A. Avella, G. Brida, I. P. Degiovanni, M. Genovese, M. Gramegna, L. Lolli, E. Monticone, C. Portesi, M. Rajteri, M. L. Rastello, E. Taralli, P. Traina, and M. White, “Self consistent, absolute calibration technique for photon number resolving detectors,” Opt. Express 19, 23249–23257 (2011).

[Crossref]
[PubMed]

A. R. Beaumont, J. Y. Cheung, C. J. Chunnilall, J. Ireland, and M. G. White, “Providing reference standards and metrology for the few photon counting community,” Nucl. Inst. and Meth. A 610, 183–187 (2009).

[Crossref]

A. Avella, G. Brida, I. P. Degiovanni, M. Genovese, M. Gramegna, L. Lolli, E. Monticone, C. Portesi, M. Rajteri, M. L. Rastello, E. Taralli, P. Traina, and M. White, “Self consistent, absolute calibration technique for photon number resolving detectors,” Opt. Express 19, 23249–23257 (2011).

[Crossref]
[PubMed]

Z. H. Levine, B. L. Glebov, A. L. Midgall, T. Gerrits, B. Calkins, A. E. Lita, and S. W. Nam, “Photon-number uncertainty in a superconducting transition-edge sensor beyond resolved-photon-number determination,” J. Opt. Soc. Am. B 31, B20–B24 (2014).

[Crossref]

Z. H. Levine, T. Gerrits, A. L. Migdall, D. V. Samarov, B. Calkins, A. E. Lita, and S. W. Nam, “An algorithm for finding clusters with a known distribution and its application to photon-number resolution using a superconducting transition-edge sensor,” J. Opt. Soc. Am. B 29, 2066–2073 (2012).

[Crossref]

A. Gelman, J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari, and D. B. Rubin, Bayesian Data Analysis (Chapman & Hall/CRC, Boca Raton, FL, 2014).

H. K. Lo, X. F. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94, 230504 (2005).

[Crossref]
[PubMed]

A. R. Beaumont, J. Y. Cheung, C. J. Chunnilall, J. Ireland, and M. G. White, “Providing reference standards and metrology for the few photon counting community,” Nucl. Inst. and Meth. A 610, 183–187 (2009).

[Crossref]

A. R. Beaumont, J. Y. Cheung, C. J. Chunnilall, J. Ireland, and M. G. White, “Providing reference standards and metrology for the few photon counting community,” Nucl. Inst. and Meth. A 610, 183–187 (2009).

[Crossref]

A. P. Worsley, H. B. Coldenstrodt-Ronge, J. S. Lundeen, P. J. Mosley, B. J. Smith, G. Puentes, N. Thomas-Peter, and I. A. Walmsley, “Absolute efficiency estimation of photon-number-resolving detectors using twin beams,” Opt. Express 17, 4397–4411 (2009).

[Crossref]
[PubMed]

J. H. Lehman and C. L. Cromer, “Optical trap detector for calibration of optical fiber powermeters: coupling efficiency,” Appl. Opt. 31, 6531–6536 (2002).

[Crossref]

A. Czitrovszky, A. Sergienko, P. Jani, and A. Nagy, “Measurement of quantum efficiency using entangled photons,” Laser Phys. 10, 86–89 (2000).

P. C. Humphreys, B. J. Metcalf, T. Gerrits, T. Hiemstra, A. E. Lita, S. W. Nam, A. Datta, W. S. Kolthammer, and I. A. Walmsley, “Tomography of photon-number resolving continuous-output detectors,” arXiv:1502.07649 (2015).

A. Avella, G. Brida, I. P. Degiovanni, M. Genovese, M. Gramegna, L. Lolli, E. Monticone, C. Portesi, M. Rajteri, M. L. Rastello, E. Taralli, P. Traina, and M. White, “Self consistent, absolute calibration technique for photon number resolving detectors,” Opt. Express 19, 23249–23257 (2011).

[Crossref]
[PubMed]

A. Gelman, J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari, and D. B. Rubin, Bayesian Data Analysis (Chapman & Hall/CRC, Boca Raton, FL, 2014).

G. Eppeldauer, “Noise-optimized silicon radiometers,” J. Res. Natl. Inst. Stand. Technol. 105, 209–219 (2000).

[Crossref]

M. D. Hoffman and A. Gelman, “The no-U-turn sampler: Adaptively setting path lengths in Hamiltonian Monte Carlo,” J. Machine Learning Research (2014).

A. Gelman, J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari, and D. B. Rubin, Bayesian Data Analysis (Chapman & Hall/CRC, Boca Raton, FL, 2014).

A. Avella, G. Brida, I. P. Degiovanni, M. Genovese, M. Gramegna, L. Lolli, E. Monticone, C. Portesi, M. Rajteri, M. L. Rastello, E. Taralli, P. Traina, and M. White, “Self consistent, absolute calibration technique for photon number resolving detectors,” Opt. Express 19, 23249–23257 (2011).

[Crossref]
[PubMed]

Z. H. Levine, B. L. Glebov, A. L. Midgall, T. Gerrits, B. Calkins, A. E. Lita, and S. W. Nam, “Photon-number uncertainty in a superconducting transition-edge sensor beyond resolved-photon-number determination,” J. Opt. Soc. Am. B 31, B20–B24 (2014).

[Crossref]

Z. H. Levine, T. Gerrits, A. L. Migdall, D. V. Samarov, B. Calkins, A. E. Lita, and S. W. Nam, “An algorithm for finding clusters with a known distribution and its application to photon-number resolution using a superconducting transition-edge sensor,” J. Opt. Soc. Am. B 29, 2066–2073 (2012).

[Crossref]

P. C. Humphreys, B. J. Metcalf, T. Gerrits, T. Hiemstra, A. E. Lita, S. W. Nam, A. Datta, W. S. Kolthammer, and I. A. Walmsley, “Tomography of photon-number resolving continuous-output detectors,” arXiv:1502.07649 (2015).

D. Gottlieb and S. A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications (Society of Industrial and Applied Mathematics, Philadelphia, PA, 1977). P. 159.

A. Avella, G. Brida, I. P. Degiovanni, M. Genovese, M. Gramegna, L. Lolli, E. Monticone, C. Portesi, M. Rajteri, M. L. Rastello, E. Taralli, P. Traina, and M. White, “Self consistent, absolute calibration technique for photon number resolving detectors,” Opt. Express 19, 23249–23257 (2011).

[Crossref]
[PubMed]

H. A. Haus, Electromagnetic Noise and Quantum Optical Measurements (Springer, Berlin, 2000). Sect. 9.2.

[Crossref]

P. C. Humphreys, B. J. Metcalf, T. Gerrits, T. Hiemstra, A. E. Lita, S. W. Nam, A. Datta, W. S. Kolthammer, and I. A. Walmsley, “Tomography of photon-number resolving continuous-output detectors,” arXiv:1502.07649 (2015).

M. D. Hoffman and A. Gelman, “The no-U-turn sampler: Adaptively setting path lengths in Hamiltonian Monte Carlo,” J. Machine Learning Research (2014).

P. C. Humphreys, B. J. Metcalf, T. Gerrits, T. Hiemstra, A. E. Lita, S. W. Nam, A. Datta, W. S. Kolthammer, and I. A. Walmsley, “Tomography of photon-number resolving continuous-output detectors,” arXiv:1502.07649 (2015).

A. R. Beaumont, J. Y. Cheung, C. J. Chunnilall, J. Ireland, and M. G. White, “Providing reference standards and metrology for the few photon counting community,” Nucl. Inst. and Meth. A 610, 183–187 (2009).

[Crossref]

A. Czitrovszky, A. Sergienko, P. Jani, and A. Nagy, “Measurement of quantum efficiency using entangled photons,” Laser Phys. 10, 86–89 (2000).

R. Klein, R. Thornagel, and G. Ulm, “From single photons to milliwatt radiant power in electron storage rings as radiation sources with a high dynamic range,” Metrologia 47, R33–R40 (2010).

[Crossref]

P. C. Humphreys, B. J. Metcalf, T. Gerrits, T. Hiemstra, A. E. Lita, S. W. Nam, A. Datta, W. S. Kolthammer, and I. A. Walmsley, “Tomography of photon-number resolving continuous-output detectors,” arXiv:1502.07649 (2015).

J. H. Lehman and C. L. Cromer, “Optical trap detector for calibration of optical fiber powermeters: coupling efficiency,” Appl. Opt. 31, 6531–6536 (2002).

[Crossref]

Z. H. Levine, B. L. Glebov, A. L. Midgall, T. Gerrits, B. Calkins, A. E. Lita, and S. W. Nam, “Photon-number uncertainty in a superconducting transition-edge sensor beyond resolved-photon-number determination,” J. Opt. Soc. Am. B 31, B20–B24 (2014).

[Crossref]

Z. H. Levine, T. Gerrits, A. L. Migdall, D. V. Samarov, B. Calkins, A. E. Lita, and S. W. Nam, “An algorithm for finding clusters with a known distribution and its application to photon-number resolution using a superconducting transition-edge sensor,” J. Opt. Soc. Am. B 29, 2066–2073 (2012).

[Crossref]

Z. H. Levine, B. L. Glebov, A. L. Midgall, T. Gerrits, B. Calkins, A. E. Lita, and S. W. Nam, “Photon-number uncertainty in a superconducting transition-edge sensor beyond resolved-photon-number determination,” J. Opt. Soc. Am. B 31, B20–B24 (2014).

[Crossref]

Z. H. Levine, T. Gerrits, A. L. Migdall, D. V. Samarov, B. Calkins, A. E. Lita, and S. W. Nam, “An algorithm for finding clusters with a known distribution and its application to photon-number resolution using a superconducting transition-edge sensor,” J. Opt. Soc. Am. B 29, 2066–2073 (2012).

[Crossref]

P. C. Humphreys, B. J. Metcalf, T. Gerrits, T. Hiemstra, A. E. Lita, S. W. Nam, A. Datta, W. S. Kolthammer, and I. A. Walmsley, “Tomography of photon-number resolving continuous-output detectors,” arXiv:1502.07649 (2015).

H. K. Lo, X. F. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94, 230504 (2005).

[Crossref]
[PubMed]

A. Avella, G. Brida, I. P. Degiovanni, M. Genovese, M. Gramegna, L. Lolli, E. Monticone, C. Portesi, M. Rajteri, M. L. Rastello, E. Taralli, P. Traina, and M. White, “Self consistent, absolute calibration technique for photon number resolving detectors,” Opt. Express 19, 23249–23257 (2011).

[Crossref]
[PubMed]

A. P. Worsley, H. B. Coldenstrodt-Ronge, J. S. Lundeen, P. J. Mosley, B. J. Smith, G. Puentes, N. Thomas-Peter, and I. A. Walmsley, “Absolute efficiency estimation of photon-number-resolving detectors using twin beams,” Opt. Express 17, 4397–4411 (2009).

[Crossref]
[PubMed]

H. K. Lo, X. F. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94, 230504 (2005).

[Crossref]
[PubMed]

P. C. Humphreys, B. J. Metcalf, T. Gerrits, T. Hiemstra, A. E. Lita, S. W. Nam, A. Datta, W. S. Kolthammer, and I. A. Walmsley, “Tomography of photon-number resolving continuous-output detectors,” arXiv:1502.07649 (2015).

A. Migdall, “Correlated-photon metrology without absolute standards,” Phys. Tod. 52, 41–46 (1999).

[Crossref]

A. Avella, G. Brida, I. P. Degiovanni, M. Genovese, M. Gramegna, L. Lolli, E. Monticone, C. Portesi, M. Rajteri, M. L. Rastello, E. Taralli, P. Traina, and M. White, “Self consistent, absolute calibration technique for photon number resolving detectors,” Opt. Express 19, 23249–23257 (2011).

[Crossref]
[PubMed]

A. P. Worsley, H. B. Coldenstrodt-Ronge, J. S. Lundeen, P. J. Mosley, B. J. Smith, G. Puentes, N. Thomas-Peter, and I. A. Walmsley, “Absolute efficiency estimation of photon-number-resolving detectors using twin beams,” Opt. Express 17, 4397–4411 (2009).

[Crossref]
[PubMed]

A. Czitrovszky, A. Sergienko, P. Jani, and A. Nagy, “Measurement of quantum efficiency using entangled photons,” Laser Phys. 10, 86–89 (2000).

Z. H. Levine, B. L. Glebov, A. L. Midgall, T. Gerrits, B. Calkins, A. E. Lita, and S. W. Nam, “Photon-number uncertainty in a superconducting transition-edge sensor beyond resolved-photon-number determination,” J. Opt. Soc. Am. B 31, B20–B24 (2014).

[Crossref]

Z. H. Levine, T. Gerrits, A. L. Migdall, D. V. Samarov, B. Calkins, A. E. Lita, and S. W. Nam, “An algorithm for finding clusters with a known distribution and its application to photon-number resolution using a superconducting transition-edge sensor,” J. Opt. Soc. Am. B 29, 2066–2073 (2012).

[Crossref]

P. C. Humphreys, B. J. Metcalf, T. Gerrits, T. Hiemstra, A. E. Lita, S. W. Nam, A. Datta, W. S. Kolthammer, and I. A. Walmsley, “Tomography of photon-number resolving continuous-output detectors,” arXiv:1502.07649 (2015).

D. Gottlieb and S. A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications (Society of Industrial and Applied Mathematics, Philadelphia, PA, 1977). P. 159.

A. Avella, G. Brida, I. P. Degiovanni, M. Genovese, M. Gramegna, L. Lolli, E. Monticone, C. Portesi, M. Rajteri, M. L. Rastello, E. Taralli, P. Traina, and M. White, “Self consistent, absolute calibration technique for photon number resolving detectors,” Opt. Express 19, 23249–23257 (2011).

[Crossref]
[PubMed]

A. P. Worsley, H. B. Coldenstrodt-Ronge, J. S. Lundeen, P. J. Mosley, B. J. Smith, G. Puentes, N. Thomas-Peter, and I. A. Walmsley, “Absolute efficiency estimation of photon-number-resolving detectors using twin beams,” Opt. Express 17, 4397–4411 (2009).

[Crossref]
[PubMed]

A. Avella, G. Brida, I. P. Degiovanni, M. Genovese, M. Gramegna, L. Lolli, E. Monticone, C. Portesi, M. Rajteri, M. L. Rastello, E. Taralli, P. Traina, and M. White, “Self consistent, absolute calibration technique for photon number resolving detectors,” Opt. Express 19, 23249–23257 (2011).

[Crossref]
[PubMed]

A. Avella, G. Brida, I. P. Degiovanni, M. Genovese, M. Gramegna, L. Lolli, E. Monticone, C. Portesi, M. Rajteri, M. L. Rastello, E. Taralli, P. Traina, and M. White, “Self consistent, absolute calibration technique for photon number resolving detectors,” Opt. Express 19, 23249–23257 (2011).

[Crossref]
[PubMed]

A. Gelman, J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari, and D. B. Rubin, Bayesian Data Analysis (Chapman & Hall/CRC, Boca Raton, FL, 2014).

A. Czitrovszky, A. Sergienko, P. Jani, and A. Nagy, “Measurement of quantum efficiency using entangled photons,” Laser Phys. 10, 86–89 (2000).

A. P. Worsley, H. B. Coldenstrodt-Ronge, J. S. Lundeen, P. J. Mosley, B. J. Smith, G. Puentes, N. Thomas-Peter, and I. A. Walmsley, “Absolute efficiency estimation of photon-number-resolving detectors using twin beams,” Opt. Express 17, 4397–4411 (2009).

[Crossref]
[PubMed]

A. Gelman, J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari, and D. B. Rubin, Bayesian Data Analysis (Chapman & Hall/CRC, Boca Raton, FL, 2014).

A. Avella, G. Brida, I. P. Degiovanni, M. Genovese, M. Gramegna, L. Lolli, E. Monticone, C. Portesi, M. Rajteri, M. L. Rastello, E. Taralli, P. Traina, and M. White, “Self consistent, absolute calibration technique for photon number resolving detectors,” Opt. Express 19, 23249–23257 (2011).

[Crossref]
[PubMed]

A. P. Worsley, H. B. Coldenstrodt-Ronge, J. S. Lundeen, P. J. Mosley, B. J. Smith, G. Puentes, N. Thomas-Peter, and I. A. Walmsley, “Absolute efficiency estimation of photon-number-resolving detectors using twin beams,” Opt. Express 17, 4397–4411 (2009).

[Crossref]
[PubMed]

R. Klein, R. Thornagel, and G. Ulm, “From single photons to milliwatt radiant power in electron storage rings as radiation sources with a high dynamic range,” Metrologia 47, R33–R40 (2010).

[Crossref]

A. Avella, G. Brida, I. P. Degiovanni, M. Genovese, M. Gramegna, L. Lolli, E. Monticone, C. Portesi, M. Rajteri, M. L. Rastello, E. Taralli, P. Traina, and M. White, “Self consistent, absolute calibration technique for photon number resolving detectors,” Opt. Express 19, 23249–23257 (2011).

[Crossref]
[PubMed]

R. Klein, R. Thornagel, and G. Ulm, “From single photons to milliwatt radiant power in electron storage rings as radiation sources with a high dynamic range,” Metrologia 47, R33–R40 (2010).

[Crossref]

A. Gelman, J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari, and D. B. Rubin, Bayesian Data Analysis (Chapman & Hall/CRC, Boca Raton, FL, 2014).

A. P. Worsley, H. B. Coldenstrodt-Ronge, J. S. Lundeen, P. J. Mosley, B. J. Smith, G. Puentes, N. Thomas-Peter, and I. A. Walmsley, “Absolute efficiency estimation of photon-number-resolving detectors using twin beams,” Opt. Express 17, 4397–4411 (2009).

[Crossref]
[PubMed]

P. C. Humphreys, B. J. Metcalf, T. Gerrits, T. Hiemstra, A. E. Lita, S. W. Nam, A. Datta, W. S. Kolthammer, and I. A. Walmsley, “Tomography of photon-number resolving continuous-output detectors,” arXiv:1502.07649 (2015).

A. Avella, G. Brida, I. P. Degiovanni, M. Genovese, M. Gramegna, L. Lolli, E. Monticone, C. Portesi, M. Rajteri, M. L. Rastello, E. Taralli, P. Traina, and M. White, “Self consistent, absolute calibration technique for photon number resolving detectors,” Opt. Express 19, 23249–23257 (2011).

[Crossref]
[PubMed]

A. R. Beaumont, J. Y. Cheung, C. J. Chunnilall, J. Ireland, and M. G. White, “Providing reference standards and metrology for the few photon counting community,” Nucl. Inst. and Meth. A 610, 183–187 (2009).

[Crossref]

A. P. Worsley, H. B. Coldenstrodt-Ronge, J. S. Lundeen, P. J. Mosley, B. J. Smith, G. Puentes, N. Thomas-Peter, and I. A. Walmsley, “Absolute efficiency estimation of photon-number-resolving detectors using twin beams,” Opt. Express 17, 4397–4411 (2009).

[Crossref]
[PubMed]

J. H. Lehman and C. L. Cromer, “Optical trap detector for calibration of optical fiber powermeters: coupling efficiency,” Appl. Opt. 31, 6531–6536 (2002).

[Crossref]

J. G. Rarity, K. D. Ridley, and P. R. Tapster, “Absolute measurement of detector quantum efficiency using parametric downconversion,” Appl. Opt. 26, 4616–4619 (1987).

[Crossref]
[PubMed]

M. Fujiwara and M. Sasaki, “Direct measurement of photon number statistics at telecom wavelengths using a charge integration photon detector,” Appl. Opt. 46, 3069–3074 (2007).

[Crossref]
[PubMed]

Z. H. Levine, T. Gerrits, A. L. Migdall, D. V. Samarov, B. Calkins, A. E. Lita, and S. W. Nam, “An algorithm for finding clusters with a known distribution and its application to photon-number resolution using a superconducting transition-edge sensor,” J. Opt. Soc. Am. B 29, 2066–2073 (2012).

[Crossref]

Z. H. Levine, B. L. Glebov, A. L. Midgall, T. Gerrits, B. Calkins, A. E. Lita, and S. W. Nam, “Photon-number uncertainty in a superconducting transition-edge sensor beyond resolved-photon-number determination,” J. Opt. Soc. Am. B 31, B20–B24 (2014).

[Crossref]

G. Eppeldauer, “Noise-optimized silicon radiometers,” J. Res. Natl. Inst. Stand. Technol. 105, 209–219 (2000).

[Crossref]

A. Czitrovszky, A. Sergienko, P. Jani, and A. Nagy, “Measurement of quantum efficiency using entangled photons,” Laser Phys. 10, 86–89 (2000).

R. Klein, R. Thornagel, and G. Ulm, “From single photons to milliwatt radiant power in electron storage rings as radiation sources with a high dynamic range,” Metrologia 47, R33–R40 (2010).

[Crossref]

A. R. Beaumont, J. Y. Cheung, C. J. Chunnilall, J. Ireland, and M. G. White, “Providing reference standards and metrology for the few photon counting community,” Nucl. Inst. and Meth. A 610, 183–187 (2009).

[Crossref]

A. P. Worsley, H. B. Coldenstrodt-Ronge, J. S. Lundeen, P. J. Mosley, B. J. Smith, G. Puentes, N. Thomas-Peter, and I. A. Walmsley, “Absolute efficiency estimation of photon-number-resolving detectors using twin beams,” Opt. Express 17, 4397–4411 (2009).

[Crossref]
[PubMed]

A. Avella, G. Brida, I. P. Degiovanni, M. Genovese, M. Gramegna, L. Lolli, E. Monticone, C. Portesi, M. Rajteri, M. L. Rastello, E. Taralli, P. Traina, and M. White, “Self consistent, absolute calibration technique for photon number resolving detectors,” Opt. Express 19, 23249–23257 (2011).

[Crossref]
[PubMed]

H. K. Lo, X. F. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94, 230504 (2005).

[Crossref]
[PubMed]

A. Migdall, “Correlated-photon metrology without absolute standards,” Phys. Tod. 52, 41–46 (1999).

[Crossref]

P. C. Humphreys, B. J. Metcalf, T. Gerrits, T. Hiemstra, A. E. Lita, S. W. Nam, A. Datta, W. S. Kolthammer, and I. A. Walmsley, “Tomography of photon-number resolving continuous-output detectors,” arXiv:1502.07649 (2015).

A. Gelman, J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari, and D. B. Rubin, Bayesian Data Analysis (Chapman & Hall/CRC, Boca Raton, FL, 2014).

The mention of commercial products does not imply endorsement by the authors’ institutions nor does it imply that they are the best available for the purpose.

D. Gottlieb and S. A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications (Society of Industrial and Applied Mathematics, Philadelphia, PA, 1977). P. 159.

OZ Optics Limited, “Digital variable attenuator,” http://www.ozoptics.com/ALLNEW_PDF/DTS0007.pdf , 2013, p. 3.

H. A. Haus, Electromagnetic Noise and Quantum Optical Measurements (Springer, Berlin, 2000). Sect. 9.2.

[Crossref]

R Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria (2014).

Stan Development Team, Stan: A C++ Library for Probability and Sampling, Version 2.5.0 (2014).

Stan Development Team, Stan Modeling Language User’s Guide and Reference Manual, Version 2.5.0 (2014).

M. D. Hoffman and A. Gelman, “The no-U-turn sampler: Adaptively setting path lengths in Hamiltonian Monte Carlo,” J. Machine Learning Research (2014).