Abstract

We present an exact model of the detection statistics of a probabilistic source of photon pairs from which a fast, simple and precise method to measure the source’s brightness and photon channel transmissions is demonstrated. We measure such properties for a source based on spontaneous parametric downconversion in a periodically poled LiNbO3 crystal producing pairs at 810 and 1550 nm wavelengths. We further validate the model by comparing the predicted and measured values for the g (2) (0) of a heralded single photon source over a wide range of the brightness. Our model is of particular use for monitoring and tuning the brightness on demand as required for various quantum communication applications. We comment on its applicability to sources involving spectral and/or spatial filtering.

© 2008 Optical Society of America

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    [CrossRef]
  4. L.-M. Duan, M. D. Lukin, J. I. Cirac and P. Zoller, "Long-distance quantum communication with atomic ensembles and linear optics," Nature (London) 414413-418 (2001).
    [CrossRef] [PubMed]
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    [CrossRef]
  6. M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, "All-fiber photon-pair source for quantum communications," IEEE Phot. Technol. Lett. 14, 983-985 (2002).
    [CrossRef]
  7. A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L.-M. Duan, and H. J. Kimble, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles," Nature (London) 423, 731-734 (2003).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  14. Y. Adachi,T. Yamamoto, M. Koashi, and N. Imoto, "Simple and Efficient Quantum Key Distribution with Parametric Down-Conversion," Phys. Rev. Lett. 99, 180503 (2007).
    [CrossRef] [PubMed]
  15. W. Mauerer and C. Silberhorn, "Quantum key distribution with passive decoy state selection," Phys. Rev. A 75, 050305(R) (2007).
    [CrossRef]
  16. H. de Riedmatten, I. Marcikic, W. Tittel, H. Zbinden, and N. Gisin, "Quantum interference with photon pairs created in spatially separated sources," Phys. Rev. A 67, 022301 (2003).
    [CrossRef]
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    [CrossRef]
  22. H. de Riedmatten, V. Scarani, I. Marcikic, A. Ac�??ın,W. Tittel, H. Zbinden, and N. Gisin, "Two independent photon pairs versus four-photon entangled states in parametric down conversion," J. Mod. Opt. 51, 1637-1649 (2004).
  23. R. Hanbury Brown, and R. Q. Twiss, "A Test of a New Type of Stellar Interferometer on Sirius," Nature (London) 178, 1046-1048 (1956).
    [CrossRef]
  24. For a Thermal distribution the g(2)(0) is higher by a factor of 2: g(2)(0) = 2�??(2�??|H). In the case of spectral and/or spatial correlations with a Poissonian source, as discussed in section 4, g(2)(0) =�??(2/c�??|H).
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  26. J. D. Franson, "Nonlocal cancellation of dispersion," Phys. Rev. A 45, 3126-3132 (1992).
    [CrossRef] [PubMed]
  27. P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U�??Ren, C. Silberhorn, and I. A.Walmsley, "Heralded Generation of Ultrafast Single Photons in Pure Quantum States," Phys. Rev. Lett. 100, 133601 (2008).
    [CrossRef] [PubMed]
  28. C. H. Bennett, G. Brassard, and J.-M. Robert, "Privacy amplification by public discussion," SIAM J. Comput. 17, 210-229 (1988).
    [CrossRef]
  29. C. H. Bennett, G. Brassard, C. Cr�??epeau, and U. M. Maurer, "Generalized privacy amplification," IEEE Trans. Inf. Theory 41, 1915-1923 (1995).
    [CrossRef]

2008 (2)

Q. W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z.-F. Han, G.-C. Guo, and A. Karlsson, "Experimental Decoy-State Quantum Key Distribution with a Sub-Poissionian Heralded Single-Photon Source," Phys. Rev. Lett. 100, 090501 (2008).
[CrossRef] [PubMed]

P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U�??Ren, C. Silberhorn, and I. A.Walmsley, "Heralded Generation of Ultrafast Single Photons in Pure Quantum States," Phys. Rev. Lett. 100, 133601 (2008).
[CrossRef] [PubMed]

2007 (3)

Y. Adachi,T. Yamamoto, M. Koashi, and N. Imoto, "Simple and Efficient Quantum Key Distribution with Parametric Down-Conversion," Phys. Rev. Lett. 99, 180503 (2007).
[CrossRef] [PubMed]

X. Ma, C.-H. Fred Fung, and H.-K. Lo, "Quantum key distribution with entangled photon sources," Phys. Rev. A 76, 012307 (2007).
[CrossRef]

J. Simon, H. Tanji, J. K. Thompson, and V. Vuletic, "Interfacing Collective Atomic Excitations and Single Photons," Phys. Rev. Lett. 98183601 (2007).
[CrossRef] [PubMed]

2005 (1)

2004 (2)

S. Takeuchi, R. Okamoto, and K. Sasaki, "High-Yield Single-Photon Source Using Gated Spontaneous Parametric Downconversion," Appl. Opt. 43, 5708-5711 (2004).
[CrossRef] [PubMed]

H. de Riedmatten, V. Scarani, I. Marcikic, A. Ac�??ın,W. Tittel, H. Zbinden, and N. Gisin, "Two independent photon pairs versus four-photon entangled states in parametric down conversion," J. Mod. Opt. 51, 1637-1649 (2004).

2003 (2)

H. de Riedmatten, I. Marcikic, W. Tittel, H. Zbinden, and N. Gisin, "Quantum interference with photon pairs created in spatially separated sources," Phys. Rev. A 67, 022301 (2003).
[CrossRef]

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L.-M. Duan, and H. J. Kimble, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles," Nature (London) 423, 731-734 (2003).
[CrossRef] [PubMed]

2002 (3)

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, "All-fiber photon-pair source for quantum communications," IEEE Phot. Technol. Lett. 14, 983-985 (2002).
[CrossRef]

I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, "Time-bin entangled qubits for quantum communication created by femtosecond pulses," Phys. Rev. A 66, 062308 (2002).
[CrossRef]

E. Waks, C. Santori, and Y. Yamamoto, "Security aspects of quantum key distribution with sub-Poisson light," Phys. Rev. A 66, 042315 (2002).
[CrossRef]

2001 (2)

W. Tittel and G. Weihs, "Photonic Entanglement for Fundamental Tests and Quantum Communication," Quantum Inf. and Comp. 1, 3-56 (2001).

L.-M. Duan, M. D. Lukin, J. I. Cirac and P. Zoller, "Long-distance quantum communication with atomic ensembles and linear optics," Nature (London) 414413-418 (2001).
[CrossRef] [PubMed]

1998 (1)

H.-J. Briegel, W. D¨ur, J. I. Cirac and P. Zoller, "Quantum Repeaters: the Role of Imperfect Local Operations in Quantum Communication," Phys. Rev. Lett. 81, 5932-5935 (1998).
[CrossRef]

1995 (1)

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

1992 (1)

J. D. Franson, "Nonlocal cancellation of dispersion," Phys. Rev. A 45, 3126-3132 (1992).
[CrossRef] [PubMed]

1991 (1)

A. Ekert, "Quantum Cryptography Based on Bell�??s Theorem," Phys. Rev. Lett. 67, 661-663 (1991).
[CrossRef] [PubMed]

1988 (1)

C. H. Bennett, G. Brassard, and J.-M. Robert, "Privacy amplification by public discussion," SIAM J. Comput. 17, 210-229 (1988).
[CrossRef]

1986 (1)

C. K. Hong and L. Mandel, "Experimental realization of a localized one-photon state," Phys. Rev. Lett. 56, 58-60 (1986).
[CrossRef] [PubMed]

1970 (1)

D. C. Burnham and D. L. Weinberg, "Observation of Simultaneity in Parametric Production of Optical Photon Pairs," Phys. Rev. Lett. 25, 84-87 (1970).
[CrossRef]

1956 (1)

R. Hanbury Brown, and R. Q. Twiss, "A Test of a New Type of Stellar Interferometer on Sirius," Nature (London) 178, 1046-1048 (1956).
[CrossRef]

Ac???in, A.

H. de Riedmatten, V. Scarani, I. Marcikic, A. Ac�??ın,W. Tittel, H. Zbinden, and N. Gisin, "Two independent photon pairs versus four-photon entangled states in parametric down conversion," J. Mod. Opt. 51, 1637-1649 (2004).

Adachi, Y.

Y. Adachi,T. Yamamoto, M. Koashi, and N. Imoto, "Simple and Efficient Quantum Key Distribution with Parametric Down-Conversion," Phys. Rev. Lett. 99, 180503 (2007).
[CrossRef] [PubMed]

Bennett, C. H.

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

C. H. Bennett, G. Brassard, and J.-M. Robert, "Privacy amplification by public discussion," SIAM J. Comput. 17, 210-229 (1988).
[CrossRef]

Boca, A.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L.-M. Duan, and H. J. Kimble, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles," Nature (London) 423, 731-734 (2003).
[CrossRef] [PubMed]

Boozer, A. D.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L.-M. Duan, and H. J. Kimble, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles," Nature (London) 423, 731-734 (2003).
[CrossRef] [PubMed]

Bowen, W. P.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L.-M. Duan, and H. J. Kimble, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles," Nature (London) 423, 731-734 (2003).
[CrossRef] [PubMed]

Brassard, G.

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

C. H. Bennett, G. Brassard, and J.-M. Robert, "Privacy amplification by public discussion," SIAM J. Comput. 17, 210-229 (1988).
[CrossRef]

Briegel, H.-J.

H.-J. Briegel, W. D¨ur, J. I. Cirac and P. Zoller, "Quantum Repeaters: the Role of Imperfect Local Operations in Quantum Communication," Phys. Rev. Lett. 81, 5932-5935 (1998).
[CrossRef]

Burnham, D. C.

D. C. Burnham and D. L. Weinberg, "Observation of Simultaneity in Parametric Production of Optical Photon Pairs," Phys. Rev. Lett. 25, 84-87 (1970).
[CrossRef]

Chen, Q. W.

Q. W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z.-F. Han, G.-C. Guo, and A. Karlsson, "Experimental Decoy-State Quantum Key Distribution with a Sub-Poissionian Heralded Single-Photon Source," Phys. Rev. Lett. 100, 090501 (2008).
[CrossRef] [PubMed]

Chou, C. W.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L.-M. Duan, and H. J. Kimble, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles," Nature (London) 423, 731-734 (2003).
[CrossRef] [PubMed]

Cirac, J. I.

L.-M. Duan, M. D. Lukin, J. I. Cirac and P. Zoller, "Long-distance quantum communication with atomic ensembles and linear optics," Nature (London) 414413-418 (2001).
[CrossRef] [PubMed]

H.-J. Briegel, W. D¨ur, J. I. Cirac and P. Zoller, "Quantum Repeaters: the Role of Imperfect Local Operations in Quantum Communication," Phys. Rev. Lett. 81, 5932-5935 (1998).
[CrossRef]

Cr???epeau, C.

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

D¨ur, W.

H.-J. Briegel, W. D¨ur, J. I. Cirac and P. Zoller, "Quantum Repeaters: the Role of Imperfect Local Operations in Quantum Communication," Phys. Rev. Lett. 81, 5932-5935 (1998).
[CrossRef]

de Riedmatten, H.

H. de Riedmatten, V. Scarani, I. Marcikic, A. Ac�??ın,W. Tittel, H. Zbinden, and N. Gisin, "Two independent photon pairs versus four-photon entangled states in parametric down conversion," J. Mod. Opt. 51, 1637-1649 (2004).

H. de Riedmatten, I. Marcikic, W. Tittel, H. Zbinden, and N. Gisin, "Quantum interference with photon pairs created in spatially separated sources," Phys. Rev. A 67, 022301 (2003).
[CrossRef]

I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, "Time-bin entangled qubits for quantum communication created by femtosecond pulses," Phys. Rev. A 66, 062308 (2002).
[CrossRef]

Duan, L.-M.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L.-M. Duan, and H. J. Kimble, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles," Nature (London) 423, 731-734 (2003).
[CrossRef] [PubMed]

L.-M. Duan, M. D. Lukin, J. I. Cirac and P. Zoller, "Long-distance quantum communication with atomic ensembles and linear optics," Nature (London) 414413-418 (2001).
[CrossRef] [PubMed]

Ekert, A.

A. Ekert, "Quantum Cryptography Based on Bell�??s Theorem," Phys. Rev. Lett. 67, 661-663 (1991).
[CrossRef] [PubMed]

Fiorentino, M.

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, "All-fiber photon-pair source for quantum communications," IEEE Phot. Technol. Lett. 14, 983-985 (2002).
[CrossRef]

Franson, J. D.

J. D. Franson, "Nonlocal cancellation of dispersion," Phys. Rev. A 45, 3126-3132 (1992).
[CrossRef] [PubMed]

Fred Fung, C.-H.

X. Ma, C.-H. Fred Fung, and H.-K. Lo, "Quantum key distribution with entangled photon sources," Phys. Rev. A 76, 012307 (2007).
[CrossRef]

Gisin, N.

H. de Riedmatten, V. Scarani, I. Marcikic, A. Ac�??ın,W. Tittel, H. Zbinden, and N. Gisin, "Two independent photon pairs versus four-photon entangled states in parametric down conversion," J. Mod. Opt. 51, 1637-1649 (2004).

H. de Riedmatten, I. Marcikic, W. Tittel, H. Zbinden, and N. Gisin, "Quantum interference with photon pairs created in spatially separated sources," Phys. Rev. A 67, 022301 (2003).
[CrossRef]

I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, "Time-bin entangled qubits for quantum communication created by femtosecond pulses," Phys. Rev. A 66, 062308 (2002).
[CrossRef]

Guo, G.-C.

Q. W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z.-F. Han, G.-C. Guo, and A. Karlsson, "Experimental Decoy-State Quantum Key Distribution with a Sub-Poissionian Heralded Single-Photon Source," Phys. Rev. Lett. 100, 090501 (2008).
[CrossRef] [PubMed]

Han, Z.-F.

Q. W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z.-F. Han, G.-C. Guo, and A. Karlsson, "Experimental Decoy-State Quantum Key Distribution with a Sub-Poissionian Heralded Single-Photon Source," Phys. Rev. Lett. 100, 090501 (2008).
[CrossRef] [PubMed]

Hanbury Brown, R.

R. Hanbury Brown, and R. Q. Twiss, "A Test of a New Type of Stellar Interferometer on Sirius," Nature (London) 178, 1046-1048 (1956).
[CrossRef]

Hong, C. K.

C. K. Hong and L. Mandel, "Experimental realization of a localized one-photon state," Phys. Rev. Lett. 56, 58-60 (1986).
[CrossRef] [PubMed]

Imoto, N.

Y. Adachi,T. Yamamoto, M. Koashi, and N. Imoto, "Simple and Efficient Quantum Key Distribution with Parametric Down-Conversion," Phys. Rev. Lett. 99, 180503 (2007).
[CrossRef] [PubMed]

Karlsson, A.

Q. W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z.-F. Han, G.-C. Guo, and A. Karlsson, "Experimental Decoy-State Quantum Key Distribution with a Sub-Poissionian Heralded Single-Photon Source," Phys. Rev. Lett. 100, 090501 (2008).
[CrossRef] [PubMed]

Kimble, H. J.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L.-M. Duan, and H. J. Kimble, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles," Nature (London) 423, 731-734 (2003).
[CrossRef] [PubMed]

Koashi, M.

Y. Adachi,T. Yamamoto, M. Koashi, and N. Imoto, "Simple and Efficient Quantum Key Distribution with Parametric Down-Conversion," Phys. Rev. Lett. 99, 180503 (2007).
[CrossRef] [PubMed]

Kumar, P.

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, "All-fiber photon-pair source for quantum communications," IEEE Phot. Technol. Lett. 14, 983-985 (2002).
[CrossRef]

Kuzmich, A.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L.-M. Duan, and H. J. Kimble, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles," Nature (London) 423, 731-734 (2003).
[CrossRef] [PubMed]

Lo, H.-K.

X. Ma, C.-H. Fred Fung, and H.-K. Lo, "Quantum key distribution with entangled photon sources," Phys. Rev. A 76, 012307 (2007).
[CrossRef]

Lukin, M. D.

L.-M. Duan, M. D. Lukin, J. I. Cirac and P. Zoller, "Long-distance quantum communication with atomic ensembles and linear optics," Nature (London) 414413-418 (2001).
[CrossRef] [PubMed]

Lundeen, J. S.

P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U�??Ren, C. Silberhorn, and I. A.Walmsley, "Heralded Generation of Ultrafast Single Photons in Pure Quantum States," Phys. Rev. Lett. 100, 133601 (2008).
[CrossRef] [PubMed]

Ma, X.

X. Ma, C.-H. Fred Fung, and H.-K. Lo, "Quantum key distribution with entangled photon sources," Phys. Rev. A 76, 012307 (2007).
[CrossRef]

Mandel, L.

C. K. Hong and L. Mandel, "Experimental realization of a localized one-photon state," Phys. Rev. Lett. 56, 58-60 (1986).
[CrossRef] [PubMed]

Marcikic, I.

H. de Riedmatten, V. Scarani, I. Marcikic, A. Ac�??ın,W. Tittel, H. Zbinden, and N. Gisin, "Two independent photon pairs versus four-photon entangled states in parametric down conversion," J. Mod. Opt. 51, 1637-1649 (2004).

H. de Riedmatten, I. Marcikic, W. Tittel, H. Zbinden, and N. Gisin, "Quantum interference with photon pairs created in spatially separated sources," Phys. Rev. A 67, 022301 (2003).
[CrossRef]

I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, "Time-bin entangled qubits for quantum communication created by femtosecond pulses," Phys. Rev. A 66, 062308 (2002).
[CrossRef]

Mauerer, W.

W. Mauerer and C. Silberhorn, "Quantum key distribution with passive decoy state selection," Phys. Rev. A 75, 050305(R) (2007).
[CrossRef]

Maurer, U. M.

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

Mosley, P. J.

P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U�??Ren, C. Silberhorn, and I. A.Walmsley, "Heralded Generation of Ultrafast Single Photons in Pure Quantum States," Phys. Rev. Lett. 100, 133601 (2008).
[CrossRef] [PubMed]

Okamoto, R.

Robert, J.-M.

C. H. Bennett, G. Brassard, and J.-M. Robert, "Privacy amplification by public discussion," SIAM J. Comput. 17, 210-229 (1988).
[CrossRef]

Santori, C.

E. Waks, C. Santori, and Y. Yamamoto, "Security aspects of quantum key distribution with sub-Poisson light," Phys. Rev. A 66, 042315 (2002).
[CrossRef]

Sasaki, K.

Sauge, S.

Q. W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z.-F. Han, G.-C. Guo, and A. Karlsson, "Experimental Decoy-State Quantum Key Distribution with a Sub-Poissionian Heralded Single-Photon Source," Phys. Rev. Lett. 100, 090501 (2008).
[CrossRef] [PubMed]

Scarani, V.

H. de Riedmatten, V. Scarani, I. Marcikic, A. Ac�??ın,W. Tittel, H. Zbinden, and N. Gisin, "Two independent photon pairs versus four-photon entangled states in parametric down conversion," J. Mod. Opt. 51, 1637-1649 (2004).

I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, "Time-bin entangled qubits for quantum communication created by femtosecond pulses," Phys. Rev. A 66, 062308 (2002).
[CrossRef]

Sharping, J. E.

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, "All-fiber photon-pair source for quantum communications," IEEE Phot. Technol. Lett. 14, 983-985 (2002).
[CrossRef]

Silberhorn, C.

W. Mauerer and C. Silberhorn, "Quantum key distribution with passive decoy state selection," Phys. Rev. A 75, 050305(R) (2007).
[CrossRef]

Simon, J.

J. Simon, H. Tanji, J. K. Thompson, and V. Vuletic, "Interfacing Collective Atomic Excitations and Single Photons," Phys. Rev. Lett. 98183601 (2007).
[CrossRef] [PubMed]

Smith, B. J.

P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U�??Ren, C. Silberhorn, and I. A.Walmsley, "Heralded Generation of Ultrafast Single Photons in Pure Quantum States," Phys. Rev. Lett. 100, 133601 (2008).
[CrossRef] [PubMed]

Swillo, M.

Q. W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z.-F. Han, G.-C. Guo, and A. Karlsson, "Experimental Decoy-State Quantum Key Distribution with a Sub-Poissionian Heralded Single-Photon Source," Phys. Rev. Lett. 100, 090501 (2008).
[CrossRef] [PubMed]

Takeuchi, S.

Tanji, H.

J. Simon, H. Tanji, J. K. Thompson, and V. Vuletic, "Interfacing Collective Atomic Excitations and Single Photons," Phys. Rev. Lett. 98183601 (2007).
[CrossRef] [PubMed]

Tengner, M.

Q. W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z.-F. Han, G.-C. Guo, and A. Karlsson, "Experimental Decoy-State Quantum Key Distribution with a Sub-Poissionian Heralded Single-Photon Source," Phys. Rev. Lett. 100, 090501 (2008).
[CrossRef] [PubMed]

Thompson, J. K.

J. Simon, H. Tanji, J. K. Thompson, and V. Vuletic, "Interfacing Collective Atomic Excitations and Single Photons," Phys. Rev. Lett. 98183601 (2007).
[CrossRef] [PubMed]

Tittel, W.

H. de Riedmatten, V. Scarani, I. Marcikic, A. Ac�??ın,W. Tittel, H. Zbinden, and N. Gisin, "Two independent photon pairs versus four-photon entangled states in parametric down conversion," J. Mod. Opt. 51, 1637-1649 (2004).

H. de Riedmatten, I. Marcikic, W. Tittel, H. Zbinden, and N. Gisin, "Quantum interference with photon pairs created in spatially separated sources," Phys. Rev. A 67, 022301 (2003).
[CrossRef]

I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, "Time-bin entangled qubits for quantum communication created by femtosecond pulses," Phys. Rev. A 66, 062308 (2002).
[CrossRef]

W. Tittel and G. Weihs, "Photonic Entanglement for Fundamental Tests and Quantum Communication," Quantum Inf. and Comp. 1, 3-56 (2001).

Twiss, R. Q.

R. Hanbury Brown, and R. Q. Twiss, "A Test of a New Type of Stellar Interferometer on Sirius," Nature (London) 178, 1046-1048 (1956).
[CrossRef]

Voss, P. L.

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, "All-fiber photon-pair source for quantum communications," IEEE Phot. Technol. Lett. 14, 983-985 (2002).
[CrossRef]

Vuletic, V.

J. Simon, H. Tanji, J. K. Thompson, and V. Vuletic, "Interfacing Collective Atomic Excitations and Single Photons," Phys. Rev. Lett. 98183601 (2007).
[CrossRef] [PubMed]

Waks, E.

E. Waks, C. Santori, and Y. Yamamoto, "Security aspects of quantum key distribution with sub-Poisson light," Phys. Rev. A 66, 042315 (2002).
[CrossRef]

Wasylczyk, P.

P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U�??Ren, C. Silberhorn, and I. A.Walmsley, "Heralded Generation of Ultrafast Single Photons in Pure Quantum States," Phys. Rev. Lett. 100, 133601 (2008).
[CrossRef] [PubMed]

Weihs, G.

W. Tittel and G. Weihs, "Photonic Entanglement for Fundamental Tests and Quantum Communication," Quantum Inf. and Comp. 1, 3-56 (2001).

Weinberg, D. L.

D. C. Burnham and D. L. Weinberg, "Observation of Simultaneity in Parametric Production of Optical Photon Pairs," Phys. Rev. Lett. 25, 84-87 (1970).
[CrossRef]

Xavier, G.

Q. W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z.-F. Han, G.-C. Guo, and A. Karlsson, "Experimental Decoy-State Quantum Key Distribution with a Sub-Poissionian Heralded Single-Photon Source," Phys. Rev. Lett. 100, 090501 (2008).
[CrossRef] [PubMed]

Yamamoto, T.

Y. Adachi,T. Yamamoto, M. Koashi, and N. Imoto, "Simple and Efficient Quantum Key Distribution with Parametric Down-Conversion," Phys. Rev. Lett. 99, 180503 (2007).
[CrossRef] [PubMed]

Yamamoto, Y.

E. Waks, C. Santori, and Y. Yamamoto, "Security aspects of quantum key distribution with sub-Poisson light," Phys. Rev. A 66, 042315 (2002).
[CrossRef]

Zbinden, H.

H. de Riedmatten, V. Scarani, I. Marcikic, A. Ac�??ın,W. Tittel, H. Zbinden, and N. Gisin, "Two independent photon pairs versus four-photon entangled states in parametric down conversion," J. Mod. Opt. 51, 1637-1649 (2004).

H. de Riedmatten, I. Marcikic, W. Tittel, H. Zbinden, and N. Gisin, "Quantum interference with photon pairs created in spatially separated sources," Phys. Rev. A 67, 022301 (2003).
[CrossRef]

I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, "Time-bin entangled qubits for quantum communication created by femtosecond pulses," Phys. Rev. A 66, 062308 (2002).
[CrossRef]

Zhang, T.

Q. W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z.-F. Han, G.-C. Guo, and A. Karlsson, "Experimental Decoy-State Quantum Key Distribution with a Sub-Poissionian Heralded Single-Photon Source," Phys. Rev. Lett. 100, 090501 (2008).
[CrossRef] [PubMed]

Zoller, P.

L.-M. Duan, M. D. Lukin, J. I. Cirac and P. Zoller, "Long-distance quantum communication with atomic ensembles and linear optics," Nature (London) 414413-418 (2001).
[CrossRef] [PubMed]

H.-J. Briegel, W. D¨ur, J. I. Cirac and P. Zoller, "Quantum Repeaters: the Role of Imperfect Local Operations in Quantum Communication," Phys. Rev. Lett. 81, 5932-5935 (1998).
[CrossRef]

Appl. Opt. (1)

IEEE Phot. Technol. Lett. (1)

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, "All-fiber photon-pair source for quantum communications," IEEE Phot. Technol. Lett. 14, 983-985 (2002).
[CrossRef]

IEEE Trans. Inf. Theory (1)

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

J. Mod. Opt. (1)

H. de Riedmatten, V. Scarani, I. Marcikic, A. Ac�??ın,W. Tittel, H. Zbinden, and N. Gisin, "Two independent photon pairs versus four-photon entangled states in parametric down conversion," J. Mod. Opt. 51, 1637-1649 (2004).

J. Opt. Soc. Am. B (1)

Nature (London) (3)

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L.-M. Duan, and H. J. Kimble, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles," Nature (London) 423, 731-734 (2003).
[CrossRef] [PubMed]

L.-M. Duan, M. D. Lukin, J. I. Cirac and P. Zoller, "Long-distance quantum communication with atomic ensembles and linear optics," Nature (London) 414413-418 (2001).
[CrossRef] [PubMed]

R. Hanbury Brown, and R. Q. Twiss, "A Test of a New Type of Stellar Interferometer on Sirius," Nature (London) 178, 1046-1048 (1956).
[CrossRef]

Phys. Rev. A (5)

H. de Riedmatten, I. Marcikic, W. Tittel, H. Zbinden, and N. Gisin, "Quantum interference with photon pairs created in spatially separated sources," Phys. Rev. A 67, 022301 (2003).
[CrossRef]

I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, "Time-bin entangled qubits for quantum communication created by femtosecond pulses," Phys. Rev. A 66, 062308 (2002).
[CrossRef]

J. D. Franson, "Nonlocal cancellation of dispersion," Phys. Rev. A 45, 3126-3132 (1992).
[CrossRef] [PubMed]

X. Ma, C.-H. Fred Fung, and H.-K. Lo, "Quantum key distribution with entangled photon sources," Phys. Rev. A 76, 012307 (2007).
[CrossRef]

E. Waks, C. Santori, and Y. Yamamoto, "Security aspects of quantum key distribution with sub-Poisson light," Phys. Rev. A 66, 042315 (2002).
[CrossRef]

Phys. Rev. Lett. (8)

Q. W. Chen, G. Xavier, M. Swillo, T. Zhang, S. Sauge, M. Tengner, Z.-F. Han, G.-C. Guo, and A. Karlsson, "Experimental Decoy-State Quantum Key Distribution with a Sub-Poissionian Heralded Single-Photon Source," Phys. Rev. Lett. 100, 090501 (2008).
[CrossRef] [PubMed]

Y. Adachi,T. Yamamoto, M. Koashi, and N. Imoto, "Simple and Efficient Quantum Key Distribution with Parametric Down-Conversion," Phys. Rev. Lett. 99, 180503 (2007).
[CrossRef] [PubMed]

D. C. Burnham and D. L. Weinberg, "Observation of Simultaneity in Parametric Production of Optical Photon Pairs," Phys. Rev. Lett. 25, 84-87 (1970).
[CrossRef]

A. Ekert, "Quantum Cryptography Based on Bell�??s Theorem," Phys. Rev. Lett. 67, 661-663 (1991).
[CrossRef] [PubMed]

H.-J. Briegel, W. D¨ur, J. I. Cirac and P. Zoller, "Quantum Repeaters: the Role of Imperfect Local Operations in Quantum Communication," Phys. Rev. Lett. 81, 5932-5935 (1998).
[CrossRef]

J. Simon, H. Tanji, J. K. Thompson, and V. Vuletic, "Interfacing Collective Atomic Excitations and Single Photons," Phys. Rev. Lett. 98183601 (2007).
[CrossRef] [PubMed]

P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U�??Ren, C. Silberhorn, and I. A.Walmsley, "Heralded Generation of Ultrafast Single Photons in Pure Quantum States," Phys. Rev. Lett. 100, 133601 (2008).
[CrossRef] [PubMed]

C. K. Hong and L. Mandel, "Experimental realization of a localized one-photon state," Phys. Rev. Lett. 56, 58-60 (1986).
[CrossRef] [PubMed]

Quantum Inf. and Comp. (1)

W. Tittel and G. Weihs, "Photonic Entanglement for Fundamental Tests and Quantum Communication," Quantum Inf. and Comp. 1, 3-56 (2001).

SIAM J. Comput. (1)

C. H. Bennett, G. Brassard, and J.-M. Robert, "Privacy amplification by public discussion," SIAM J. Comput. 17, 210-229 (1988).
[CrossRef]

Other (6)

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

For a Thermal distribution the g(2)(0) is higher by a factor of 2: g(2)(0) = 2�??(2�??|H). In the case of spectral and/or spatial correlations with a Poissonian source, as discussed in section 4, g(2)(0) =�??(2/c�??|H).

M. Zukowski, A. Zeilinger, and H. Weinfurter, "Entangling Photons Radiated by Independent Pulsed Sources," in Annals of the New York Academy of Sciences, D. M. Greenberger, A. Zeilinger, ed. (New York, 1995), pp. 91- 102
[CrossRef]

W. Mauerer and C. Silberhorn, "Quantum key distribution with passive decoy state selection," Phys. Rev. A 75, 050305(R) (2007).
[CrossRef]

M. Tengner and D. Ljunggren, "Characterization of an asynchronous source of heralded single photons generated at a wavelength of 1550 nm," arXiv:0706.2985v1 [quant-ph] (2007).

L. Mandel and E. Wolf, Optical coherence and quantum optics (Cambridge University Press, 1995).

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Figures (5)

Fig. 1.
Fig. 1.

The sources of photon pairs we consider comprise all probabilistic sources, including those based on nonlinear crystals, optical fibres or atomic ensembles. The distribution of the number of produced photon pairs per measurement time window can be given by any distribution such as Poissonian or thermal and is assumed to be known in advance. The pairs are deterministically separated, potentially by a dichroic beamsplitter in the case of collinear generation with non-degenerate wavelengths, or by non-collinear generation, into two separate channels. Each beam is filtered to remove all pump light and then the pairs are coupled into optical fibres. One beam is split again at a 50/50 beamsplitter before the photons are detected by non-photon number resolving single photon detectors D H , D A and D B .

Fig. 2.
Fig. 2.

Correlation strength G versus brightness µ. The solid line corresponds to η H =60% and η A =25%. It reaches a maximum value at very low µ and then sharply decreases to 1 for µ=0 (not visible). The meanings of the dotted and dashed lines are discussed in section 3 and 4 respectively.

Fig. 3.
Fig. 3.

Experimental setup.

Fig. 4.
Fig. 4.

(a) Predicted (solid lines) and measured (points) conditional detection probabilities p A | H and p B | H . (b) Predicted (solid line) and measured (points) conditional coincidence probability p AB | H . The dashed lines on both plots are the one standard deviation uncertainty bounds on the predicted values which were generated using the uncertainty bounds on the measured transmissions.

Fig. 5.
Fig. 5.

(a) Predicted autocorrelation g (2)(0) for Poissonian (solid line) and thermal (dotted line) distributions, measured values (points), and the corresponding brightness µ (dash-dotted line). The measured data agrees very well with the Poissonian distribution. The dashed lines are the one standard deviation uncertainty bounds on the predicted values. (b) As the heralding probability reaches the noise level of D H (dashed line), the model correctly predicts that the g (2)(0) approaches one, as uncorrelated dark counts begin to dominate over photon clicks.

Equations (8)

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P = ( p A ¯ B ¯ H ¯ p A B ¯ H ¯ p A ¯ B H ¯ p A ¯ B ¯ H p A B H ¯ p A B ¯ H p A ¯ B H p A B H ) T .
M η = ( 1 η H + ( η A + η B ) ( η H 1 ) 0 0 0 0 0 0 0 η A ( 1 η H ) ( 1 η B ) ( 1 η H ) 0 0 0 0 0 0 η B ( 1 η H ) 0 ( 1 η A ) ( 1 η H ) 0 0 0 0 0 η H ( 1 ( η A + η B ) ) 0 0 1 ( η A + η B ) 0 0 0 0 0 η B ( 1 η H ) η A ( 1 η H ) 0 1 η H 0 0 0 η A η H η H ( 1 η B ) 0 η A 0 1 η B 0 0 η B η H 0 η H ( 1 η A ) η B 0 0 1 η A 0 0 η B η H η A η H 0 η H η B η A 1 ) .
M dc = ( ( 1 d A ) ( 1 d B ) ( 1 d H ) 0 0 0 0 0 0 0 d A ( 1 d B ) ( 1 d H ) ( 1 d B ) ( 1 d H ) 0 0 0 0 0 0 ( 1 d A ) d B ( 1 d H ) 0 ( 1 d A ) ( 1 d H ) 0 0 0 0 0 ( 1 d A ) ( 1 d B ) d H 0 0 ( 1 d A ) ( 1 d B ) 0 0 0 0 d A d B ( 1 d H ) d B ( 1 d H ) d A ( 1 d H ) 0 1 d H 0 0 0 d A ( 1 d B ) d H ( 1 d B ) d H 0 d A ( 1 d B ) 0 1 d B 0 0 ( 1 d A ) d B d H 0 ( 1 d A ) d H ( 1 d A ) d B 0 0 1 d A 0 d A d B d H d B d H d A d H d A d B d H d B d A 1 ) .
P = i = 0 p i M dc ( M η ) i P 0 ,
η H = p AH p H ( 1 ) d A ( 1 d H ) p A ( 1 ) d H ( 1 d A ) d A d H p A ( 1 ) ( 1 d A ) ( 1 d H ) ,
η A = p AH p H ( 1 ) d A ( 1 d H ) p A ( 1 ) d H ( 1 d A ) d A d H p H ( 1 ) ( 1 d A ) ( 1 d H ) ,
p 1 = p H ( 1 ) η H = p A ( 1 ) η A .
g ( 2 ) ( 0 ) = p AB H p A H × p B H ,

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