Abstract

A quantum secret sharing (QSS) protocol based on a differential-phase-shift scheme is proposed, which quantum mechanically provides a full secret key to one party and partial keys to two other parties. A weak coherent pulse train is utilized instead of individual photons as in conventional schemes. Compared with previous QSS protocols, the present one features a simple setup, is suitable for fiber transmission, and offers the possibility for a high key creation rate. An experiment is also carried out to demonstrate the operation.

© 2008 Optical Society of America

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  1. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, "Quantum cryptography," Rev. Mod. Phys. 74, 145-195 (2002).
    [CrossRef]
  2. K. Inoue, "Quantum key distribution technologies," IEEE J. Sel. Top. Quantum Electron. 12, 888-896 (2006).
    [CrossRef]
  3. M. Hillery, V. Bužek, and A. Berthiaume, "Quantum secret sharing," Phys. Rev. A 59, 1829 (1999).
    [CrossRef]
  4. A. Karlsson, M. Koashi, and N. Imoto, "Quantum entanglement for secret sharing and secret splitting," Phys. Rev. A 59, 162 (1999).
    [CrossRef]
  5. L. Xiao, G. Long, F. Deng, and J. Pan, "Efficient multiparty quantum-secret-sharing schemes," Phys. Rev. A 69, 052307 (2004).
    [CrossRef]
  6. S. K. Singh and R. Srikanth, "Generalized quantum secret sharing," Phys. Rev. A 71, 012328 (2005).
    [CrossRef]
  7. Z. Zhang, Y. Li, and Z. Man, "Multiparty quantum secret sharing," Phys. Rev. A 71, 044301 (2005).
    [CrossRef]
  8. C. Schmid, P. Trojek, M. Bourennane, C. Kurtsiefer, M. Zukowski, and H. Weinfurter, "Experimental single qubit quantum secret sharing," Phys. Rev. Lett. 95, 230505 (2005).
    [CrossRef] [PubMed]
  9. H. Takesue and K. Inoue, "Quantum secret sharing based on modulated high-dimension time-bin entanglement," Phys. Rev. A 74, 012315 (2006).
    [CrossRef]
  10. J. Chen, G. Wu, Y. Li, E. Wu, and H. Zeng, "Active polarization in optical fibers suitable for quantum key distribution," Opt. Express 15, 17928-17936 (2007).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  12. N. Lütkenhaus, "Security against individual attacks for realistic quantum key distribution," Phys. Rev. A 61, 052304 (2000).
    [CrossRef]
  13. K. Inoue, E. Waks, and Y. Yamamoto, "Differential-phase-shift quantum key distribution using coherent light," Phys. Rev. A 68, 022317 (2003).
    [CrossRef]
  14. E. Waks, H. Takesue, and Y. Yamamoto, "Security of differential-phase-shift quantum key distribution against individual attacks," Phys. Rev. A 73, 012344 (2006).
    [CrossRef]
  15. G. Brassard and L. Salvail, "Secret-key reconciliation by public discussion in advances," in Cryptography-EUROCRYPT???93, Lecture Notes in Computer Science, 765, T. Helleseth, (Springer Verlag, Berlin, Germany, 1994), pp. 410-423.
  16. C. H. Bennett, G. Brassard, C. Crepeau, and U. M. Maurer, "Generalized privacy amplification," IEEE Trans. Info. Theory 41, 1915-1923 (1995).
    [CrossRef]
  17. T. Honjo, K. Inoue and H. Takahashi, "Differential-phase-shift quantum key distribution experiment with a planar light-wave circuit Mach-Zehnder interferometer," Opt. Lett. 29, 2797-2799 (2004).
    [CrossRef] [PubMed]

2008 (1)

2007 (1)

2006 (3)

H. Takesue and K. Inoue, "Quantum secret sharing based on modulated high-dimension time-bin entanglement," Phys. Rev. A 74, 012315 (2006).
[CrossRef]

K. Inoue, "Quantum key distribution technologies," IEEE J. Sel. Top. Quantum Electron. 12, 888-896 (2006).
[CrossRef]

E. Waks, H. Takesue, and Y. Yamamoto, "Security of differential-phase-shift quantum key distribution against individual attacks," Phys. Rev. A 73, 012344 (2006).
[CrossRef]

2005 (3)

S. K. Singh and R. Srikanth, "Generalized quantum secret sharing," Phys. Rev. A 71, 012328 (2005).
[CrossRef]

Z. Zhang, Y. Li, and Z. Man, "Multiparty quantum secret sharing," Phys. Rev. A 71, 044301 (2005).
[CrossRef]

C. Schmid, P. Trojek, M. Bourennane, C. Kurtsiefer, M. Zukowski, and H. Weinfurter, "Experimental single qubit quantum secret sharing," Phys. Rev. Lett. 95, 230505 (2005).
[CrossRef] [PubMed]

2004 (2)

2003 (1)

K. Inoue, E. Waks, and Y. Yamamoto, "Differential-phase-shift quantum key distribution using coherent light," Phys. Rev. A 68, 022317 (2003).
[CrossRef]

2002 (1)

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

2000 (1)

N. Lütkenhaus, "Security against individual attacks for realistic quantum key distribution," Phys. Rev. A 61, 052304 (2000).
[CrossRef]

1999 (2)

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

A. Karlsson, M. Koashi, and N. Imoto, "Quantum entanglement for secret sharing and secret splitting," Phys. Rev. A 59, 162 (1999).
[CrossRef]

1995 (1)

C. H. Bennett, G. Brassard, C. Crepeau, and U. M. Maurer, "Generalized privacy amplification," IEEE Trans. Info. Theory 41, 1915-1923 (1995).
[CrossRef]

Bennett, C. H.

C. H. Bennett, G. Brassard, C. Crepeau, and U. M. Maurer, "Generalized privacy amplification," IEEE Trans. Info. Theory 41, 1915-1923 (1995).
[CrossRef]

Berthiaume, A.

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

Bourennane, M.

C. Schmid, P. Trojek, M. Bourennane, C. Kurtsiefer, M. Zukowski, and H. Weinfurter, "Experimental single qubit quantum secret sharing," Phys. Rev. Lett. 95, 230505 (2005).
[CrossRef] [PubMed]

Brassard, G.

C. H. Bennett, G. Brassard, C. Crepeau, and U. M. Maurer, "Generalized privacy amplification," IEEE Trans. Info. Theory 41, 1915-1923 (1995).
[CrossRef]

Bužek, V.

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

Chen, J.

Crepeau, C.

C. H. Bennett, G. Brassard, C. Crepeau, and U. M. Maurer, "Generalized privacy amplification," IEEE Trans. Info. Theory 41, 1915-1923 (1995).
[CrossRef]

Deng, F.

L. Xiao, G. Long, F. Deng, and J. Pan, "Efficient multiparty quantum-secret-sharing schemes," Phys. Rev. A 69, 052307 (2004).
[CrossRef]

Gisin, N.

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

Hillery, M.

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

Honjo, T.

Imoto, N.

A. Karlsson, M. Koashi, and N. Imoto, "Quantum entanglement for secret sharing and secret splitting," Phys. Rev. A 59, 162 (1999).
[CrossRef]

Inoue, K.

K. Inoue, "Quantum key distribution technologies," IEEE J. Sel. Top. Quantum Electron. 12, 888-896 (2006).
[CrossRef]

H. Takesue and K. Inoue, "Quantum secret sharing based on modulated high-dimension time-bin entanglement," Phys. Rev. A 74, 012315 (2006).
[CrossRef]

T. Honjo, K. Inoue and H. Takahashi, "Differential-phase-shift quantum key distribution experiment with a planar light-wave circuit Mach-Zehnder interferometer," Opt. Lett. 29, 2797-2799 (2004).
[CrossRef] [PubMed]

K. Inoue, E. Waks, and Y. Yamamoto, "Differential-phase-shift quantum key distribution using coherent light," Phys. Rev. A 68, 022317 (2003).
[CrossRef]

Karlsson, A.

A. Karlsson, M. Koashi, and N. Imoto, "Quantum entanglement for secret sharing and secret splitting," Phys. Rev. A 59, 162 (1999).
[CrossRef]

Koashi, M.

A. Karlsson, M. Koashi, and N. Imoto, "Quantum entanglement for secret sharing and secret splitting," Phys. Rev. A 59, 162 (1999).
[CrossRef]

Kurtsiefer, C.

C. Schmid, P. Trojek, M. Bourennane, C. Kurtsiefer, M. Zukowski, and H. Weinfurter, "Experimental single qubit quantum secret sharing," Phys. Rev. Lett. 95, 230505 (2005).
[CrossRef] [PubMed]

Li, Y.

Long, G.

L. Xiao, G. Long, F. Deng, and J. Pan, "Efficient multiparty quantum-secret-sharing schemes," Phys. Rev. A 69, 052307 (2004).
[CrossRef]

Lütkenhaus, N.

N. Lütkenhaus, "Security against individual attacks for realistic quantum key distribution," Phys. Rev. A 61, 052304 (2000).
[CrossRef]

Man, Z.

Z. Zhang, Y. Li, and Z. Man, "Multiparty quantum secret sharing," Phys. Rev. A 71, 044301 (2005).
[CrossRef]

Maurer, U. M.

C. H. Bennett, G. Brassard, C. Crepeau, and U. M. Maurer, "Generalized privacy amplification," IEEE Trans. Info. Theory 41, 1915-1923 (1995).
[CrossRef]

Pan, J.

L. Xiao, G. Long, F. Deng, and J. Pan, "Efficient multiparty quantum-secret-sharing schemes," Phys. Rev. A 69, 052307 (2004).
[CrossRef]

Ribordy, G.

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

Schmid, C.

C. Schmid, P. Trojek, M. Bourennane, C. Kurtsiefer, M. Zukowski, and H. Weinfurter, "Experimental single qubit quantum secret sharing," Phys. Rev. Lett. 95, 230505 (2005).
[CrossRef] [PubMed]

Singh, S. K.

S. K. Singh and R. Srikanth, "Generalized quantum secret sharing," Phys. Rev. A 71, 012328 (2005).
[CrossRef]

Srikanth, R.

S. K. Singh and R. Srikanth, "Generalized quantum secret sharing," Phys. Rev. A 71, 012328 (2005).
[CrossRef]

Takahashi, H.

Takesue, H.

E. Waks, H. Takesue, and Y. Yamamoto, "Security of differential-phase-shift quantum key distribution against individual attacks," Phys. Rev. A 73, 012344 (2006).
[CrossRef]

H. Takesue and K. Inoue, "Quantum secret sharing based on modulated high-dimension time-bin entanglement," Phys. Rev. A 74, 012315 (2006).
[CrossRef]

Temporão, G. P.

Tittel, W.

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

Trojek, P.

C. Schmid, P. Trojek, M. Bourennane, C. Kurtsiefer, M. Zukowski, and H. Weinfurter, "Experimental single qubit quantum secret sharing," Phys. Rev. Lett. 95, 230505 (2005).
[CrossRef] [PubMed]

Vilela de Faria, G.

von der Weid, J. P.

Waks, E.

E. Waks, H. Takesue, and Y. Yamamoto, "Security of differential-phase-shift quantum key distribution against individual attacks," Phys. Rev. A 73, 012344 (2006).
[CrossRef]

K. Inoue, E. Waks, and Y. Yamamoto, "Differential-phase-shift quantum key distribution using coherent light," Phys. Rev. A 68, 022317 (2003).
[CrossRef]

Weinfurter, H.

C. Schmid, P. Trojek, M. Bourennane, C. Kurtsiefer, M. Zukowski, and H. Weinfurter, "Experimental single qubit quantum secret sharing," Phys. Rev. Lett. 95, 230505 (2005).
[CrossRef] [PubMed]

Wu, E.

Wu, G.

Xavier, G. B.

Xiao, L.

L. Xiao, G. Long, F. Deng, and J. Pan, "Efficient multiparty quantum-secret-sharing schemes," Phys. Rev. A 69, 052307 (2004).
[CrossRef]

Yamamoto, Y.

E. Waks, H. Takesue, and Y. Yamamoto, "Security of differential-phase-shift quantum key distribution against individual attacks," Phys. Rev. A 73, 012344 (2006).
[CrossRef]

K. Inoue, E. Waks, and Y. Yamamoto, "Differential-phase-shift quantum key distribution using coherent light," Phys. Rev. A 68, 022317 (2003).
[CrossRef]

Zbinden, H.

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

Zeng, H.

Zhang, Z.

Z. Zhang, Y. Li, and Z. Man, "Multiparty quantum secret sharing," Phys. Rev. A 71, 044301 (2005).
[CrossRef]

Zukowski, M.

C. Schmid, P. Trojek, M. Bourennane, C. Kurtsiefer, M. Zukowski, and H. Weinfurter, "Experimental single qubit quantum secret sharing," Phys. Rev. Lett. 95, 230505 (2005).
[CrossRef] [PubMed]

IEEE J. Sel. Top. Quantum Electron. (1)

K. Inoue, "Quantum key distribution technologies," IEEE J. Sel. Top. Quantum Electron. 12, 888-896 (2006).
[CrossRef]

IEEE Trans. Info. Theory (1)

C. H. Bennett, G. Brassard, C. Crepeau, and U. M. Maurer, "Generalized privacy amplification," IEEE Trans. Info. Theory 41, 1915-1923 (1995).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. A (9)

H. Takesue and K. Inoue, "Quantum secret sharing based on modulated high-dimension time-bin entanglement," Phys. Rev. A 74, 012315 (2006).
[CrossRef]

N. Lütkenhaus, "Security against individual attacks for realistic quantum key distribution," Phys. Rev. A 61, 052304 (2000).
[CrossRef]

K. Inoue, E. Waks, and Y. Yamamoto, "Differential-phase-shift quantum key distribution using coherent light," Phys. Rev. A 68, 022317 (2003).
[CrossRef]

E. Waks, H. Takesue, and Y. Yamamoto, "Security of differential-phase-shift quantum key distribution against individual attacks," Phys. Rev. A 73, 012344 (2006).
[CrossRef]

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

A. Karlsson, M. Koashi, and N. Imoto, "Quantum entanglement for secret sharing and secret splitting," Phys. Rev. A 59, 162 (1999).
[CrossRef]

L. Xiao, G. Long, F. Deng, and J. Pan, "Efficient multiparty quantum-secret-sharing schemes," Phys. Rev. A 69, 052307 (2004).
[CrossRef]

S. K. Singh and R. Srikanth, "Generalized quantum secret sharing," Phys. Rev. A 71, 012328 (2005).
[CrossRef]

Z. Zhang, Y. Li, and Z. Man, "Multiparty quantum secret sharing," Phys. Rev. A 71, 044301 (2005).
[CrossRef]

Phys. Rev. Lett. (1)

C. Schmid, P. Trojek, M. Bourennane, C. Kurtsiefer, M. Zukowski, and H. Weinfurter, "Experimental single qubit quantum secret sharing," Phys. Rev. Lett. 95, 230505 (2005).
[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 (1)

G. Brassard and L. Salvail, "Secret-key reconciliation by public discussion in advances," in Cryptography-EUROCRYPT???93, Lecture Notes in Computer Science, 765, T. Helleseth, (Springer Verlag, Berlin, Germany, 1994), pp. 410-423.

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Figures (7)

Fig. 1.
Fig. 1.

Configuration of differential-phase-shift quantum secret sharing system.

Fig. 2.
Fig. 2.

Configuration of eavesdropping by malicious Alice. PM: phase modulation, meas: measurement apparatus.

Fig. 3.
Fig. 3.

Configuration of eavesdropping by malicious Bob.

Fig. 4.
Fig. 4.

Bob’s eavesdropping. PM: phase modulator, SW: optical switch.

Fig. 5.
Fig. 5.

Bob’s general individual attack.

Fig. 6.
Fig. 6.

Simulation results for final-key creation rate as a function of fiber transmission length. Dashed line, dotted line, and solid line assume Bob’s betrayal (Fig. 4), Eve’s general individual attack, and Bob’s general individual attack (Fig. 5), respectively. Fiber length is the distance between Alice and Charlie, and Bob is assumed to be positioned at the middle between them in the normal condition. Fiber loss coefficient =0.25 dB/km, detector efficiency =10 %, detector dark-count rate =10-5/slot, error rate due to imperfect interference =1 %. The average photon number sent from Alice is optimized to obtain the highest key creation rate at each length.

Fig. 7.
Fig. 7.

Experimental setup of DPS-QSS. LD: external-cavity laser diode, IM: intensity modulator, PM: phase modulator, PG: pulse generator, DG: data generator, DET: photon detector, MZI: Mach-Zehnder interferometer, TIA: time interval analyzer.

Equations (2)

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α ( 1 2 μ 2 ) 1 2 = e ,
α = 4 e 1 2 μ .

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