Abstract

Multiphoton entanglement in the same polarization has been shown theoretically to be obtainable by type-I spontaneous parametric downconversion (SPDC), which can generate bright pulses more easily than type-II SPDC. A new quantum cryptographic protocol utilizing polarization pairs with the detected type-I entangled multiphotons is proposed as quantum key distribution. We calculate the information capacity versus photon number corresponding to polarization after considering the transmission loss inside the optical fiber, the detector efficiency, and intercept–resend attacks at the level of channel error. The result compares favorably with all other schemes employing entanglement.

© 2005 Optical Society of America

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References

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  1. C. H. Bennett, G. Brassard, in Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India (IEEE Press, Piscataway, N. J., 1984), pp. 175–179.
  2. A. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661 (1991).
    [CrossRef] [PubMed]
  3. G. A. Durkin, C. Simon, D. Bouwmeester, “Multiphoton entanglement concentration and quantum cryptography,” Phys. Rev. Lett. 88, 187902-1 (2002).
    [CrossRef] [PubMed]
  4. M. Hillery, “Quantum cryptography with squeezed states,” Phys. Rev. A 61, 022309 (2000).
    [CrossRef]
  5. F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, P. Grangier, “Quantum key distribution using gaussian-modulated coherent states,” Nature (London) 421238 (2003).
    [CrossRef]
  6. T. C. Ralph, “Continuous variable quantum cryptography,” Phys. Rev. A 61, 010302(R) (2000).
    [CrossRef]
  7. M. D. Reid, “Quantum cryptography with a predetermined key, using continuous-variable Einstein–Podolsky–Rosen correlations,” Phys. Rev. A 62, 062308 (2000).
    [CrossRef]
  8. Ch. Siberhorn, N. Korolkova, G. Leuchs, “Quantum key distribution with bright entangled beams,” Phys. Rev. Lett. 88, 167902 (2002).
    [CrossRef]
  9. Y.-H. Kim, S. P. Kulik, Y. Shih, “High-intensity pulsed source of space-time and polarization double-entangled photon pairs,” Phys. Rev. A 62, 011802(R) (2000).
    [CrossRef]
  10. Y.-H. Kim, S. P. Kulik, Y. Shih, “Bell-state preparation using pulsed nondegenerate two-photon entanglement,” Phys. Rev. A 63, 060301 (R) (2001).
    [CrossRef]
  11. Y.-H. Kim, M. V. Chekhova, S. P. Kulik, M. H. Rubin, Y. Shih, “Interferometric Bell-state preparation using femtosecond-pulse-pumped spontaneous para - metric down-conversion,” Phys. Rev. A 63, 062301 (R) (2001).
    [CrossRef]
  12. D. F. Walls, G. J. Milburn, Quantum Optics (Springer-Verlag, Berlin 1994), p. 83.
  13. T. M. Cover, J. A. Thomas, Elements of Information Theory (Wiley-Interscience, New York, 1991), Chap. 2, p. 20.
  14. C. H. Bennett, G. Brassard, C. Crépeau, U. M. Maurer, “Generalized privacy amplification,” IEEE Trans. Inf. Theory 41, 1915 (1995).
    [CrossRef]

2003 (1)

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, P. Grangier, “Quantum key distribution using gaussian-modulated coherent states,” Nature (London) 421238 (2003).
[CrossRef]

2002 (2)

G. A. Durkin, C. Simon, D. Bouwmeester, “Multiphoton entanglement concentration and quantum cryptography,” Phys. Rev. Lett. 88, 187902-1 (2002).
[CrossRef] [PubMed]

Ch. Siberhorn, N. Korolkova, G. Leuchs, “Quantum key distribution with bright entangled beams,” Phys. Rev. Lett. 88, 167902 (2002).
[CrossRef]

2001 (2)

Y.-H. Kim, S. P. Kulik, Y. Shih, “Bell-state preparation using pulsed nondegenerate two-photon entanglement,” Phys. Rev. A 63, 060301 (R) (2001).
[CrossRef]

Y.-H. Kim, M. V. Chekhova, S. P. Kulik, M. H. Rubin, Y. Shih, “Interferometric Bell-state preparation using femtosecond-pulse-pumped spontaneous para - metric down-conversion,” Phys. Rev. A 63, 062301 (R) (2001).
[CrossRef]

2000 (4)

Y.-H. Kim, S. P. Kulik, Y. Shih, “High-intensity pulsed source of space-time and polarization double-entangled photon pairs,” Phys. Rev. A 62, 011802(R) (2000).
[CrossRef]

M. Hillery, “Quantum cryptography with squeezed states,” Phys. Rev. A 61, 022309 (2000).
[CrossRef]

T. C. Ralph, “Continuous variable quantum cryptography,” Phys. Rev. A 61, 010302(R) (2000).
[CrossRef]

M. D. Reid, “Quantum cryptography with a predetermined key, using continuous-variable Einstein–Podolsky–Rosen correlations,” Phys. Rev. A 62, 062308 (2000).
[CrossRef]

1995 (1)

C. H. Bennett, G. Brassard, C. Crépeau, U. M. Maurer, “Generalized privacy amplification,” IEEE Trans. Inf. Theory 41, 1915 (1995).
[CrossRef]

1991 (1)

A. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661 (1991).
[CrossRef] [PubMed]

Bennett, C. H.

C. H. Bennett, G. Brassard, C. Crépeau, U. M. Maurer, “Generalized privacy amplification,” IEEE Trans. Inf. Theory 41, 1915 (1995).
[CrossRef]

C. H. Bennett, G. Brassard, in Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India (IEEE Press, Piscataway, N. J., 1984), pp. 175–179.

Bouwmeester, D.

G. A. Durkin, C. Simon, D. Bouwmeester, “Multiphoton entanglement concentration and quantum cryptography,” Phys. Rev. Lett. 88, 187902-1 (2002).
[CrossRef] [PubMed]

Brassard, G.

C. H. Bennett, G. Brassard, C. Crépeau, U. M. Maurer, “Generalized privacy amplification,” IEEE Trans. Inf. Theory 41, 1915 (1995).
[CrossRef]

C. H. Bennett, G. Brassard, in Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India (IEEE Press, Piscataway, N. J., 1984), pp. 175–179.

Brouri, R.

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, P. Grangier, “Quantum key distribution using gaussian-modulated coherent states,” Nature (London) 421238 (2003).
[CrossRef]

Cerf, N. J.

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, P. Grangier, “Quantum key distribution using gaussian-modulated coherent states,” Nature (London) 421238 (2003).
[CrossRef]

Chekhova, M. V.

Y.-H. Kim, M. V. Chekhova, S. P. Kulik, M. H. Rubin, Y. Shih, “Interferometric Bell-state preparation using femtosecond-pulse-pumped spontaneous para - metric down-conversion,” Phys. Rev. A 63, 062301 (R) (2001).
[CrossRef]

Cover, T. M.

T. M. Cover, J. A. Thomas, Elements of Information Theory (Wiley-Interscience, New York, 1991), Chap. 2, p. 20.

Crépeau, C.

C. H. Bennett, G. Brassard, C. Crépeau, U. M. Maurer, “Generalized privacy amplification,” IEEE Trans. Inf. Theory 41, 1915 (1995).
[CrossRef]

Durkin, G. A.

G. A. Durkin, C. Simon, D. Bouwmeester, “Multiphoton entanglement concentration and quantum cryptography,” Phys. Rev. Lett. 88, 187902-1 (2002).
[CrossRef] [PubMed]

Ekert, A.

A. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661 (1991).
[CrossRef] [PubMed]

Grangier, P.

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, P. Grangier, “Quantum key distribution using gaussian-modulated coherent states,” Nature (London) 421238 (2003).
[CrossRef]

Grosshans, F.

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, P. Grangier, “Quantum key distribution using gaussian-modulated coherent states,” Nature (London) 421238 (2003).
[CrossRef]

Hillery, M.

M. Hillery, “Quantum cryptography with squeezed states,” Phys. Rev. A 61, 022309 (2000).
[CrossRef]

Kim, Y.-H.

Y.-H. Kim, S. P. Kulik, Y. Shih, “Bell-state preparation using pulsed nondegenerate two-photon entanglement,” Phys. Rev. A 63, 060301 (R) (2001).
[CrossRef]

Y.-H. Kim, M. V. Chekhova, S. P. Kulik, M. H. Rubin, Y. Shih, “Interferometric Bell-state preparation using femtosecond-pulse-pumped spontaneous para - metric down-conversion,” Phys. Rev. A 63, 062301 (R) (2001).
[CrossRef]

Y.-H. Kim, S. P. Kulik, Y. Shih, “High-intensity pulsed source of space-time and polarization double-entangled photon pairs,” Phys. Rev. A 62, 011802(R) (2000).
[CrossRef]

Korolkova, N.

Ch. Siberhorn, N. Korolkova, G. Leuchs, “Quantum key distribution with bright entangled beams,” Phys. Rev. Lett. 88, 167902 (2002).
[CrossRef]

Kulik, S. P.

Y.-H. Kim, S. P. Kulik, Y. Shih, “Bell-state preparation using pulsed nondegenerate two-photon entanglement,” Phys. Rev. A 63, 060301 (R) (2001).
[CrossRef]

Y.-H. Kim, M. V. Chekhova, S. P. Kulik, M. H. Rubin, Y. Shih, “Interferometric Bell-state preparation using femtosecond-pulse-pumped spontaneous para - metric down-conversion,” Phys. Rev. A 63, 062301 (R) (2001).
[CrossRef]

Y.-H. Kim, S. P. Kulik, Y. Shih, “High-intensity pulsed source of space-time and polarization double-entangled photon pairs,” Phys. Rev. A 62, 011802(R) (2000).
[CrossRef]

Leuchs, G.

Ch. Siberhorn, N. Korolkova, G. Leuchs, “Quantum key distribution with bright entangled beams,” Phys. Rev. Lett. 88, 167902 (2002).
[CrossRef]

Maurer, U. M.

C. H. Bennett, G. Brassard, C. Crépeau, U. M. Maurer, “Generalized privacy amplification,” IEEE Trans. Inf. Theory 41, 1915 (1995).
[CrossRef]

Milburn, G. J.

D. F. Walls, G. J. Milburn, Quantum Optics (Springer-Verlag, Berlin 1994), p. 83.

Ralph, T. C.

T. C. Ralph, “Continuous variable quantum cryptography,” Phys. Rev. A 61, 010302(R) (2000).
[CrossRef]

Reid, M. D.

M. D. Reid, “Quantum cryptography with a predetermined key, using continuous-variable Einstein–Podolsky–Rosen correlations,” Phys. Rev. A 62, 062308 (2000).
[CrossRef]

Rubin, M. H.

Y.-H. Kim, M. V. Chekhova, S. P. Kulik, M. H. Rubin, Y. Shih, “Interferometric Bell-state preparation using femtosecond-pulse-pumped spontaneous para - metric down-conversion,” Phys. Rev. A 63, 062301 (R) (2001).
[CrossRef]

Shih, Y.

Y.-H. Kim, M. V. Chekhova, S. P. Kulik, M. H. Rubin, Y. Shih, “Interferometric Bell-state preparation using femtosecond-pulse-pumped spontaneous para - metric down-conversion,” Phys. Rev. A 63, 062301 (R) (2001).
[CrossRef]

Y.-H. Kim, S. P. Kulik, Y. Shih, “Bell-state preparation using pulsed nondegenerate two-photon entanglement,” Phys. Rev. A 63, 060301 (R) (2001).
[CrossRef]

Y.-H. Kim, S. P. Kulik, Y. Shih, “High-intensity pulsed source of space-time and polarization double-entangled photon pairs,” Phys. Rev. A 62, 011802(R) (2000).
[CrossRef]

Siberhorn, Ch.

Ch. Siberhorn, N. Korolkova, G. Leuchs, “Quantum key distribution with bright entangled beams,” Phys. Rev. Lett. 88, 167902 (2002).
[CrossRef]

Simon, C.

G. A. Durkin, C. Simon, D. Bouwmeester, “Multiphoton entanglement concentration and quantum cryptography,” Phys. Rev. Lett. 88, 187902-1 (2002).
[CrossRef] [PubMed]

Thomas, J. A.

T. M. Cover, J. A. Thomas, Elements of Information Theory (Wiley-Interscience, New York, 1991), Chap. 2, p. 20.

Van Assche, G.

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, P. Grangier, “Quantum key distribution using gaussian-modulated coherent states,” Nature (London) 421238 (2003).
[CrossRef]

Walls, D. F.

D. F. Walls, G. J. Milburn, Quantum Optics (Springer-Verlag, Berlin 1994), p. 83.

Wenger, J.

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, P. Grangier, “Quantum key distribution using gaussian-modulated coherent states,” Nature (London) 421238 (2003).
[CrossRef]

IEEE Trans. Inf. Theory (1)

C. H. Bennett, G. Brassard, C. Crépeau, U. M. Maurer, “Generalized privacy amplification,” IEEE Trans. Inf. Theory 41, 1915 (1995).
[CrossRef]

Nature (London) (1)

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, P. Grangier, “Quantum key distribution using gaussian-modulated coherent states,” Nature (London) 421238 (2003).
[CrossRef]

Phys. Rev. A (6)

T. C. Ralph, “Continuous variable quantum cryptography,” Phys. Rev. A 61, 010302(R) (2000).
[CrossRef]

M. D. Reid, “Quantum cryptography with a predetermined key, using continuous-variable Einstein–Podolsky–Rosen correlations,” Phys. Rev. A 62, 062308 (2000).
[CrossRef]

M. Hillery, “Quantum cryptography with squeezed states,” Phys. Rev. A 61, 022309 (2000).
[CrossRef]

Y.-H. Kim, S. P. Kulik, Y. Shih, “High-intensity pulsed source of space-time and polarization double-entangled photon pairs,” Phys. Rev. A 62, 011802(R) (2000).
[CrossRef]

Y.-H. Kim, S. P. Kulik, Y. Shih, “Bell-state preparation using pulsed nondegenerate two-photon entanglement,” Phys. Rev. A 63, 060301 (R) (2001).
[CrossRef]

Y.-H. Kim, M. V. Chekhova, S. P. Kulik, M. H. Rubin, Y. Shih, “Interferometric Bell-state preparation using femtosecond-pulse-pumped spontaneous para - metric down-conversion,” Phys. Rev. A 63, 062301 (R) (2001).
[CrossRef]

Phys. Rev. Lett. (3)

A. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661 (1991).
[CrossRef] [PubMed]

G. A. Durkin, C. Simon, D. Bouwmeester, “Multiphoton entanglement concentration and quantum cryptography,” Phys. Rev. Lett. 88, 187902-1 (2002).
[CrossRef] [PubMed]

Ch. Siberhorn, N. Korolkova, G. Leuchs, “Quantum key distribution with bright entangled beams,” Phys. Rev. Lett. 88, 167902 (2002).
[CrossRef]

Other (3)

C. H. Bennett, G. Brassard, in Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India (IEEE Press, Piscataway, N. J., 1984), pp. 175–179.

D. F. Walls, G. J. Milburn, Quantum Optics (Springer-Verlag, Berlin 1994), p. 83.

T. M. Cover, J. A. Thomas, Elements of Information Theory (Wiley-Interscience, New York, 1991), Chap. 2, p. 20.

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Figures (2)

Fig. 1
Fig. 1

Minimum C s versus photon number at optimum χ t .

Fig. 2
Fig. 2

Minimum C s versus source-to-end user distance and detector efficiency.

Equations (11)

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H ̂ = i χ ( a ̂ h b ̂ h a ̂ h + b ̂ h + + a ̂ v b ̂ v a ̂ v + b ̂ v + ) ,
Ψ = exp ( i H ̂ t ) 0 = 1 cosh 2 ( χ t ) n = 0 ( n + 1 ) 1 2 tanh n ( χ t ) ψ + n ,
ψ + n = 1 ( n + 1 ) 1 2 1 n ! ( a ̂ h + b ̂ h + + a ̂ v + b ̂ v + ) n 0 = 1 ( n + 1 ) 1 2 m = 0 n ( n m ) , m ; ( n m ) , m .
η p = 10 α L 10 ,
E k = n = k ( n k ) η k ( 1 η ) n k n a h n .
p i ( k ) = Ψ E i Ψ = 1 cosh 4 ( χ t ) n = k tanh 2 n ( χ t ) ( n k ) η k ( 1 η ) n k ,
p j ( m ) = Ψ E j Ψ = 1 cosh 4 ( χ t ) n = m tanh 2 n ( χ t ) ( n m ) η m ( 1 η ) n m ,
I A B = i , j p ( A i , B j ) log 2 p ( A i , B j ) i p ( A i ) log 2 p ( A i ) j p ( B j ) log 2 p ( B j ) ,
C s I A B min ( I A E , I B E ) .
ρ ̂ Eve = P 1 , 1 ρ ̂ 1 , 1 + P 2 , 2 ρ ̂ 2 , 2 + P 3 , 3 ρ ̂ 3 , 3 + P 4 , 4 ρ ̂ 4 , 4 + ( 1 P 1 , 1 P 2 , 2 P 3 , 3 P 4 , 4 ) ρ ̂ rest ,
ρ ̂ 1 , 1 = ( 1 γ ) ψ 1 + ψ 1 + + γ 4 ( 1 , 0 ; 1 , 0 0 , 1 ; 0 , 1 + 1 , 0 ; 1 , 0 0 , 1 ; 0 , 1 + 0 , 1 ; 0 , 1 1 , 0 ; 1 , 0 + 0 , 1 ; 0 , 1 1 , 0 ; 1 , 0 ) .

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