Grajales-Coutin, and P. Zaca-Moran, "Fiber optical loop mirror with a symmetrical coupler nand a quarter-wave retarder plate in the loop," Opt. Commun. 242, 191-197 (2004).
[CrossRef]

D. B. Mortimore, "Fiber loop reflectors," Opt. Commun. 6, 1217-1224 (1988).

Phys. Rev. A (2)

W. Tittel, H. Zbinden, and N. Gisin, "Experimental demonstration of quantum secret sharing," Phys. Rev. A 63, 042301-042306 (2001).
[CrossRef]

M. Hillery, V. Buzek, and A. Berthiaume, "Quantum secret sharing," Phys. Rev. A 59, 1829-1834 (1999).
[CrossRef]

Phys. Rev. Lett. (1)

R. Cleve, D. Gottesmann, and H.-K. Lo, "How to Share a Quantum Secret," Phys. Rev. Lett. 83, 648-651 (1999).
[CrossRef]

Proc. SPIE (1)

E. Udd, "Sensing and instrumentation applications of the Sagnac fiber optic interferometer," Proc. SPIE 2341, 52-59 (1994).
[CrossRef]

Rev. Mod. Phys. (1)

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

Other (7)

B. Schneier, Applied Cryptography (John Wiley & Sons, Inc. 1996).

Y. A. Chen, A. N. Zhang, Z. Zhao, X. Q. Zhou, C. Y. Lu, C. Z. Peng, T. Yang, and J. W. Pan, "Experimental quantum secret sharing and third-man quantum cryptography," Phys. Rev. Lett.  95, 200502.1-200502.4 (2005).
[CrossRef]

S. Gaertner, C. Kurtsiefer, M. Bourennane, and H. Weinfurter, "Experimental demonstration of four-party quantum secret sharing," Phys. Rev. Lett.  98, 020503.1-020503.4 (2007).
[CrossRef]

C. Schmid, P. Trojek, H. Weinfurter, M. Bourennane, M. Zukowski, and C. Kurtsiefer, "Experimental single qubit quantum secret sharing," Phys. Rev. Lett.  95, 230505.1-230505.4 (2005).
[CrossRef]

C. Schmid, P. Trojek, M . Bourennane, C . Kurtsiefer, M . Zukowski, and H . Weinfurter, "Comment on experimental single qubit quantum secret sharing," Phys. Rev. Lett.  98, 028901.1 (2007).

C. Tsao, Optical fibre waveguide analysis, (Oxford Science Publ. 1992).

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

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Figures (5)

Fig. 1.
Fig. 1.

N-party single qubit secret sharing. A qubit (in our case a photon) is prepared in an initial state by the part R 1, using a single qubit source, and is sent sequentially, from R 1 to RN , over the quantum channel, until it is measured by the last part RN . Each party modulates the photon with a randomly chosen phase ϕi (i = 1,…,N - 1) of 0, π/2, π or 3π/2. The part RN , carrying out the measurement, sets measurement’s base with its phase modulator by choosing ϕN between 0 and π/2. In half of the cases the phases add up in such a way that the measurement results are deterministic. These cases can be used for the secret sharing.

Fig. 2.
Fig. 2.

Four party Sagnac secret sharing. All the measurements were carried out at μ = 0.1 and μ = 0.3. The laser pulse repetition rate in the burst mode was set to 2 MHz with the burst duty cycle of 20 %. The setup does not show a control electronics and wavelength-division multiplexing (WDM) layer used to send synchronization and trigger from Alice’s station to Bob’s, Charlie’s, and David’s stations. For this purpose a second pulsed laser with 1538 nm wavelength was used.

Fig. 3.
Fig. 3.

Polarization insensitive phase modulator. The R output of the PBS denotes the reflected component (vertical), while the T output denotes the transmitted component (horizontal).

Fig. 4.
Fig. 4.

Three-party Sagnac secret sharing. All the measurements were carried out at μ = 0.1 and μ = 0.3. The laser pulse repetition rate in the burst mode was set to 2 MHz with the burst duty cycle of 20 %

Fig. 5.
Fig. 5.

Four-party Sagnac secret sharing. All the measurements were carried out at μ = 0.1 and μ = 0.3. The laser pulse repetition rate in the burst mode was set to 2 MHz with the burst duty cycle of 20 %.

Equations (3)

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

Û(ϕi)={00;1eiϕi1}.
p±(ϕ1,,ϕN)=12(1±cos(jNϕj)).
E(ϕ1,,ϕN)=cos(ϕ1++ϕN).

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