Abstract

Photon-number resolving detectors are a fundamental building-block of optical quantum information processing protocols. A loop detector, combined with appropriate statistical processing, can be used to convert a binary on/off photon counter into a photon-number-resolving detector. Here we describe the idea of a signature of photon-counts, which may be used to more robustly reconstruct the photon number distribution of a quantum state. The methodology is applied experimentally in a 9-port loop detector operating at a telecommunications wavelength and compared directly to the approach whereby only the number of photon-counts is used to reconstruct the input distribution. The signature approach is shown to be more robust against calibration errors, exhibit reduced statistical uncertainty, and reduced reliance on a-priori assumptions about the input state.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, UK, 2000).
  2. J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, "Demonstration of an all-optical quantum controlled-not gate", Nature 426, 264-267 (2003).
    [CrossRef] [PubMed]
  3. B. P. Lanyon, T. J. Weinhold, N. K. Langford, M. Barbieri, D. F. V. James, A. Gilchrist and A. G. White, "Experimental Demonstration of a Compiled Version of Shor’s Algorithm with Quantum Entanglement", Phys. Rev. Lett. 99, 250505 (2007).
    [CrossRef]
  4. P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, "Review article: Linear optical quantum computing", arXiv:quant-ph/0512071 (2005).
  5. T. C. Ralph, "Quantum optical systems for the implementation of quantum information processing", Rep. Prog. Phys. 69, 853-898 (2006).
    [CrossRef]
  6. M. Bondani, A. Allevi, A. Agliati, and A. Andreoni, "Self-consistent characterization of light statistics", arXiv:quant-ph/0810.4055v1 (2008).
  7. M. Fujiwara and M. Sasaki, "Direct measurement of photon number statistics at telecom wavelengths using a charge integration photon detector", Appl. Opt. 46, 16, 3069-3074 (2007).
    [CrossRef] [PubMed]
  8. A. J. Pearlman, S. V. Polyakov, A. Migdall, and S.W. Nam, "Number-resolving, single photon detection with no deadtime", Conference on CLEO/QELS, pp 1-2, May 2008.
  9. A. V. Sergienko, "Quantum optics: Beyond single-photon counting", Nat. Photon. 2, 268-269 (2008).
    [CrossRef]
  10. P. Kok and S. Braunstein, "Detection devices in entanglement-based optical state preparation", Phys. Rev. A 63, 033812 (2001).
    [CrossRef]
  11. H. Paul, P. Törmä, T. Kiss, and I. Jex, "Photon Chopping: New Way to Measure the Quantum State of Light", Phys. Rev. Lett. 76, 2464 (1996).
    [CrossRef] [PubMed]
  12. S. D. Bartlett, E. Diamanti, B. C. Sanders, and Y. Yamamoto, "Photon counting schemes and performance of non-deterministic nonlinear gates in linear optics", arXiv:quant-ph/0204073v1 (2002).
  13. P. P. Rohde, "Non-deterministic approximation of photon number discriminating detectors using nondiscriminating detectors", J. Opt. B: Quant. Semiclass. 7, 82-86 (2005).
    [CrossRef]
  14. D. Achilles, C. Silberhorn, C. Śliwa, K. Banaszek, I. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, "Photon-number-resolving detection using time-multiplexing", J. Mod. Opt. 51, 9-10, 1499-1515 (2004).
  15. K. Banaszek and I. A. Walmsley, "Photon counting with a loop detector", Opt. Lett. 28, 1, 52-54 (2003).
    [CrossRef] [PubMed]
  16. M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, "Photon-number resolution using time-multiplexed single-photon detectors", Phys. Rev. A 68, 043814 (2003).
    [CrossRef]
  17. G. A. P. Thé and R. V. Ramos, "Multiple-photon number resolving detector using fibre ring and single-photon detector", J. Mod. Opt. 54, 8, 1187-1202 (2007).
    [CrossRef]
  18. J. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, "Multiphoton detection using visible light photon counter", Appl. Phys. Lett. 74, 7, 902 (1999).
    [CrossRef]
  19. S. Takeuchi, J. Kim, Y. Yamamoto, and H. H. Hogue, "Development of a high-quantum-efficiency single-photon counting system", Appl. Phys. Lett. 74, 8, 1063 (1999).
    [CrossRef]
  20. T. Opatrný and D.-G. Welsch, "Density-matrix reconstruction by unbalanced homodyning", Phys. Rev. A 55, 1462 (1997).
    [CrossRef]
  21. G. Brida, M. Genovese, M. Gramegna, P. Traina, E. Predazzi, S. Olivares, and M. G. A. Paris, "Toward a full reconstruction of density matrix by on/off measurements", Int. J. Quant. Inf. 7, 27-32 (2009).
    [CrossRef]
  22. G. Zambra and M. G. A. Paris, "Reconstruction of photon-number distribution using low-performance photon counters", Phys. Rev. A 74, 063830 (2006).
    [CrossRef]
  23. D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, Berlin, 1995).
  24. G. M. D’Ariano and C. Macchiavello, "Loss-error compensation in quantum-state measurements", Phys. Rev. A 57, 4, 3131-3133 (1998).
    [CrossRef]
  25. D. Mogilevtsev, "Diagonal element inference by direct detection", Opt. Comm. 156, 307-310 (1998).
    [CrossRef]
  26. G. Zambra, A. Allevi, A. Andreoni, M. Bondani, and M. G. A. Paris, "Nontrivial photon statistics with low resolution-threshold photon counters", Int. J. Quant. Inf. 5, 1-2, 305-309 (2007).
  27. H. Lee, U. Yurtsever, P. Kok, G. M. Hockney, C. Adami, S. L. Braunstein, and J. P. Dowling, "Towards photostatistics from photon-number discriminating detectors", J. Mod. Opt. 51, 9-10, 1517-1528 (2004).
  28. J. Reháček, Z. Hradil, O. Haderka, J. PerinaJr., and M. Hamar, "Multiple-photon resolving fiber-loop detector", Phys. Rev. A 67, 061801 (2003).
  29. G. Brida, M. Genovese, M. G. A. Paris, F. Piacentini, E. Predazzi, and E. Vallauri, "On Reconstructing Photon Statistics by on/off Detectors: Toward the Multi-Partite Case", Opt. Spect. 103, 1, 90-97 (2007).
    [CrossRef]
  30. P. P. Rohde, J. G. Webb, E. H. Huntington, and T. C. Ralph, "Photon number projection using non-number-resolving detectors", New J. Phys. 9, 233 (2007).
    [CrossRef]
  31. Z. Hradil and J. Reháček, "Likelihood and entropy for statistical inversion", J. Phys: Conf. Series 36, 55-59 (2006).
    [CrossRef]
  32. G. Zambra, A. Andreoni, M. Bondani, M. Gramegna, M. Genovese, G. Brida, A. Rossi, and M. G. A. Paris, "Experimental reconstruction of photon statistics without photon counting", Phys. Rev. Lett. 95, 063602 (2005).
    [CrossRef] [PubMed]
  33. J. A. Nelder and R. Mead, "A simplex method for function minimization", Computer Journal 7, 308-313 (1965).
  34. W. H. Press et al, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University Press, Cambridge, England, 2nd edition, 1992).
  35. J. C. Lagaris, J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence properties of the Nelder-Mead simplex method in low dimensions", SIAM J. Optim. 9, 1, 112-147 (1998).
    [CrossRef]
  36. G. Ribordy, J-D. Gautier, H. Zbinden, and N. Gisin, "Performance of InGaAs/InP avalanche photodiodes as gated-mode photon counters", Appl. Opt. 37, 12, 2272-2277 (1998).
    [CrossRef]
  37. M. Höbel and J. Ricka, "Dead-time and afterpulsing correction in multiphoton timing with nonideal detectors", Rev. Sci. Instrum. 65, 7, 2326-2336 (1994).
    [CrossRef]
  38. D. Achilles, C. Silberhorn, and I. A. Walmsley, "Direct, loss-tolerant characterization of nonclassical photon statistics", Phys. Rev. Lett. 97, 043602 (2006).
    [CrossRef] [PubMed]

2009 (1)

G. Brida, M. Genovese, M. Gramegna, P. Traina, E. Predazzi, S. Olivares, and M. G. A. Paris, "Toward a full reconstruction of density matrix by on/off measurements", Int. J. Quant. Inf. 7, 27-32 (2009).
[CrossRef]

2008 (1)

A. V. Sergienko, "Quantum optics: Beyond single-photon counting", Nat. Photon. 2, 268-269 (2008).
[CrossRef]

2007 (6)

B. P. Lanyon, T. J. Weinhold, N. K. Langford, M. Barbieri, D. F. V. James, A. Gilchrist and A. G. White, "Experimental Demonstration of a Compiled Version of Shor’s Algorithm with Quantum Entanglement", Phys. Rev. Lett. 99, 250505 (2007).
[CrossRef]

M. Fujiwara and M. Sasaki, "Direct measurement of photon number statistics at telecom wavelengths using a charge integration photon detector", Appl. Opt. 46, 16, 3069-3074 (2007).
[CrossRef] [PubMed]

G. A. P. Thé and R. V. Ramos, "Multiple-photon number resolving detector using fibre ring and single-photon detector", J. Mod. Opt. 54, 8, 1187-1202 (2007).
[CrossRef]

G. Brida, M. Genovese, M. G. A. Paris, F. Piacentini, E. Predazzi, and E. Vallauri, "On Reconstructing Photon Statistics by on/off Detectors: Toward the Multi-Partite Case", Opt. Spect. 103, 1, 90-97 (2007).
[CrossRef]

P. P. Rohde, J. G. Webb, E. H. Huntington, and T. C. Ralph, "Photon number projection using non-number-resolving detectors", New J. Phys. 9, 233 (2007).
[CrossRef]

G. Zambra, A. Allevi, A. Andreoni, M. Bondani, and M. G. A. Paris, "Nontrivial photon statistics with low resolution-threshold photon counters", Int. J. Quant. Inf. 5, 1-2, 305-309 (2007).

2006 (4)

Z. Hradil and J. Reháček, "Likelihood and entropy for statistical inversion", J. Phys: Conf. Series 36, 55-59 (2006).
[CrossRef]

G. Zambra and M. G. A. Paris, "Reconstruction of photon-number distribution using low-performance photon counters", Phys. Rev. A 74, 063830 (2006).
[CrossRef]

T. C. Ralph, "Quantum optical systems for the implementation of quantum information processing", Rep. Prog. Phys. 69, 853-898 (2006).
[CrossRef]

D. Achilles, C. Silberhorn, and I. A. Walmsley, "Direct, loss-tolerant characterization of nonclassical photon statistics", Phys. Rev. Lett. 97, 043602 (2006).
[CrossRef] [PubMed]

2005 (2)

P. P. Rohde, "Non-deterministic approximation of photon number discriminating detectors using nondiscriminating detectors", J. Opt. B: Quant. Semiclass. 7, 82-86 (2005).
[CrossRef]

G. Zambra, A. Andreoni, M. Bondani, M. Gramegna, M. Genovese, G. Brida, A. Rossi, and M. G. A. Paris, "Experimental reconstruction of photon statistics without photon counting", Phys. Rev. Lett. 95, 063602 (2005).
[CrossRef] [PubMed]

2004 (2)

H. Lee, U. Yurtsever, P. Kok, G. M. Hockney, C. Adami, S. L. Braunstein, and J. P. Dowling, "Towards photostatistics from photon-number discriminating detectors", J. Mod. Opt. 51, 9-10, 1517-1528 (2004).

D. Achilles, C. Silberhorn, C. Śliwa, K. Banaszek, I. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, "Photon-number-resolving detection using time-multiplexing", J. Mod. Opt. 51, 9-10, 1499-1515 (2004).

2003 (4)

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, "Demonstration of an all-optical quantum controlled-not gate", Nature 426, 264-267 (2003).
[CrossRef] [PubMed]

K. Banaszek and I. A. Walmsley, "Photon counting with a loop detector", Opt. Lett. 28, 1, 52-54 (2003).
[CrossRef] [PubMed]

J. Reháček, Z. Hradil, O. Haderka, J. PerinaJr., and M. Hamar, "Multiple-photon resolving fiber-loop detector", Phys. Rev. A 67, 061801 (2003).

M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, "Photon-number resolution using time-multiplexed single-photon detectors", Phys. Rev. A 68, 043814 (2003).
[CrossRef]

2001 (1)

P. Kok and S. Braunstein, "Detection devices in entanglement-based optical state preparation", Phys. Rev. A 63, 033812 (2001).
[CrossRef]

1999 (2)

J. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, "Multiphoton detection using visible light photon counter", Appl. Phys. Lett. 74, 7, 902 (1999).
[CrossRef]

S. Takeuchi, J. Kim, Y. Yamamoto, and H. H. Hogue, "Development of a high-quantum-efficiency single-photon counting system", Appl. Phys. Lett. 74, 8, 1063 (1999).
[CrossRef]

1998 (4)

G. M. D’Ariano and C. Macchiavello, "Loss-error compensation in quantum-state measurements", Phys. Rev. A 57, 4, 3131-3133 (1998).
[CrossRef]

D. Mogilevtsev, "Diagonal element inference by direct detection", Opt. Comm. 156, 307-310 (1998).
[CrossRef]

J. C. Lagaris, J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence properties of the Nelder-Mead simplex method in low dimensions", SIAM J. Optim. 9, 1, 112-147 (1998).
[CrossRef]

G. Ribordy, J-D. Gautier, H. Zbinden, and N. Gisin, "Performance of InGaAs/InP avalanche photodiodes as gated-mode photon counters", Appl. Opt. 37, 12, 2272-2277 (1998).
[CrossRef]

1997 (1)

T. Opatrný and D.-G. Welsch, "Density-matrix reconstruction by unbalanced homodyning", Phys. Rev. A 55, 1462 (1997).
[CrossRef]

1996 (1)

H. Paul, P. Törmä, T. Kiss, and I. Jex, "Photon Chopping: New Way to Measure the Quantum State of Light", Phys. Rev. Lett. 76, 2464 (1996).
[CrossRef] [PubMed]

1994 (1)

M. Höbel and J. Ricka, "Dead-time and afterpulsing correction in multiphoton timing with nonideal detectors", Rev. Sci. Instrum. 65, 7, 2326-2336 (1994).
[CrossRef]

1965 (1)

J. A. Nelder and R. Mead, "A simplex method for function minimization", Computer Journal 7, 308-313 (1965).

Achilles, D.

D. Achilles, C. Silberhorn, and I. A. Walmsley, "Direct, loss-tolerant characterization of nonclassical photon statistics", Phys. Rev. Lett. 97, 043602 (2006).
[CrossRef] [PubMed]

D. Achilles, C. Silberhorn, C. Śliwa, K. Banaszek, I. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, "Photon-number-resolving detection using time-multiplexing", J. Mod. Opt. 51, 9-10, 1499-1515 (2004).

Adami, C.

H. Lee, U. Yurtsever, P. Kok, G. M. Hockney, C. Adami, S. L. Braunstein, and J. P. Dowling, "Towards photostatistics from photon-number discriminating detectors", J. Mod. Opt. 51, 9-10, 1517-1528 (2004).

Allevi, A.

G. Zambra, A. Allevi, A. Andreoni, M. Bondani, and M. G. A. Paris, "Nontrivial photon statistics with low resolution-threshold photon counters", Int. J. Quant. Inf. 5, 1-2, 305-309 (2007).

Andreoni, A.

G. Zambra, A. Allevi, A. Andreoni, M. Bondani, and M. G. A. Paris, "Nontrivial photon statistics with low resolution-threshold photon counters", Int. J. Quant. Inf. 5, 1-2, 305-309 (2007).

G. Zambra, A. Andreoni, M. Bondani, M. Gramegna, M. Genovese, G. Brida, A. Rossi, and M. G. A. Paris, "Experimental reconstruction of photon statistics without photon counting", Phys. Rev. Lett. 95, 063602 (2005).
[CrossRef] [PubMed]

Banaszek, K.

D. Achilles, C. Silberhorn, C. Śliwa, K. Banaszek, I. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, "Photon-number-resolving detection using time-multiplexing", J. Mod. Opt. 51, 9-10, 1499-1515 (2004).

K. Banaszek and I. A. Walmsley, "Photon counting with a loop detector", Opt. Lett. 28, 1, 52-54 (2003).
[CrossRef] [PubMed]

Barbieri, M.

B. P. Lanyon, T. J. Weinhold, N. K. Langford, M. Barbieri, D. F. V. James, A. Gilchrist and A. G. White, "Experimental Demonstration of a Compiled Version of Shor’s Algorithm with Quantum Entanglement", Phys. Rev. Lett. 99, 250505 (2007).
[CrossRef]

Bondani, M.

G. Zambra, A. Allevi, A. Andreoni, M. Bondani, and M. G. A. Paris, "Nontrivial photon statistics with low resolution-threshold photon counters", Int. J. Quant. Inf. 5, 1-2, 305-309 (2007).

G. Zambra, A. Andreoni, M. Bondani, M. Gramegna, M. Genovese, G. Brida, A. Rossi, and M. G. A. Paris, "Experimental reconstruction of photon statistics without photon counting", Phys. Rev. Lett. 95, 063602 (2005).
[CrossRef] [PubMed]

Branning, D.

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, "Demonstration of an all-optical quantum controlled-not gate", Nature 426, 264-267 (2003).
[CrossRef] [PubMed]

Braunstein, S.

P. Kok and S. Braunstein, "Detection devices in entanglement-based optical state preparation", Phys. Rev. A 63, 033812 (2001).
[CrossRef]

Braunstein, S. L.

H. Lee, U. Yurtsever, P. Kok, G. M. Hockney, C. Adami, S. L. Braunstein, and J. P. Dowling, "Towards photostatistics from photon-number discriminating detectors", J. Mod. Opt. 51, 9-10, 1517-1528 (2004).

Brida, G.

G. Brida, M. Genovese, M. Gramegna, P. Traina, E. Predazzi, S. Olivares, and M. G. A. Paris, "Toward a full reconstruction of density matrix by on/off measurements", Int. J. Quant. Inf. 7, 27-32 (2009).
[CrossRef]

G. Brida, M. Genovese, M. G. A. Paris, F. Piacentini, E. Predazzi, and E. Vallauri, "On Reconstructing Photon Statistics by on/off Detectors: Toward the Multi-Partite Case", Opt. Spect. 103, 1, 90-97 (2007).
[CrossRef]

G. Zambra, A. Andreoni, M. Bondani, M. Gramegna, M. Genovese, G. Brida, A. Rossi, and M. G. A. Paris, "Experimental reconstruction of photon statistics without photon counting", Phys. Rev. Lett. 95, 063602 (2005).
[CrossRef] [PubMed]

D’Ariano, G. M.

G. M. D’Ariano and C. Macchiavello, "Loss-error compensation in quantum-state measurements", Phys. Rev. A 57, 4, 3131-3133 (1998).
[CrossRef]

Dowling, J. P.

H. Lee, U. Yurtsever, P. Kok, G. M. Hockney, C. Adami, S. L. Braunstein, and J. P. Dowling, "Towards photostatistics from photon-number discriminating detectors", J. Mod. Opt. 51, 9-10, 1517-1528 (2004).

Fitch, M. J.

D. Achilles, C. Silberhorn, C. Śliwa, K. Banaszek, I. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, "Photon-number-resolving detection using time-multiplexing", J. Mod. Opt. 51, 9-10, 1499-1515 (2004).

M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, "Photon-number resolution using time-multiplexed single-photon detectors", Phys. Rev. A 68, 043814 (2003).
[CrossRef]

Franson, J. D.

D. Achilles, C. Silberhorn, C. Śliwa, K. Banaszek, I. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, "Photon-number-resolving detection using time-multiplexing", J. Mod. Opt. 51, 9-10, 1499-1515 (2004).

M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, "Photon-number resolution using time-multiplexed single-photon detectors", Phys. Rev. A 68, 043814 (2003).
[CrossRef]

Fujiwara, M.

Gautier, J-D.

Genovese, M.

G. Brida, M. Genovese, M. Gramegna, P. Traina, E. Predazzi, S. Olivares, and M. G. A. Paris, "Toward a full reconstruction of density matrix by on/off measurements", Int. J. Quant. Inf. 7, 27-32 (2009).
[CrossRef]

G. Brida, M. Genovese, M. G. A. Paris, F. Piacentini, E. Predazzi, and E. Vallauri, "On Reconstructing Photon Statistics by on/off Detectors: Toward the Multi-Partite Case", Opt. Spect. 103, 1, 90-97 (2007).
[CrossRef]

G. Zambra, A. Andreoni, M. Bondani, M. Gramegna, M. Genovese, G. Brida, A. Rossi, and M. G. A. Paris, "Experimental reconstruction of photon statistics without photon counting", Phys. Rev. Lett. 95, 063602 (2005).
[CrossRef] [PubMed]

Gilchrist, A.

B. P. Lanyon, T. J. Weinhold, N. K. Langford, M. Barbieri, D. F. V. James, A. Gilchrist and A. G. White, "Experimental Demonstration of a Compiled Version of Shor’s Algorithm with Quantum Entanglement", Phys. Rev. Lett. 99, 250505 (2007).
[CrossRef]

Gisin, N.

Gramegna, M.

G. Brida, M. Genovese, M. Gramegna, P. Traina, E. Predazzi, S. Olivares, and M. G. A. Paris, "Toward a full reconstruction of density matrix by on/off measurements", Int. J. Quant. Inf. 7, 27-32 (2009).
[CrossRef]

G. Zambra, A. Andreoni, M. Bondani, M. Gramegna, M. Genovese, G. Brida, A. Rossi, and M. G. A. Paris, "Experimental reconstruction of photon statistics without photon counting", Phys. Rev. Lett. 95, 063602 (2005).
[CrossRef] [PubMed]

Haderka, O.

J. Reháček, Z. Hradil, O. Haderka, J. PerinaJr., and M. Hamar, "Multiple-photon resolving fiber-loop detector", Phys. Rev. A 67, 061801 (2003).

Hamar, M.

J. Reháček, Z. Hradil, O. Haderka, J. PerinaJr., and M. Hamar, "Multiple-photon resolving fiber-loop detector", Phys. Rev. A 67, 061801 (2003).

Höbel, M.

M. Höbel and J. Ricka, "Dead-time and afterpulsing correction in multiphoton timing with nonideal detectors", Rev. Sci. Instrum. 65, 7, 2326-2336 (1994).
[CrossRef]

Hockney, G. M.

H. Lee, U. Yurtsever, P. Kok, G. M. Hockney, C. Adami, S. L. Braunstein, and J. P. Dowling, "Towards photostatistics from photon-number discriminating detectors", J. Mod. Opt. 51, 9-10, 1517-1528 (2004).

Hogue, H. H.

J. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, "Multiphoton detection using visible light photon counter", Appl. Phys. Lett. 74, 7, 902 (1999).
[CrossRef]

S. Takeuchi, J. Kim, Y. Yamamoto, and H. H. Hogue, "Development of a high-quantum-efficiency single-photon counting system", Appl. Phys. Lett. 74, 8, 1063 (1999).
[CrossRef]

Hradil, Z.

Z. Hradil and J. Reháček, "Likelihood and entropy for statistical inversion", J. Phys: Conf. Series 36, 55-59 (2006).
[CrossRef]

J. Reháček, Z. Hradil, O. Haderka, J. PerinaJr., and M. Hamar, "Multiple-photon resolving fiber-loop detector", Phys. Rev. A 67, 061801 (2003).

Huntington, E. H.

P. P. Rohde, J. G. Webb, E. H. Huntington, and T. C. Ralph, "Photon number projection using non-number-resolving detectors", New J. Phys. 9, 233 (2007).
[CrossRef]

Jacobs, B. C.

D. Achilles, C. Silberhorn, C. Śliwa, K. Banaszek, I. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, "Photon-number-resolving detection using time-multiplexing", J. Mod. Opt. 51, 9-10, 1499-1515 (2004).

M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, "Photon-number resolution using time-multiplexed single-photon detectors", Phys. Rev. A 68, 043814 (2003).
[CrossRef]

James, D. F. V.

B. P. Lanyon, T. J. Weinhold, N. K. Langford, M. Barbieri, D. F. V. James, A. Gilchrist and A. G. White, "Experimental Demonstration of a Compiled Version of Shor’s Algorithm with Quantum Entanglement", Phys. Rev. Lett. 99, 250505 (2007).
[CrossRef]

Jex, I.

H. Paul, P. Törmä, T. Kiss, and I. Jex, "Photon Chopping: New Way to Measure the Quantum State of Light", Phys. Rev. Lett. 76, 2464 (1996).
[CrossRef] [PubMed]

Kim, J.

S. Takeuchi, J. Kim, Y. Yamamoto, and H. H. Hogue, "Development of a high-quantum-efficiency single-photon counting system", Appl. Phys. Lett. 74, 8, 1063 (1999).
[CrossRef]

J. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, "Multiphoton detection using visible light photon counter", Appl. Phys. Lett. 74, 7, 902 (1999).
[CrossRef]

Kiss, T.

H. Paul, P. Törmä, T. Kiss, and I. Jex, "Photon Chopping: New Way to Measure the Quantum State of Light", Phys. Rev. Lett. 76, 2464 (1996).
[CrossRef] [PubMed]

Kok, P.

H. Lee, U. Yurtsever, P. Kok, G. M. Hockney, C. Adami, S. L. Braunstein, and J. P. Dowling, "Towards photostatistics from photon-number discriminating detectors", J. Mod. Opt. 51, 9-10, 1517-1528 (2004).

P. Kok and S. Braunstein, "Detection devices in entanglement-based optical state preparation", Phys. Rev. A 63, 033812 (2001).
[CrossRef]

Lagaris, J. C.

J. C. Lagaris, J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence properties of the Nelder-Mead simplex method in low dimensions", SIAM J. Optim. 9, 1, 112-147 (1998).
[CrossRef]

Langford, N. K.

B. P. Lanyon, T. J. Weinhold, N. K. Langford, M. Barbieri, D. F. V. James, A. Gilchrist and A. G. White, "Experimental Demonstration of a Compiled Version of Shor’s Algorithm with Quantum Entanglement", Phys. Rev. Lett. 99, 250505 (2007).
[CrossRef]

Lanyon, B. P.

B. P. Lanyon, T. J. Weinhold, N. K. Langford, M. Barbieri, D. F. V. James, A. Gilchrist and A. G. White, "Experimental Demonstration of a Compiled Version of Shor’s Algorithm with Quantum Entanglement", Phys. Rev. Lett. 99, 250505 (2007).
[CrossRef]

Lee, H.

H. Lee, U. Yurtsever, P. Kok, G. M. Hockney, C. Adami, S. L. Braunstein, and J. P. Dowling, "Towards photostatistics from photon-number discriminating detectors", J. Mod. Opt. 51, 9-10, 1517-1528 (2004).

Macchiavello, C.

G. M. D’Ariano and C. Macchiavello, "Loss-error compensation in quantum-state measurements", Phys. Rev. A 57, 4, 3131-3133 (1998).
[CrossRef]

Mead, R.

J. A. Nelder and R. Mead, "A simplex method for function minimization", Computer Journal 7, 308-313 (1965).

Mogilevtsev, D.

D. Mogilevtsev, "Diagonal element inference by direct detection", Opt. Comm. 156, 307-310 (1998).
[CrossRef]

Nelder, J. A.

J. A. Nelder and R. Mead, "A simplex method for function minimization", Computer Journal 7, 308-313 (1965).

O’Brien, J. L.

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, "Demonstration of an all-optical quantum controlled-not gate", Nature 426, 264-267 (2003).
[CrossRef] [PubMed]

Olivares, S.

G. Brida, M. Genovese, M. Gramegna, P. Traina, E. Predazzi, S. Olivares, and M. G. A. Paris, "Toward a full reconstruction of density matrix by on/off measurements", Int. J. Quant. Inf. 7, 27-32 (2009).
[CrossRef]

Opatrný, T.

T. Opatrný and D.-G. Welsch, "Density-matrix reconstruction by unbalanced homodyning", Phys. Rev. A 55, 1462 (1997).
[CrossRef]

Paris, M. G. A.

G. Brida, M. Genovese, M. Gramegna, P. Traina, E. Predazzi, S. Olivares, and M. G. A. Paris, "Toward a full reconstruction of density matrix by on/off measurements", Int. J. Quant. Inf. 7, 27-32 (2009).
[CrossRef]

G. Zambra, A. Allevi, A. Andreoni, M. Bondani, and M. G. A. Paris, "Nontrivial photon statistics with low resolution-threshold photon counters", Int. J. Quant. Inf. 5, 1-2, 305-309 (2007).

G. Brida, M. Genovese, M. G. A. Paris, F. Piacentini, E. Predazzi, and E. Vallauri, "On Reconstructing Photon Statistics by on/off Detectors: Toward the Multi-Partite Case", Opt. Spect. 103, 1, 90-97 (2007).
[CrossRef]

G. Zambra and M. G. A. Paris, "Reconstruction of photon-number distribution using low-performance photon counters", Phys. Rev. A 74, 063830 (2006).
[CrossRef]

G. Zambra, A. Andreoni, M. Bondani, M. Gramegna, M. Genovese, G. Brida, A. Rossi, and M. G. A. Paris, "Experimental reconstruction of photon statistics without photon counting", Phys. Rev. Lett. 95, 063602 (2005).
[CrossRef] [PubMed]

Paul, H.

H. Paul, P. Törmä, T. Kiss, and I. Jex, "Photon Chopping: New Way to Measure the Quantum State of Light", Phys. Rev. Lett. 76, 2464 (1996).
[CrossRef] [PubMed]

Perina, J.

J. Reháček, Z. Hradil, O. Haderka, J. PerinaJr., and M. Hamar, "Multiple-photon resolving fiber-loop detector", Phys. Rev. A 67, 061801 (2003).

Piacentini, F.

G. Brida, M. Genovese, M. G. A. Paris, F. Piacentini, E. Predazzi, and E. Vallauri, "On Reconstructing Photon Statistics by on/off Detectors: Toward the Multi-Partite Case", Opt. Spect. 103, 1, 90-97 (2007).
[CrossRef]

Pittman, T. B.

D. Achilles, C. Silberhorn, C. Śliwa, K. Banaszek, I. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, "Photon-number-resolving detection using time-multiplexing", J. Mod. Opt. 51, 9-10, 1499-1515 (2004).

M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, "Photon-number resolution using time-multiplexed single-photon detectors", Phys. Rev. A 68, 043814 (2003).
[CrossRef]

Predazzi, E.

G. Brida, M. Genovese, M. Gramegna, P. Traina, E. Predazzi, S. Olivares, and M. G. A. Paris, "Toward a full reconstruction of density matrix by on/off measurements", Int. J. Quant. Inf. 7, 27-32 (2009).
[CrossRef]

G. Brida, M. Genovese, M. G. A. Paris, F. Piacentini, E. Predazzi, and E. Vallauri, "On Reconstructing Photon Statistics by on/off Detectors: Toward the Multi-Partite Case", Opt. Spect. 103, 1, 90-97 (2007).
[CrossRef]

Pryde, G. J.

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, "Demonstration of an all-optical quantum controlled-not gate", Nature 426, 264-267 (2003).
[CrossRef] [PubMed]

Ralph, T. C.

P. P. Rohde, J. G. Webb, E. H. Huntington, and T. C. Ralph, "Photon number projection using non-number-resolving detectors", New J. Phys. 9, 233 (2007).
[CrossRef]

T. C. Ralph, "Quantum optical systems for the implementation of quantum information processing", Rep. Prog. Phys. 69, 853-898 (2006).
[CrossRef]

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, "Demonstration of an all-optical quantum controlled-not gate", Nature 426, 264-267 (2003).
[CrossRef] [PubMed]

Ramos, R. V.

G. A. P. Thé and R. V. Ramos, "Multiple-photon number resolving detector using fibre ring and single-photon detector", J. Mod. Opt. 54, 8, 1187-1202 (2007).
[CrossRef]

Reeds, J. A.

J. C. Lagaris, J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence properties of the Nelder-Mead simplex method in low dimensions", SIAM J. Optim. 9, 1, 112-147 (1998).
[CrossRef]

Rehácek, J.

Z. Hradil and J. Reháček, "Likelihood and entropy for statistical inversion", J. Phys: Conf. Series 36, 55-59 (2006).
[CrossRef]

J. Reháček, Z. Hradil, O. Haderka, J. PerinaJr., and M. Hamar, "Multiple-photon resolving fiber-loop detector", Phys. Rev. A 67, 061801 (2003).

Ribordy, G.

Ricka, J.

M. Höbel and J. Ricka, "Dead-time and afterpulsing correction in multiphoton timing with nonideal detectors", Rev. Sci. Instrum. 65, 7, 2326-2336 (1994).
[CrossRef]

Rohde, P. P.

P. P. Rohde, J. G. Webb, E. H. Huntington, and T. C. Ralph, "Photon number projection using non-number-resolving detectors", New J. Phys. 9, 233 (2007).
[CrossRef]

P. P. Rohde, "Non-deterministic approximation of photon number discriminating detectors using nondiscriminating detectors", J. Opt. B: Quant. Semiclass. 7, 82-86 (2005).
[CrossRef]

Rossi, A.

G. Zambra, A. Andreoni, M. Bondani, M. Gramegna, M. Genovese, G. Brida, A. Rossi, and M. G. A. Paris, "Experimental reconstruction of photon statistics without photon counting", Phys. Rev. Lett. 95, 063602 (2005).
[CrossRef] [PubMed]

Sasaki, M.

Sergienko, A. V.

A. V. Sergienko, "Quantum optics: Beyond single-photon counting", Nat. Photon. 2, 268-269 (2008).
[CrossRef]

Silberhorn, C.

D. Achilles, C. Silberhorn, and I. A. Walmsley, "Direct, loss-tolerant characterization of nonclassical photon statistics", Phys. Rev. Lett. 97, 043602 (2006).
[CrossRef] [PubMed]

D. Achilles, C. Silberhorn, C. Śliwa, K. Banaszek, I. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, "Photon-number-resolving detection using time-multiplexing", J. Mod. Opt. 51, 9-10, 1499-1515 (2004).

Sliwa, C.

D. Achilles, C. Silberhorn, C. Śliwa, K. Banaszek, I. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, "Photon-number-resolving detection using time-multiplexing", J. Mod. Opt. 51, 9-10, 1499-1515 (2004).

Takeuchi, S.

J. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, "Multiphoton detection using visible light photon counter", Appl. Phys. Lett. 74, 7, 902 (1999).
[CrossRef]

S. Takeuchi, J. Kim, Y. Yamamoto, and H. H. Hogue, "Development of a high-quantum-efficiency single-photon counting system", Appl. Phys. Lett. 74, 8, 1063 (1999).
[CrossRef]

Thé, G. A. P.

G. A. P. Thé and R. V. Ramos, "Multiple-photon number resolving detector using fibre ring and single-photon detector", J. Mod. Opt. 54, 8, 1187-1202 (2007).
[CrossRef]

Törmä, P.

H. Paul, P. Törmä, T. Kiss, and I. Jex, "Photon Chopping: New Way to Measure the Quantum State of Light", Phys. Rev. Lett. 76, 2464 (1996).
[CrossRef] [PubMed]

Traina, P.

G. Brida, M. Genovese, M. Gramegna, P. Traina, E. Predazzi, S. Olivares, and M. G. A. Paris, "Toward a full reconstruction of density matrix by on/off measurements", Int. J. Quant. Inf. 7, 27-32 (2009).
[CrossRef]

Vallauri, E.

G. Brida, M. Genovese, M. G. A. Paris, F. Piacentini, E. Predazzi, and E. Vallauri, "On Reconstructing Photon Statistics by on/off Detectors: Toward the Multi-Partite Case", Opt. Spect. 103, 1, 90-97 (2007).
[CrossRef]

Walmsley, I.

D. Achilles, C. Silberhorn, C. Śliwa, K. Banaszek, I. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, "Photon-number-resolving detection using time-multiplexing", J. Mod. Opt. 51, 9-10, 1499-1515 (2004).

Walmsley, I. A.

D. Achilles, C. Silberhorn, and I. A. Walmsley, "Direct, loss-tolerant characterization of nonclassical photon statistics", Phys. Rev. Lett. 97, 043602 (2006).
[CrossRef] [PubMed]

K. Banaszek and I. A. Walmsley, "Photon counting with a loop detector", Opt. Lett. 28, 1, 52-54 (2003).
[CrossRef] [PubMed]

Webb, J. G.

P. P. Rohde, J. G. Webb, E. H. Huntington, and T. C. Ralph, "Photon number projection using non-number-resolving detectors", New J. Phys. 9, 233 (2007).
[CrossRef]

Weinhold, T. J.

B. P. Lanyon, T. J. Weinhold, N. K. Langford, M. Barbieri, D. F. V. James, A. Gilchrist and A. G. White, "Experimental Demonstration of a Compiled Version of Shor’s Algorithm with Quantum Entanglement", Phys. Rev. Lett. 99, 250505 (2007).
[CrossRef]

Welsch, D.-G.

T. Opatrný and D.-G. Welsch, "Density-matrix reconstruction by unbalanced homodyning", Phys. Rev. A 55, 1462 (1997).
[CrossRef]

White, A. G.

B. P. Lanyon, T. J. Weinhold, N. K. Langford, M. Barbieri, D. F. V. James, A. Gilchrist and A. G. White, "Experimental Demonstration of a Compiled Version of Shor’s Algorithm with Quantum Entanglement", Phys. Rev. Lett. 99, 250505 (2007).
[CrossRef]

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, "Demonstration of an all-optical quantum controlled-not gate", Nature 426, 264-267 (2003).
[CrossRef] [PubMed]

Wright, M. H.

J. C. Lagaris, J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence properties of the Nelder-Mead simplex method in low dimensions", SIAM J. Optim. 9, 1, 112-147 (1998).
[CrossRef]

Wright, P. E.

J. C. Lagaris, J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence properties of the Nelder-Mead simplex method in low dimensions", SIAM J. Optim. 9, 1, 112-147 (1998).
[CrossRef]

Yamamoto, Y.

S. Takeuchi, J. Kim, Y. Yamamoto, and H. H. Hogue, "Development of a high-quantum-efficiency single-photon counting system", Appl. Phys. Lett. 74, 8, 1063 (1999).
[CrossRef]

J. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, "Multiphoton detection using visible light photon counter", Appl. Phys. Lett. 74, 7, 902 (1999).
[CrossRef]

Yurtsever, U.

H. Lee, U. Yurtsever, P. Kok, G. M. Hockney, C. Adami, S. L. Braunstein, and J. P. Dowling, "Towards photostatistics from photon-number discriminating detectors", J. Mod. Opt. 51, 9-10, 1517-1528 (2004).

Zambra, G.

G. Zambra, A. Allevi, A. Andreoni, M. Bondani, and M. G. A. Paris, "Nontrivial photon statistics with low resolution-threshold photon counters", Int. J. Quant. Inf. 5, 1-2, 305-309 (2007).

G. Zambra and M. G. A. Paris, "Reconstruction of photon-number distribution using low-performance photon counters", Phys. Rev. A 74, 063830 (2006).
[CrossRef]

G. Zambra, A. Andreoni, M. Bondani, M. Gramegna, M. Genovese, G. Brida, A. Rossi, and M. G. A. Paris, "Experimental reconstruction of photon statistics without photon counting", Phys. Rev. Lett. 95, 063602 (2005).
[CrossRef] [PubMed]

Zbinden, H.

Appl. Opt. (2)

Appl. Phys. Lett. (2)

J. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, "Multiphoton detection using visible light photon counter", Appl. Phys. Lett. 74, 7, 902 (1999).
[CrossRef]

S. Takeuchi, J. Kim, Y. Yamamoto, and H. H. Hogue, "Development of a high-quantum-efficiency single-photon counting system", Appl. Phys. Lett. 74, 8, 1063 (1999).
[CrossRef]

Computer Journal (1)

J. A. Nelder and R. Mead, "A simplex method for function minimization", Computer Journal 7, 308-313 (1965).

Int. J. Quant. Inf. (2)

G. Brida, M. Genovese, M. Gramegna, P. Traina, E. Predazzi, S. Olivares, and M. G. A. Paris, "Toward a full reconstruction of density matrix by on/off measurements", Int. J. Quant. Inf. 7, 27-32 (2009).
[CrossRef]

G. Zambra, A. Allevi, A. Andreoni, M. Bondani, and M. G. A. Paris, "Nontrivial photon statistics with low resolution-threshold photon counters", Int. J. Quant. Inf. 5, 1-2, 305-309 (2007).

J. Mod. Opt. (3)

H. Lee, U. Yurtsever, P. Kok, G. M. Hockney, C. Adami, S. L. Braunstein, and J. P. Dowling, "Towards photostatistics from photon-number discriminating detectors", J. Mod. Opt. 51, 9-10, 1517-1528 (2004).

G. A. P. Thé and R. V. Ramos, "Multiple-photon number resolving detector using fibre ring and single-photon detector", J. Mod. Opt. 54, 8, 1187-1202 (2007).
[CrossRef]

D. Achilles, C. Silberhorn, C. Śliwa, K. Banaszek, I. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, "Photon-number-resolving detection using time-multiplexing", J. Mod. Opt. 51, 9-10, 1499-1515 (2004).

J. Opt. B: Quant. Semiclass. (1)

P. P. Rohde, "Non-deterministic approximation of photon number discriminating detectors using nondiscriminating detectors", J. Opt. B: Quant. Semiclass. 7, 82-86 (2005).
[CrossRef]

J. Phys: Conf. Series (1)

Z. Hradil and J. Reháček, "Likelihood and entropy for statistical inversion", J. Phys: Conf. Series 36, 55-59 (2006).
[CrossRef]

Nat. Photon. (1)

A. V. Sergienko, "Quantum optics: Beyond single-photon counting", Nat. Photon. 2, 268-269 (2008).
[CrossRef]

Nature (1)

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, "Demonstration of an all-optical quantum controlled-not gate", Nature 426, 264-267 (2003).
[CrossRef] [PubMed]

New J. Phys. (1)

P. P. Rohde, J. G. Webb, E. H. Huntington, and T. C. Ralph, "Photon number projection using non-number-resolving detectors", New J. Phys. 9, 233 (2007).
[CrossRef]

Opt. Comm. (1)

D. Mogilevtsev, "Diagonal element inference by direct detection", Opt. Comm. 156, 307-310 (1998).
[CrossRef]

Opt. Lett. (1)

Opt. Spect. (1)

G. Brida, M. Genovese, M. G. A. Paris, F. Piacentini, E. Predazzi, and E. Vallauri, "On Reconstructing Photon Statistics by on/off Detectors: Toward the Multi-Partite Case", Opt. Spect. 103, 1, 90-97 (2007).
[CrossRef]

Phys. Rev. A (6)

J. Reháček, Z. Hradil, O. Haderka, J. PerinaJr., and M. Hamar, "Multiple-photon resolving fiber-loop detector", Phys. Rev. A 67, 061801 (2003).

G. M. D’Ariano and C. Macchiavello, "Loss-error compensation in quantum-state measurements", Phys. Rev. A 57, 4, 3131-3133 (1998).
[CrossRef]

G. Zambra and M. G. A. Paris, "Reconstruction of photon-number distribution using low-performance photon counters", Phys. Rev. A 74, 063830 (2006).
[CrossRef]

M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, "Photon-number resolution using time-multiplexed single-photon detectors", Phys. Rev. A 68, 043814 (2003).
[CrossRef]

T. Opatrný and D.-G. Welsch, "Density-matrix reconstruction by unbalanced homodyning", Phys. Rev. A 55, 1462 (1997).
[CrossRef]

P. Kok and S. Braunstein, "Detection devices in entanglement-based optical state preparation", Phys. Rev. A 63, 033812 (2001).
[CrossRef]

Phys. Rev. Lett. (4)

H. Paul, P. Törmä, T. Kiss, and I. Jex, "Photon Chopping: New Way to Measure the Quantum State of Light", Phys. Rev. Lett. 76, 2464 (1996).
[CrossRef] [PubMed]

B. P. Lanyon, T. J. Weinhold, N. K. Langford, M. Barbieri, D. F. V. James, A. Gilchrist and A. G. White, "Experimental Demonstration of a Compiled Version of Shor’s Algorithm with Quantum Entanglement", Phys. Rev. Lett. 99, 250505 (2007).
[CrossRef]

G. Zambra, A. Andreoni, M. Bondani, M. Gramegna, M. Genovese, G. Brida, A. Rossi, and M. G. A. Paris, "Experimental reconstruction of photon statistics without photon counting", Phys. Rev. Lett. 95, 063602 (2005).
[CrossRef] [PubMed]

D. Achilles, C. Silberhorn, and I. A. Walmsley, "Direct, loss-tolerant characterization of nonclassical photon statistics", Phys. Rev. Lett. 97, 043602 (2006).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

T. C. Ralph, "Quantum optical systems for the implementation of quantum information processing", Rep. Prog. Phys. 69, 853-898 (2006).
[CrossRef]

Rev. Sci. Instrum. (1)

M. Höbel and J. Ricka, "Dead-time and afterpulsing correction in multiphoton timing with nonideal detectors", Rev. Sci. Instrum. 65, 7, 2326-2336 (1994).
[CrossRef]

SIAM J. Optim. (1)

J. C. Lagaris, J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence properties of the Nelder-Mead simplex method in low dimensions", SIAM J. Optim. 9, 1, 112-147 (1998).
[CrossRef]

Other (7)

W. H. Press et al, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University Press, Cambridge, England, 2nd edition, 1992).

D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, Berlin, 1995).

M. Bondani, A. Allevi, A. Agliati, and A. Andreoni, "Self-consistent characterization of light statistics", arXiv:quant-ph/0810.4055v1 (2008).

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, "Review article: Linear optical quantum computing", arXiv:quant-ph/0512071 (2005).

S. D. Bartlett, E. Diamanti, B. C. Sanders, and Y. Yamamoto, "Photon counting schemes and performance of non-deterministic nonlinear gates in linear optics", arXiv:quant-ph/0204073v1 (2002).

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, UK, 2000).

A. J. Pearlman, S. V. Polyakov, A. Migdall, and S.W. Nam, "Number-resolving, single photon detection with no deadtime", Conference on CLEO/QELS, pp 1-2, May 2008.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1.
Fig. 1.

Experimental configuration of the loop detector and diode laser source of pulsed coherent states. The fibre loop may be broken (disconnected) at point ’X’ for characterisation purposes as described in the text.

Fig. 2.
Fig. 2.

Determination of a) optimum SPDM trigger delay and b) clock frequency for the loop detector. The SPDM trigger delay is chosen to maximise the detection probability of the first time-bin. The clock frequency is chosen to maximise ∑5 i=2 pi.

Fig. 3.
Fig. 3.

Raw time bin detection (click) probabilities for ηd =10%, n̄=8.1 photons/pulse.

Fig. 4.
Fig. 4.

Characteristic conditional probabilities P(m|n) for the 1550 nm loop detector. Note the logarithmic vertical axis used to accommodate the rapidly diminishing higher order terms.

Fig. 5.
Fig. 5.

Measured time-bin detection probabilities for a) ηd =10% and b) ηd =25%, with the loop open-circuit.

Fig. 6.
Fig. 6.

Measurement of afterpulsing from time series data of Fig. 5 (ηd =25%).

Fig. 7.
Fig. 7.

Raw and corrected time bin detection probabilities for a)ηd =10% and b)ηd =25% with n̄=3.25 photons/pulse.

Fig. 8.
Fig. 8.

Predicted 9-bit signature probabilities for ηd =10%, n̄=8 photons/pulse.

Fig. 9.
Fig. 9.

Mean-square-error for coherent-state fits to raw, corrected and signature probability data for n̄=6.5±0.8 photons/pulse.

Fig. 10.
Fig. 10.

Photon-number distributions corresponding to the observed ε (MSE) minima of Fig. 9. The best fit to the a) corrected binomial data occurs with n̄=4.54 photons/pulse, and the b) signature data at n̄=5.95 photons/pulse. The photostatistics (and derived error bounds) of the n̄=6.5±0.8 photons/pulse. input state is shown for comparison.

Fig. 11.
Fig. 11.

Estimated mean photon numbers for binomial probability and signature based reconstruction techniques.

Fig. 12.
Fig. 12.

Reconstructed photon-number distributions for an input coherent state with a) n̄ i =4.6±0.8 and b) 6.5±0.8 photons/pulse. Poissonian distributions representing the same mean photon number as the reconstructed states (r =4.3 and 6.0 photons/pulse. respectively) are shown for comparison.

Tables (2)

Tables Icon

Table 1. Detection efficiencies corresponding to loop TDM bins.

Tables Icon

Table 2. P(m|n) for loop detector.

Equations (15)

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

Psig (d) = n1+...+nN=nn!n1!...nN! i=1NPc (i)ni
×jd [pdc+(1pdc)[1ploss(j)nj]]
×ld[(1pdc)ploss(l)nj] .
p (m|n) =d=mpsig(d) .
pout(m) =i=mim ηm (1η)im ρii .
pclick ηρ = pdc +(1pdc) n=1k jnk jn ηn (1η)jn ρnn
p mρ =d=m psig dρ
psig(d,ρ)=n=0kρnn[n1++nN=nn!n1!nN!i=1Npc(i)ni
×jd[pdc+(1pdc)[1ploss(j)nj]]
×ld[(1pdc)ploss(l)nl]]
ε=iS(pip̂i)2
psig dρN=9 psig ([d0],ρ) N=10+psig([d1],ρ)N=10
dpsig dρ N=9=1 n , ρ
ρnn =n̅nn!Σi=1Kn̅ii!
ε =(Tr[ρ]1)2 +d(p̂sigdρN=9psigdρN=9)2

Metrics