Abstract

We propose a new quantum key distribution protocol in which information is encoded on continuous variables of a single photon. In this protocol, Alice randomly encodes her information on either the central frequency of a narrowband single-photon pulse or the time delay of a broadband single-photon pulse, while Bob randomly chooses to do either frequency measurement or time measurement. The security of this protocol rests on the energy–time uncertainty relation, which prevents Eve from simultaneously determining both frequency and time information with arbitrarily high resolution. Since no interferometer is employed in this scheme, it is more robust against various channel noises, such as polarization and phase fluctuations.

© 2006 Optical Society of America

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  1. C. H. Bennett and G. Brassard, in Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing (IEEE, 1984), pp. 175-179.
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    [CrossRef] [PubMed]
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    [CrossRef]
  4. M. Hillery, Phys. Rev. A 61, 022309 (2000).
    [CrossRef]
  5. R. J. Hughes, J. E. Nordholt, D. Derkacs, and C. G. Peterson, New J. Phys. 4, 43 (2002).
    [CrossRef]
  6. C. Marand and P. D. Townsend, Opt. Lett. 20, 1695 (1995).
    [CrossRef] [PubMed]
  7. C. Gobby, Z. L. Yuan, and A. J. Shields, Appl. Phys. Lett. 84, 3762 (2004).
    [CrossRef]
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    [CrossRef] [PubMed]
  9. J. Lodewyck, T. Debuisschert, R. Tualle-Brouri, and P. Grangier, Phys. Rev. A 72, 050303R (2005).
    [CrossRef]
  10. A. Muller, T. Herzog, B. Huttner, W. Tittel, H. Zbinden, and N. Gisin, Appl. Phys. Lett. 70, 793 (1997).
    [CrossRef]
  11. N. Gisin, S. Fasel, B. Kraus, H. Zbinden, and G. Ribordy, Phys. Rev. A 73, 022320 (2006).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  14. S. N. Molotkov, JETP 87, 288 (1998).
    [CrossRef]
  15. B.-S. Shi, Y.-K. Jiang, and G.-C. Guo, Appl. Phys. B 70, 415 (2000).
    [CrossRef]
  16. M. Nazarathy, Opt. Lett. 30, 1533 (2005).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  19. J. Zhang, W. Slysz, A. Verevkin, O. Okunev, G. Chulkova, A. Korneev, A. Lipatov, G. N. Gol'tsman, and R. Sobolewski, IEEE Trans. Appl. Supercond. 13, 180 (2003).
    [CrossRef]
  20. W.-Y. Hwang, Phys. Rev. Lett. 91, 057901 (2003).
    [CrossRef] [PubMed]
  21. H.-K. Lo, X. Ma, and K. Chen, Phys. Rev. Lett. 94, 230504 (2005).
    [CrossRef] [PubMed]
  22. Y. Zhao, B. Qi, X.-F. Ma, H.-K. Lo, and L. Qian, Phys. Rev. Lett. 96, 070502 (2006).
    [CrossRef] [PubMed]

2006 (2)

N. Gisin, S. Fasel, B. Kraus, H. Zbinden, and G. Ribordy, Phys. Rev. A 73, 022320 (2006).
[CrossRef]

Y. Zhao, B. Qi, X.-F. Ma, H.-K. Lo, and L. Qian, Phys. Rev. Lett. 96, 070502 (2006).
[CrossRef] [PubMed]

2005 (4)

H.-K. Lo, X. Ma, and K. Chen, Phys. Rev. Lett. 94, 230504 (2005).
[CrossRef] [PubMed]

Z. Jiang, S.-D. Yang, D. E. Leaird, and A. M. Weiner, Opt. Lett. 30, 1449 (2005).
[CrossRef] [PubMed]

M. Nazarathy, Opt. Lett. 30, 1533 (2005).
[CrossRef] [PubMed]

J. Lodewyck, T. Debuisschert, R. Tualle-Brouri, and P. Grangier, Phys. Rev. A 72, 050303R (2005).
[CrossRef]

2004 (2)

C. Gobby, Z. L. Yuan, and A. J. Shields, Appl. Phys. Lett. 84, 3762 (2004).
[CrossRef]

G. V. Assche, J. Cardinal, and N. J. Cerf, IEEE Trans. Inf. Theory 50, 394 (2004).
[CrossRef]

2003 (3)

J. Zhang, W. Slysz, A. Verevkin, O. Okunev, G. Chulkova, A. Korneev, A. Lipatov, G. N. Gol'tsman, and R. Sobolewski, IEEE Trans. Appl. Supercond. 13, 180 (2003).
[CrossRef]

W.-Y. Hwang, Phys. Rev. Lett. 91, 057901 (2003).
[CrossRef] [PubMed]

F. Grosshans, G. V. Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, Nature 421, 238 (2003).
[CrossRef] [PubMed]

2002 (2)

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

R. J. Hughes, J. E. Nordholt, D. Derkacs, and C. G. Peterson, New J. Phys. 4, 43 (2002).
[CrossRef]

2000 (2)

M. Hillery, Phys. Rev. A 61, 022309 (2000).
[CrossRef]

B.-S. Shi, Y.-K. Jiang, and G.-C. Guo, Appl. Phys. B 70, 415 (2000).
[CrossRef]

1998 (2)

T. D. Donnelly and C. Grossman, Am. J. Phys. 66, 677 (1998).
[CrossRef]

S. N. Molotkov, JETP 87, 288 (1998).
[CrossRef]

1997 (1)

A. Muller, T. Herzog, B. Huttner, W. Tittel, H. Zbinden, and N. Gisin, Appl. Phys. Lett. 70, 793 (1997).
[CrossRef]

1996 (1)

S. N. Molotkov and S. S. Nazin, JETP Lett. 63, 924 (1996).
[CrossRef]

1995 (1)

1991 (1)

A. K. Ekert, Phys. Rev. Lett. 67, 661 (1991).
[CrossRef] [PubMed]

Assche, G. V.

G. V. Assche, J. Cardinal, and N. J. Cerf, IEEE Trans. Inf. Theory 50, 394 (2004).
[CrossRef]

F. Grosshans, G. V. Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, Nature 421, 238 (2003).
[CrossRef] [PubMed]

Bennett, C. H.

C. H. Bennett and G. Brassard, in Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing (IEEE, 1984), pp. 175-179.

Brassard, G.

C. H. Bennett and G. Brassard, in Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing (IEEE, 1984), pp. 175-179.

Brouri, R.

F. Grosshans, G. V. Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, Nature 421, 238 (2003).
[CrossRef] [PubMed]

Cardinal, J.

G. V. Assche, J. Cardinal, and N. J. Cerf, IEEE Trans. Inf. Theory 50, 394 (2004).
[CrossRef]

Cerf, N. J.

G. V. Assche, J. Cardinal, and N. J. Cerf, IEEE Trans. Inf. Theory 50, 394 (2004).
[CrossRef]

F. Grosshans, G. V. Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, Nature 421, 238 (2003).
[CrossRef] [PubMed]

Chen, K.

H.-K. Lo, X. Ma, and K. Chen, Phys. Rev. Lett. 94, 230504 (2005).
[CrossRef] [PubMed]

Chulkova, G.

J. Zhang, W. Slysz, A. Verevkin, O. Okunev, G. Chulkova, A. Korneev, A. Lipatov, G. N. Gol'tsman, and R. Sobolewski, IEEE Trans. Appl. Supercond. 13, 180 (2003).
[CrossRef]

Debuisschert, T.

J. Lodewyck, T. Debuisschert, R. Tualle-Brouri, and P. Grangier, Phys. Rev. A 72, 050303R (2005).
[CrossRef]

Derkacs, D.

R. J. Hughes, J. E. Nordholt, D. Derkacs, and C. G. Peterson, New J. Phys. 4, 43 (2002).
[CrossRef]

Donnelly, T. D.

T. D. Donnelly and C. Grossman, Am. J. Phys. 66, 677 (1998).
[CrossRef]

Ekert, A. K.

A. K. Ekert, Phys. Rev. Lett. 67, 661 (1991).
[CrossRef] [PubMed]

Fasel, S.

N. Gisin, S. Fasel, B. Kraus, H. Zbinden, and G. Ribordy, Phys. Rev. A 73, 022320 (2006).
[CrossRef]

Gisin, N.

N. Gisin, S. Fasel, B. Kraus, H. Zbinden, and G. Ribordy, Phys. Rev. A 73, 022320 (2006).
[CrossRef]

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

A. Muller, T. Herzog, B. Huttner, W. Tittel, H. Zbinden, and N. Gisin, Appl. Phys. Lett. 70, 793 (1997).
[CrossRef]

Gobby, C.

C. Gobby, Z. L. Yuan, and A. J. Shields, Appl. Phys. Lett. 84, 3762 (2004).
[CrossRef]

Gol'tsman, G. N.

J. Zhang, W. Slysz, A. Verevkin, O. Okunev, G. Chulkova, A. Korneev, A. Lipatov, G. N. Gol'tsman, and R. Sobolewski, IEEE Trans. Appl. Supercond. 13, 180 (2003).
[CrossRef]

Grangier, P.

J. Lodewyck, T. Debuisschert, R. Tualle-Brouri, and P. Grangier, Phys. Rev. A 72, 050303R (2005).
[CrossRef]

F. Grosshans, G. V. Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, Nature 421, 238 (2003).
[CrossRef] [PubMed]

Grosshans, F.

F. Grosshans, G. V. Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, Nature 421, 238 (2003).
[CrossRef] [PubMed]

Grossman, C.

T. D. Donnelly and C. Grossman, Am. J. Phys. 66, 677 (1998).
[CrossRef]

Guo, G.-C.

B.-S. Shi, Y.-K. Jiang, and G.-C. Guo, Appl. Phys. B 70, 415 (2000).
[CrossRef]

Herzog, T.

A. Muller, T. Herzog, B. Huttner, W. Tittel, H. Zbinden, and N. Gisin, Appl. Phys. Lett. 70, 793 (1997).
[CrossRef]

Hillery, M.

M. Hillery, Phys. Rev. A 61, 022309 (2000).
[CrossRef]

Hughes, R. J.

R. J. Hughes, J. E. Nordholt, D. Derkacs, and C. G. Peterson, New J. Phys. 4, 43 (2002).
[CrossRef]

Huttner, B.

A. Muller, T. Herzog, B. Huttner, W. Tittel, H. Zbinden, and N. Gisin, Appl. Phys. Lett. 70, 793 (1997).
[CrossRef]

Hwang, W.-Y.

W.-Y. Hwang, Phys. Rev. Lett. 91, 057901 (2003).
[CrossRef] [PubMed]

Jiang, Y.-K.

B.-S. Shi, Y.-K. Jiang, and G.-C. Guo, Appl. Phys. B 70, 415 (2000).
[CrossRef]

Jiang, Z.

Korneev, A.

J. Zhang, W. Slysz, A. Verevkin, O. Okunev, G. Chulkova, A. Korneev, A. Lipatov, G. N. Gol'tsman, and R. Sobolewski, IEEE Trans. Appl. Supercond. 13, 180 (2003).
[CrossRef]

Kraus, B.

N. Gisin, S. Fasel, B. Kraus, H. Zbinden, and G. Ribordy, Phys. Rev. A 73, 022320 (2006).
[CrossRef]

Leaird, D. E.

Lipatov, A.

J. Zhang, W. Slysz, A. Verevkin, O. Okunev, G. Chulkova, A. Korneev, A. Lipatov, G. N. Gol'tsman, and R. Sobolewski, IEEE Trans. Appl. Supercond. 13, 180 (2003).
[CrossRef]

Lo, H.-K.

Y. Zhao, B. Qi, X.-F. Ma, H.-K. Lo, and L. Qian, Phys. Rev. Lett. 96, 070502 (2006).
[CrossRef] [PubMed]

H.-K. Lo, X. Ma, and K. Chen, Phys. Rev. Lett. 94, 230504 (2005).
[CrossRef] [PubMed]

Lodewyck, J.

J. Lodewyck, T. Debuisschert, R. Tualle-Brouri, and P. Grangier, Phys. Rev. A 72, 050303R (2005).
[CrossRef]

Ma, X.

H.-K. Lo, X. Ma, and K. Chen, Phys. Rev. Lett. 94, 230504 (2005).
[CrossRef] [PubMed]

Ma, X.-F.

Y. Zhao, B. Qi, X.-F. Ma, H.-K. Lo, and L. Qian, Phys. Rev. Lett. 96, 070502 (2006).
[CrossRef] [PubMed]

Marand, C.

Molotkov, S. N.

S. N. Molotkov, JETP 87, 288 (1998).
[CrossRef]

S. N. Molotkov and S. S. Nazin, JETP Lett. 63, 924 (1996).
[CrossRef]

Muller, A.

A. Muller, T. Herzog, B. Huttner, W. Tittel, H. Zbinden, and N. Gisin, Appl. Phys. Lett. 70, 793 (1997).
[CrossRef]

Nazarathy, M.

Nazin, S. S.

S. N. Molotkov and S. S. Nazin, JETP Lett. 63, 924 (1996).
[CrossRef]

Nordholt, J. E.

R. J. Hughes, J. E. Nordholt, D. Derkacs, and C. G. Peterson, New J. Phys. 4, 43 (2002).
[CrossRef]

Okunev, O.

J. Zhang, W. Slysz, A. Verevkin, O. Okunev, G. Chulkova, A. Korneev, A. Lipatov, G. N. Gol'tsman, and R. Sobolewski, IEEE Trans. Appl. Supercond. 13, 180 (2003).
[CrossRef]

Peterson, C. G.

R. J. Hughes, J. E. Nordholt, D. Derkacs, and C. G. Peterson, New J. Phys. 4, 43 (2002).
[CrossRef]

Qi, B.

Y. Zhao, B. Qi, X.-F. Ma, H.-K. Lo, and L. Qian, Phys. Rev. Lett. 96, 070502 (2006).
[CrossRef] [PubMed]

Qian, L.

Y. Zhao, B. Qi, X.-F. Ma, H.-K. Lo, and L. Qian, Phys. Rev. Lett. 96, 070502 (2006).
[CrossRef] [PubMed]

Ribordy, G.

N. Gisin, S. Fasel, B. Kraus, H. Zbinden, and G. Ribordy, Phys. Rev. A 73, 022320 (2006).
[CrossRef]

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

Shi, B.-S.

B.-S. Shi, Y.-K. Jiang, and G.-C. Guo, Appl. Phys. B 70, 415 (2000).
[CrossRef]

Shields, A. J.

C. Gobby, Z. L. Yuan, and A. J. Shields, Appl. Phys. Lett. 84, 3762 (2004).
[CrossRef]

Slysz, W.

J. Zhang, W. Slysz, A. Verevkin, O. Okunev, G. Chulkova, A. Korneev, A. Lipatov, G. N. Gol'tsman, and R. Sobolewski, IEEE Trans. Appl. Supercond. 13, 180 (2003).
[CrossRef]

Sobolewski, R.

J. Zhang, W. Slysz, A. Verevkin, O. Okunev, G. Chulkova, A. Korneev, A. Lipatov, G. N. Gol'tsman, and R. Sobolewski, IEEE Trans. Appl. Supercond. 13, 180 (2003).
[CrossRef]

Tittel, W.

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

A. Muller, T. Herzog, B. Huttner, W. Tittel, H. Zbinden, and N. Gisin, Appl. Phys. Lett. 70, 793 (1997).
[CrossRef]

Townsend, P. D.

Tualle-Brouri, R.

J. Lodewyck, T. Debuisschert, R. Tualle-Brouri, and P. Grangier, Phys. Rev. A 72, 050303R (2005).
[CrossRef]

Verevkin, A.

J. Zhang, W. Slysz, A. Verevkin, O. Okunev, G. Chulkova, A. Korneev, A. Lipatov, G. N. Gol'tsman, and R. Sobolewski, IEEE Trans. Appl. Supercond. 13, 180 (2003).
[CrossRef]

Weiner, A. M.

Wenger, J.

F. Grosshans, G. V. Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, Nature 421, 238 (2003).
[CrossRef] [PubMed]

Yang, S.-D.

Yuan, Z. L.

C. Gobby, Z. L. Yuan, and A. J. Shields, Appl. Phys. Lett. 84, 3762 (2004).
[CrossRef]

Zbinden, H.

N. Gisin, S. Fasel, B. Kraus, H. Zbinden, and G. Ribordy, Phys. Rev. A 73, 022320 (2006).
[CrossRef]

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

A. Muller, T. Herzog, B. Huttner, W. Tittel, H. Zbinden, and N. Gisin, Appl. Phys. Lett. 70, 793 (1997).
[CrossRef]

Zhang, J.

J. Zhang, W. Slysz, A. Verevkin, O. Okunev, G. Chulkova, A. Korneev, A. Lipatov, G. N. Gol'tsman, and R. Sobolewski, IEEE Trans. Appl. Supercond. 13, 180 (2003).
[CrossRef]

Zhao, Y.

Y. Zhao, B. Qi, X.-F. Ma, H.-K. Lo, and L. Qian, Phys. Rev. Lett. 96, 070502 (2006).
[CrossRef] [PubMed]

Am. J. Phys. (1)

T. D. Donnelly and C. Grossman, Am. J. Phys. 66, 677 (1998).
[CrossRef]

Appl. Phys. B (1)

B.-S. Shi, Y.-K. Jiang, and G.-C. Guo, Appl. Phys. B 70, 415 (2000).
[CrossRef]

Appl. Phys. Lett. (2)

A. Muller, T. Herzog, B. Huttner, W. Tittel, H. Zbinden, and N. Gisin, Appl. Phys. Lett. 70, 793 (1997).
[CrossRef]

C. Gobby, Z. L. Yuan, and A. J. Shields, Appl. Phys. Lett. 84, 3762 (2004).
[CrossRef]

IEEE Trans. Appl. Supercond. (1)

J. Zhang, W. Slysz, A. Verevkin, O. Okunev, G. Chulkova, A. Korneev, A. Lipatov, G. N. Gol'tsman, and R. Sobolewski, IEEE Trans. Appl. Supercond. 13, 180 (2003).
[CrossRef]

IEEE Trans. Inf. Theory (1)

G. V. Assche, J. Cardinal, and N. J. Cerf, IEEE Trans. Inf. Theory 50, 394 (2004).
[CrossRef]

JETP (1)

S. N. Molotkov, JETP 87, 288 (1998).
[CrossRef]

JETP Lett. (1)

S. N. Molotkov and S. S. Nazin, JETP Lett. 63, 924 (1996).
[CrossRef]

Nature (1)

F. Grosshans, G. V. Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, Nature 421, 238 (2003).
[CrossRef] [PubMed]

New J. Phys. (1)

R. J. Hughes, J. E. Nordholt, D. Derkacs, and C. G. Peterson, New J. Phys. 4, 43 (2002).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (3)

N. Gisin, S. Fasel, B. Kraus, H. Zbinden, and G. Ribordy, Phys. Rev. A 73, 022320 (2006).
[CrossRef]

J. Lodewyck, T. Debuisschert, R. Tualle-Brouri, and P. Grangier, Phys. Rev. A 72, 050303R (2005).
[CrossRef]

M. Hillery, Phys. Rev. A 61, 022309 (2000).
[CrossRef]

Phys. Rev. Lett. (4)

A. K. Ekert, Phys. Rev. Lett. 67, 661 (1991).
[CrossRef] [PubMed]

W.-Y. Hwang, Phys. Rev. Lett. 91, 057901 (2003).
[CrossRef] [PubMed]

H.-K. Lo, X. Ma, and K. Chen, Phys. Rev. Lett. 94, 230504 (2005).
[CrossRef] [PubMed]

Y. Zhao, B. Qi, X.-F. Ma, H.-K. Lo, and L. Qian, Phys. Rev. Lett. 96, 070502 (2006).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

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

Other (1)

C. H. Bennett and G. Brassard, in Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing (IEEE, 1984), pp. 175-179.

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Figures (2)

Fig. 1
Fig. 1

Schematic diagram of the proposed QKD system: S 1 , narrowband frequency tunable single-photon source; S 2 , broadband single-photon source with tunable time delay; BS, beam splitter; DG, dispersive grating; TSPD, time-resolving SPD; SPDA, SPD array.

Fig. 2
Fig. 2

(Color online) Illustration of the frequency (time) domain distributions of Alice’s single-photon sources. Top left, S 1 in the frequency domain: solid curves, spectra with different central frequencies; dashed curve, frequency modulation profile. Top right, S 1 in the time domain. Bottom left, S 2 in the frequency domain. Bottom right, S 2 in the time domain: solid curves, pulse shapes with different time delays; dashed curve, time-delay modulation profile.

Equations (16)

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

σ ω σ t = 1 ,
a ̂ ξ + = d ω ξ ( ω ) a ̂ + ( ω ) ,
ξ ( ω ) = ( π σ ω 2 ) 1 4 exp [ i ( ω 0 ω ) t 0 ( ω ω 0 ) 2 2 σ ω 2 ] ,
f 1 ( ω 1 ) = ( π σ ω 2 2 ) 1 2 exp [ ( ω 1 ω 0 ) 2 σ ω 2 2 ] .
ρ ̂ 1 = f 1 ( ω 1 ) a ̂ ξ 1 + 0 0 a ̂ ξ 1 d ω 1
= ( π σ ω 2 2 ) 1 2 exp [ ( ω 1 ω 0 ) 2 σ ω 2 2 ]
× ( π σ ω 1 2 ) 1 4 exp [ ( ω 2 ω 1 ) 2 2 σ ω 1 2 ]
× ( π σ ω 1 2 ) 1 4 exp [ ( ω 3 ω 1 ) 2 2 σ ω 1 2 ]
× a ̂ + ( ω 2 ) 0 0 a ̂ ( ω 3 ) d ω 1 d ω 2 d ω 3 .
ρ ̂ 2 = f 2 ( t ) a ̂ ξ 2 + 0 0 a ̂ ξ 2 d t
= ( π ) 1 2 σ ω 1 exp [ σ ω 1 2 t 2 ]
× ( π σ ω 2 2 ) 1 4 exp [ i ( ω 0 ω 1 ) t ( ω 1 ω 0 ) 2 2 σ ω 2 2 ]
× ( π σ ω 2 2 ) 1 4 exp [ i ( ω 0 ω 2 ) t ( ω 2 ω 0 ) 2 2 σ ω 2 2 ]
× a ̂ + ( ω 1 ) 0 0 a ̂ ( ω 2 ) d ω 1 d ω 2 d t .
ρ ̂ 1 = ρ ̂ 2 = ( π σ ω 2 2 ) 1 2 exp [ ( ω 1 ω 0 ) 2 σ ω 2 2 ]
× a ̂ + ( ω 1 ) 0 0 a ̂ ( ω 1 ) d ω 1 .

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