F. E. Becerra, J. Fan, G. Baumgartner, S. V. Polyakov, J. Goldhar, J. T. Kosloski, and A. Migdall, “M-ary-state phase-shift-keying discrimination below the homodyne limit,” Phys. Rev. A 84, 062324 (2011).

[CrossRef]

M. Mehmet, A. Ast, T. Eberle, S. Steinlechner, H. Vahlbruch, and R. Schnabel, “Squeezed light at 1550 nm with a quantum noise reduction of 12.3 dB,” Opt. Express 19, 25763–25772 (2011).

[CrossRef]

M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Single-photon source and detectors,” Rev. Sci. Instrum. 82, 071101 (2011).

[CrossRef]

D. Fukuda, G. Fujii, T. Numata, K. Amemiya, A. Yoshizawa, H. Tsuchida, H. Fujino, H. Ishii, T. Itatani, S. Inoue, and T. Zama, “Titanium-based transition-edge photon number resolving detector with 98 percent detection efficiency with index-matched small-gap fiber coupling,” Opt. Express 19, 870–875 (2011).

[CrossRef]

J. C. Zwinkels, E. Ikonen, N. P. Fox, G. Ulm, and M. L. Rastello, “Photometry, radiometry and ‘the candela’: evolution in the classical and quantum world,” Metrologia 47, R15–R32 (2010).

[CrossRef]

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. 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]

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. Instrum. Methods Phys. Res. A 610, 183–187 (2009).

[CrossRef]

P. Buzhan, B. Dolgoshein, A. Ilyin, V. Kaplin, S. Klemin, R. Mirzoyan, E. Popova, and M. Teshima, “The cross-talk problem in SiPMs and their use as light sensors for imaging atmospheric Cherenkov telescopes,” Nucl. Instrum. Methods Phys. Res. A 610, 131–134 (2009).

[CrossRef]

R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photon. 3, 696–705 (2009).

[CrossRef]

A. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express 16, 3032–3040 (2008).

[CrossRef]

C. Wittmann, M. Takeoka, K. N. Cassemiro, M. Sasaki, G. Leuchs, and U. L. Andersen, “Demonstration of near-optimal discrimination of optical coherent states,” Phys. Rev. Lett. 101, 210501 (2008).

[CrossRef]

D. J. Fixsen, S. H. Moseley, B. Cabrera, and E. Figueroa-Feliciano, “Pulse estimation in nonlinear detectors with nonstationary noise,” Nucl. Instrum. Methods Phys. Res. A 520, 555–558 (2004).

[CrossRef]

L. Cai, H. Y. Huang, S. Blackshaw, J. S. Liu, C. Cepko, and W. H. Wong, “Clustering analysis of SAGE data using a Poisson approach,” Genome Biol. 5, R51.1 (2004).

[CrossRef]

A. J. Miller, S. W. Nam, J. M. Martin, and A. V. Sergienko, “Demonstration of a low-noise near-infrared photon counter with multiphoton discrimination,” Appl. Phys. Lett. 83, 791–793 (2003).

[CrossRef]

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).

[CrossRef]

A. Migdall, “Differences explained in correlated-photon metrology techniques,” Phys. Today 52, 41–46 (1999).

[CrossRef]

H. J. Briegel, W. Dur, 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]

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).

[CrossRef]

S. Dolinar, “An optimum receiver for the binary coherent state quantum channel,” Massachusetts Institute of Technology Research Laboratory of Electronics Quarterly Progress Report, Vol. 111, 115–120 (1973).

D. Fukuda, G. Fujii, T. Numata, K. Amemiya, A. Yoshizawa, H. Tsuchida, H. Fujino, H. Ishii, T. Itatani, S. Inoue, and T. Zama, “Titanium-based transition-edge photon number resolving detector with 98 percent detection efficiency with index-matched small-gap fiber coupling,” Opt. Express 19, 870–875 (2011).

[CrossRef]

C. Wittmann, M. Takeoka, K. N. Cassemiro, M. Sasaki, G. Leuchs, and U. L. Andersen, “Demonstration of near-optimal discrimination of optical coherent states,” Phys. Rev. Lett. 101, 210501 (2008).

[CrossRef]

F. E. Becerra, J. Fan, G. Baumgartner, S. V. Polyakov, J. Goldhar, J. T. Kosloski, and A. Migdall, “M-ary-state phase-shift-keying discrimination below the homodyne limit,” Phys. Rev. A 84, 062324 (2011).

[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. Instrum. Methods Phys. Res. A 610, 183–187 (2009).

[CrossRef]

F. E. Becerra, J. Fan, G. Baumgartner, S. V. Polyakov, J. Goldhar, J. T. Kosloski, and A. Migdall, “M-ary-state phase-shift-keying discrimination below the homodyne limit,” Phys. Rev. A 84, 062324 (2011).

[CrossRef]

P. E. Black, “Greedy algorithm,” in Dictionary of Algorithms and Data Structures [online], P. E. Black, ed., U. S. National Institute of Standards and Technology (2February2005) (accessed March 5, 2012). Available from http://www.nist.gov/dads/HTML/greedyalgo.html .

L. Cai, H. Y. Huang, S. Blackshaw, J. S. Liu, C. Cepko, and W. H. Wong, “Clustering analysis of SAGE data using a Poisson approach,” Genome Biol. 5, R51.1 (2004).

[CrossRef]

H. J. Briegel, W. Dur, 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]

P. Buzhan, B. Dolgoshein, A. Ilyin, V. Kaplin, S. Klemin, R. Mirzoyan, E. Popova, and M. Teshima, “The cross-talk problem in SiPMs and their use as light sensors for imaging atmospheric Cherenkov telescopes,” Nucl. Instrum. Methods Phys. Res. A 610, 131–134 (2009).

[CrossRef]

D. J. Fixsen, S. H. Moseley, B. Cabrera, and E. Figueroa-Feliciano, “Pulse estimation in nonlinear detectors with nonstationary noise,” Nucl. Instrum. Methods Phys. Res. A 520, 555–558 (2004).

[CrossRef]

L. Cai, H. Y. Huang, S. Blackshaw, J. S. Liu, C. Cepko, and W. H. Wong, “Clustering analysis of SAGE data using a Poisson approach,” Genome Biol. 5, R51.1 (2004).

[CrossRef]

T. Gerrits, B. Calkins, N. Tomlin, A. E. Lita, A. Migdall, S. W. Nam, and R. Mirin, “Extending single-photon optimized superconducting transition edge sensors beyond the single-photon counting regime,” presented at the Quantum Electronics and Laser Science Conference (2012).

C. Wittmann, M. Takeoka, K. N. Cassemiro, M. Sasaki, G. Leuchs, and U. L. Andersen, “Demonstration of near-optimal discrimination of optical coherent states,” Phys. Rev. Lett. 101, 210501 (2008).

[CrossRef]

L. Cai, H. Y. Huang, S. Blackshaw, J. S. Liu, C. Cepko, and W. H. Wong, “Clustering analysis of SAGE data using a Poisson approach,” Genome Biol. 5, R51.1 (2004).

[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. Instrum. Methods Phys. Res. 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. Instrum. Methods Phys. Res. A 610, 183–187 (2009).

[CrossRef]

H. J. Briegel, W. Dur, 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]

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]

C. Ding and X. He, “K-means clustering via principal component analysis,” in ICML Proceedings 21st International Conference on Machine Learning (Assoc. Comp. Mach., 2004), pp. 1–9.

P. Buzhan, B. Dolgoshein, A. Ilyin, V. Kaplin, S. Klemin, R. Mirzoyan, E. Popova, and M. Teshima, “The cross-talk problem in SiPMs and their use as light sensors for imaging atmospheric Cherenkov telescopes,” Nucl. Instrum. Methods Phys. Res. A 610, 131–134 (2009).

[CrossRef]

S. Dolinar, “An optimum receiver for the binary coherent state quantum channel,” Massachusetts Institute of Technology Research Laboratory of Electronics Quarterly Progress Report, Vol. 111, 115–120 (1973).

H. J. Briegel, W. Dur, 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]

M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Single-photon source and detectors,” Rev. Sci. Instrum. 82, 071101 (2011).

[CrossRef]

G. Hamerly and C. Elkan, “Alternatives to the k-means algorithm that find better clusterings,” in Proceedings of the Eleventh International Conference on Information and Knowledge Management (ACM, 2002), CIKM ’02, pp. 600–607.

M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Single-photon source and detectors,” Rev. Sci. Instrum. 82, 071101 (2011).

[CrossRef]

F. E. Becerra, J. Fan, G. Baumgartner, S. V. Polyakov, J. Goldhar, J. T. Kosloski, and A. Migdall, “M-ary-state phase-shift-keying discrimination below the homodyne limit,” Phys. Rev. A 84, 062324 (2011).

[CrossRef]

D. J. Fixsen, S. H. Moseley, B. Cabrera, and E. Figueroa-Feliciano, “Pulse estimation in nonlinear detectors with nonstationary noise,” Nucl. Instrum. Methods Phys. Res. A 520, 555–558 (2004).

[CrossRef]

D. J. Fixsen, S. H. Moseley, B. Cabrera, and E. Figueroa-Feliciano, “Pulse estimation in nonlinear detectors with nonstationary noise,” Nucl. Instrum. Methods Phys. Res. A 520, 555–558 (2004).

[CrossRef]

W. H. Press, S. A. Teukolsky, W. T. Vettenberg, and B. P. Flannery, Numerical Recipes, 3rd ed. (Cambridge University, 2007), Sections 13.3 and 16.1.

J. C. Zwinkels, E. Ikonen, N. P. Fox, G. Ulm, and M. L. Rastello, “Photometry, radiometry and ‘the candela’: evolution in the classical and quantum world,” Metrologia 47, R15–R32 (2010).

[CrossRef]

D. Fukuda, G. Fujii, T. Numata, K. Amemiya, A. Yoshizawa, H. Tsuchida, H. Fujino, H. Ishii, T. Itatani, S. Inoue, and T. Zama, “Titanium-based transition-edge photon number resolving detector with 98 percent detection efficiency with index-matched small-gap fiber coupling,” Opt. Express 19, 870–875 (2011).

[CrossRef]

D. Fukuda, G. Fujii, T. Numata, K. Amemiya, A. Yoshizawa, H. Tsuchida, H. Fujino, H. Ishii, T. Itatani, S. Inoue, and T. Zama, “Titanium-based transition-edge photon number resolving detector with 98 percent detection efficiency with index-matched small-gap fiber coupling,” Opt. Express 19, 870–875 (2011).

[CrossRef]

D. Fukuda, G. Fujii, T. Numata, K. Amemiya, A. Yoshizawa, H. Tsuchida, H. Fujino, H. Ishii, T. Itatani, S. Inoue, and T. Zama, “Titanium-based transition-edge photon number resolving detector with 98 percent detection efficiency with index-matched small-gap fiber coupling,” Opt. Express 19, 870–875 (2011).

[CrossRef]

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).

[CrossRef]

T. Gerrits, B. Calkins, N. Tomlin, A. E. Lita, A. Migdall, S. W. Nam, and R. Mirin, “Extending single-photon optimized superconducting transition edge sensors beyond the single-photon counting regime,” presented at the Quantum Electronics and Laser Science Conference (2012).

F. E. Becerra, J. Fan, G. Baumgartner, S. V. Polyakov, J. Goldhar, J. T. Kosloski, and A. Migdall, “M-ary-state phase-shift-keying discrimination below the homodyne limit,” Phys. Rev. A 84, 062324 (2011).

[CrossRef]

R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photon. 3, 696–705 (2009).

[CrossRef]

G. Hamerly and C. Elkan, “Alternatives to the k-means algorithm that find better clusterings,” in Proceedings of the Eleventh International Conference on Information and Knowledge Management (ACM, 2002), CIKM ’02, pp. 600–607.

C. Ding and X. He, “K-means clustering via principal component analysis,” in ICML Proceedings 21st International Conference on Machine Learning (Assoc. Comp. Mach., 2004), pp. 1–9.

L. Cai, H. Y. Huang, S. Blackshaw, J. S. Liu, C. Cepko, and W. H. Wong, “Clustering analysis of SAGE data using a Poisson approach,” Genome Biol. 5, R51.1 (2004).

[CrossRef]

J. C. Zwinkels, E. Ikonen, N. P. Fox, G. Ulm, and M. L. Rastello, “Photometry, radiometry and ‘the candela’: evolution in the classical and quantum world,” Metrologia 47, R15–R32 (2010).

[CrossRef]

P. Buzhan, B. Dolgoshein, A. Ilyin, V. Kaplin, S. Klemin, R. Mirzoyan, E. Popova, and M. Teshima, “The cross-talk problem in SiPMs and their use as light sensors for imaging atmospheric Cherenkov telescopes,” Nucl. Instrum. Methods Phys. Res. A 610, 131–134 (2009).

[CrossRef]

D. Fukuda, G. Fujii, T. Numata, K. Amemiya, A. Yoshizawa, H. Tsuchida, H. Fujino, H. Ishii, T. Itatani, S. Inoue, and T. Zama, “Titanium-based transition-edge photon number resolving detector with 98 percent detection efficiency with index-matched small-gap fiber coupling,” Opt. Express 19, 870–875 (2011).

[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. Instrum. Methods Phys. Res. A 610, 183–187 (2009).

[CrossRef]

D. Fukuda, G. Fujii, T. Numata, K. Amemiya, A. Yoshizawa, H. Tsuchida, H. Fujino, H. Ishii, T. Itatani, S. Inoue, and T. Zama, “Titanium-based transition-edge photon number resolving detector with 98 percent detection efficiency with index-matched small-gap fiber coupling,” Opt. Express 19, 870–875 (2011).

[CrossRef]

D. Fukuda, G. Fujii, T. Numata, K. Amemiya, A. Yoshizawa, H. Tsuchida, H. Fujino, H. Ishii, T. Itatani, S. Inoue, and T. Zama, “Titanium-based transition-edge photon number resolving detector with 98 percent detection efficiency with index-matched small-gap fiber coupling,” Opt. Express 19, 870–875 (2011).

[CrossRef]

P. Buzhan, B. Dolgoshein, A. Ilyin, V. Kaplin, S. Klemin, R. Mirzoyan, E. Popova, and M. Teshima, “The cross-talk problem in SiPMs and their use as light sensors for imaging atmospheric Cherenkov telescopes,” Nucl. Instrum. Methods Phys. Res. A 610, 131–134 (2009).

[CrossRef]

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).

[CrossRef]

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. Buzhan, B. Dolgoshein, A. Ilyin, V. Kaplin, S. Klemin, R. Mirzoyan, E. Popova, and M. Teshima, “The cross-talk problem in SiPMs and their use as light sensors for imaging atmospheric Cherenkov telescopes,” Nucl. Instrum. Methods Phys. Res. A 610, 131–134 (2009).

[CrossRef]

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).

[CrossRef]

F. E. Becerra, J. Fan, G. Baumgartner, S. V. Polyakov, J. Goldhar, J. T. Kosloski, and A. Migdall, “M-ary-state phase-shift-keying discrimination below the homodyne limit,” Phys. Rev. A 84, 062324 (2011).

[CrossRef]

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).

[CrossRef]

C. Wittmann, M. Takeoka, K. N. Cassemiro, M. Sasaki, G. Leuchs, and U. L. Andersen, “Demonstration of near-optimal discrimination of optical coherent states,” Phys. Rev. Lett. 101, 210501 (2008).

[CrossRef]

A. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express 16, 3032–3040 (2008).

[CrossRef]

T. Gerrits, B. Calkins, N. Tomlin, A. E. Lita, A. Migdall, S. W. Nam, and R. Mirin, “Extending single-photon optimized superconducting transition edge sensors beyond the single-photon counting regime,” presented at the Quantum Electronics and Laser Science Conference (2012).

L. Cai, H. Y. Huang, S. Blackshaw, J. S. Liu, C. Cepko, and W. H. Wong, “Clustering analysis of SAGE data using a Poisson approach,” Genome Biol. 5, R51.1 (2004).

[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]

A. J. Miller, S. W. Nam, J. M. Martin, and A. V. Sergienko, “Demonstration of a low-noise near-infrared photon counter with multiphoton discrimination,” Appl. Phys. Lett. 83, 791–793 (2003).

[CrossRef]

F. E. Becerra, J. Fan, G. Baumgartner, S. V. Polyakov, J. Goldhar, J. T. Kosloski, and A. Migdall, “M-ary-state phase-shift-keying discrimination below the homodyne limit,” Phys. Rev. A 84, 062324 (2011).

[CrossRef]

M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Single-photon source and detectors,” Rev. Sci. Instrum. 82, 071101 (2011).

[CrossRef]

A. Migdall, “Differences explained in correlated-photon metrology techniques,” Phys. Today 52, 41–46 (1999).

[CrossRef]

S. V. Polyakov, A. Migdall, and S. W. Nam, “Real-time data-acquisition platform for pulsed measurements,” in Advances in Quantum Theory, AIP Conference Proceedings, Vol. 1327 (Växjö, 2010), pp. 505–519.

T. Gerrits, B. Calkins, N. Tomlin, A. E. Lita, A. Migdall, S. W. Nam, and R. Mirin, “Extending single-photon optimized superconducting transition edge sensors beyond the single-photon counting regime,” presented at the Quantum Electronics and Laser Science Conference (2012).

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).

[CrossRef]

A. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express 16, 3032–3040 (2008).

[CrossRef]

A. J. Miller, S. W. Nam, J. M. Martin, and A. V. Sergienko, “Demonstration of a low-noise near-infrared photon counter with multiphoton discrimination,” Appl. Phys. Lett. 83, 791–793 (2003).

[CrossRef]

T. Gerrits, B. Calkins, N. Tomlin, A. E. Lita, A. Migdall, S. W. Nam, and R. Mirin, “Extending single-photon optimized superconducting transition edge sensors beyond the single-photon counting regime,” presented at the Quantum Electronics and Laser Science Conference (2012).

P. Buzhan, B. Dolgoshein, A. Ilyin, V. Kaplin, S. Klemin, R. Mirzoyan, E. Popova, and M. Teshima, “The cross-talk problem in SiPMs and their use as light sensors for imaging atmospheric Cherenkov telescopes,” Nucl. Instrum. Methods Phys. Res. A 610, 131–134 (2009).

[CrossRef]

D. J. Fixsen, S. H. Moseley, B. Cabrera, and E. Figueroa-Feliciano, “Pulse estimation in nonlinear detectors with nonstationary noise,” Nucl. Instrum. Methods Phys. Res. A 520, 555–558 (2004).

[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]

A. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express 16, 3032–3040 (2008).

[CrossRef]

A. J. Miller, S. W. Nam, J. M. Martin, and A. V. Sergienko, “Demonstration of a low-noise near-infrared photon counter with multiphoton discrimination,” Appl. Phys. Lett. 83, 791–793 (2003).

[CrossRef]

S. V. Polyakov, A. Migdall, and S. W. Nam, “Real-time data-acquisition platform for pulsed measurements,” in Advances in Quantum Theory, AIP Conference Proceedings, Vol. 1327 (Växjö, 2010), pp. 505–519.

T. Gerrits, B. Calkins, N. Tomlin, A. E. Lita, A. Migdall, S. W. Nam, and R. Mirin, “Extending single-photon optimized superconducting transition edge sensors beyond the single-photon counting regime,” presented at the Quantum Electronics and Laser Science Conference (2012).

D. Fukuda, G. Fujii, T. Numata, K. Amemiya, A. Yoshizawa, H. Tsuchida, H. Fujino, H. Ishii, T. Itatani, S. Inoue, and T. Zama, “Titanium-based transition-edge photon number resolving detector with 98 percent detection efficiency with index-matched small-gap fiber coupling,” Opt. Express 19, 870–875 (2011).

[CrossRef]

F. E. Becerra, J. Fan, G. Baumgartner, S. V. Polyakov, J. Goldhar, J. T. Kosloski, and A. Migdall, “M-ary-state phase-shift-keying discrimination below the homodyne limit,” Phys. Rev. A 84, 062324 (2011).

[CrossRef]

M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Single-photon source and detectors,” Rev. Sci. Instrum. 82, 071101 (2011).

[CrossRef]

S. V. Polyakov, A. Migdall, and S. W. Nam, “Real-time data-acquisition platform for pulsed measurements,” in Advances in Quantum Theory, AIP Conference Proceedings, Vol. 1327 (Växjö, 2010), pp. 505–519.

P. Buzhan, B. Dolgoshein, A. Ilyin, V. Kaplin, S. Klemin, R. Mirzoyan, E. Popova, and M. Teshima, “The cross-talk problem in SiPMs and their use as light sensors for imaging atmospheric Cherenkov telescopes,” Nucl. Instrum. Methods Phys. Res. A 610, 131–134 (2009).

[CrossRef]

W. H. Press, S. A. Teukolsky, W. T. Vettenberg, and B. P. Flannery, Numerical Recipes, 3rd ed. (Cambridge University, 2007), Sections 13.3 and 16.1.

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]

J. C. Zwinkels, E. Ikonen, N. P. Fox, G. Ulm, and M. L. Rastello, “Photometry, radiometry and ‘the candela’: evolution in the classical and quantum world,” Metrologia 47, R15–R32 (2010).

[CrossRef]

C. Wittmann, M. Takeoka, K. N. Cassemiro, M. Sasaki, G. Leuchs, and U. L. Andersen, “Demonstration of near-optimal discrimination of optical coherent states,” Phys. Rev. Lett. 101, 210501 (2008).

[CrossRef]

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]

A. J. Miller, S. W. Nam, J. M. Martin, and A. V. Sergienko, “Demonstration of a low-noise near-infrared photon counter with multiphoton discrimination,” Appl. Phys. Lett. 83, 791–793 (2003).

[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]

C. Wittmann, M. Takeoka, K. N. Cassemiro, M. Sasaki, G. Leuchs, and U. L. Andersen, “Demonstration of near-optimal discrimination of optical coherent states,” Phys. Rev. Lett. 101, 210501 (2008).

[CrossRef]

P. Buzhan, B. Dolgoshein, A. Ilyin, V. Kaplin, S. Klemin, R. Mirzoyan, E. Popova, and M. Teshima, “The cross-talk problem in SiPMs and their use as light sensors for imaging atmospheric Cherenkov telescopes,” Nucl. Instrum. Methods Phys. Res. A 610, 131–134 (2009).

[CrossRef]

W. H. Press, S. A. Teukolsky, W. T. Vettenberg, and B. P. Flannery, Numerical Recipes, 3rd ed. (Cambridge University, 2007), Sections 13.3 and 16.1.

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]

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]

T. Gerrits, B. Calkins, N. Tomlin, A. E. Lita, A. Migdall, S. W. Nam, and R. Mirin, “Extending single-photon optimized superconducting transition edge sensors beyond the single-photon counting regime,” presented at the Quantum Electronics and Laser Science Conference (2012).

D. Fukuda, G. Fujii, T. Numata, K. Amemiya, A. Yoshizawa, H. Tsuchida, H. Fujino, H. Ishii, T. Itatani, S. Inoue, and T. Zama, “Titanium-based transition-edge photon number resolving detector with 98 percent detection efficiency with index-matched small-gap fiber coupling,” Opt. Express 19, 870–875 (2011).

[CrossRef]

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]

J. C. Zwinkels, E. Ikonen, N. P. Fox, G. Ulm, and M. L. Rastello, “Photometry, radiometry and ‘the candela’: evolution in the classical and quantum world,” Metrologia 47, R15–R32 (2010).

[CrossRef]

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).

[CrossRef]

W. H. Press, S. A. Teukolsky, W. T. Vettenberg, and B. P. Flannery, Numerical Recipes, 3rd ed. (Cambridge University, 2007), Sections 13.3 and 16.1.

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]

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. Instrum. Methods Phys. Res. A 610, 183–187 (2009).

[CrossRef]

C. Wittmann, M. Takeoka, K. N. Cassemiro, M. Sasaki, G. Leuchs, and U. L. Andersen, “Demonstration of near-optimal discrimination of optical coherent states,” Phys. Rev. Lett. 101, 210501 (2008).

[CrossRef]

L. Cai, H. Y. Huang, S. Blackshaw, J. S. Liu, C. Cepko, and W. H. Wong, “Clustering analysis of SAGE data using a Poisson approach,” Genome Biol. 5, R51.1 (2004).

[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]

D. Fukuda, G. Fujii, T. Numata, K. Amemiya, A. Yoshizawa, H. Tsuchida, H. Fujino, H. Ishii, T. Itatani, S. Inoue, and T. Zama, “Titanium-based transition-edge photon number resolving detector with 98 percent detection efficiency with index-matched small-gap fiber coupling,” Opt. Express 19, 870–875 (2011).

[CrossRef]

D. Fukuda, G. Fujii, T. Numata, K. Amemiya, A. Yoshizawa, H. Tsuchida, H. Fujino, H. Ishii, T. Itatani, S. Inoue, and T. Zama, “Titanium-based transition-edge photon number resolving detector with 98 percent detection efficiency with index-matched small-gap fiber coupling,” Opt. Express 19, 870–875 (2011).

[CrossRef]

H. J. Briegel, W. Dur, 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. C. Zwinkels, E. Ikonen, N. P. Fox, G. Ulm, and M. L. Rastello, “Photometry, radiometry and ‘the candela’: evolution in the classical and quantum world,” Metrologia 47, R15–R32 (2010).

[CrossRef]

A. J. Miller, S. W. Nam, J. M. Martin, and A. V. Sergienko, “Demonstration of a low-noise near-infrared photon counter with multiphoton discrimination,” Appl. Phys. Lett. 83, 791–793 (2003).

[CrossRef]

L. Cai, H. Y. Huang, S. Blackshaw, J. S. Liu, C. Cepko, and W. H. Wong, “Clustering analysis of SAGE data using a Poisson approach,” Genome Biol. 5, R51.1 (2004).

[CrossRef]

S. Dolinar, “An optimum receiver for the binary coherent state quantum channel,” Massachusetts Institute of Technology Research Laboratory of Electronics Quarterly Progress Report, Vol. 111, 115–120 (1973).

J. C. Zwinkels, E. Ikonen, N. P. Fox, G. Ulm, and M. L. Rastello, “Photometry, radiometry and ‘the candela’: evolution in the classical and quantum world,” Metrologia 47, R15–R32 (2010).

[CrossRef]

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]

R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photon. 3, 696–705 (2009).

[CrossRef]

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).

[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. Instrum. Methods Phys. Res. A 610, 183–187 (2009).

[CrossRef]

P. Buzhan, B. Dolgoshein, A. Ilyin, V. Kaplin, S. Klemin, R. Mirzoyan, E. Popova, and M. Teshima, “The cross-talk problem in SiPMs and their use as light sensors for imaging atmospheric Cherenkov telescopes,” Nucl. Instrum. Methods Phys. Res. A 610, 131–134 (2009).

[CrossRef]

D. J. Fixsen, S. H. Moseley, B. Cabrera, and E. Figueroa-Feliciano, “Pulse estimation in nonlinear detectors with nonstationary noise,” Nucl. Instrum. Methods Phys. Res. A 520, 555–558 (2004).

[CrossRef]

D. Fukuda, G. Fujii, T. Numata, K. Amemiya, A. Yoshizawa, H. Tsuchida, H. Fujino, H. Ishii, T. Itatani, S. Inoue, and T. Zama, “Titanium-based transition-edge photon number resolving detector with 98 percent detection efficiency with index-matched small-gap fiber coupling,” Opt. Express 19, 870–875 (2011).

[CrossRef]

A. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express 16, 3032–3040 (2008).

[CrossRef]

M. Mehmet, A. Ast, T. Eberle, S. Steinlechner, H. Vahlbruch, and R. Schnabel, “Squeezed light at 1550 nm with a quantum noise reduction of 12.3 dB,” Opt. Express 19, 25763–25772 (2011).

[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]

F. E. Becerra, J. Fan, G. Baumgartner, S. V. Polyakov, J. Goldhar, J. T. Kosloski, and A. Migdall, “M-ary-state phase-shift-keying discrimination below the homodyne limit,” Phys. Rev. A 84, 062324 (2011).

[CrossRef]

H. J. Briegel, W. Dur, 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]

C. Wittmann, M. Takeoka, K. N. Cassemiro, M. Sasaki, G. Leuchs, and U. L. Andersen, “Demonstration of near-optimal discrimination of optical coherent states,” Phys. Rev. Lett. 101, 210501 (2008).

[CrossRef]

A. Migdall, “Differences explained in correlated-photon metrology techniques,” Phys. Today 52, 41–46 (1999).

[CrossRef]

M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Single-photon source and detectors,” Rev. Sci. Instrum. 82, 071101 (2011).

[CrossRef]

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).

[CrossRef]

C. Ding and X. He, “K-means clustering via principal component analysis,” in ICML Proceedings 21st International Conference on Machine Learning (Assoc. Comp. Mach., 2004), pp. 1–9.

G. Hamerly and C. Elkan, “Alternatives to the k-means algorithm that find better clusterings,” in Proceedings of the Eleventh International Conference on Information and Knowledge Management (ACM, 2002), CIKM ’02, pp. 600–607.

W. H. Press, S. A. Teukolsky, W. T. Vettenberg, and B. P. Flannery, Numerical Recipes, 3rd ed. (Cambridge University, 2007), Sections 13.3 and 16.1.

T. Gerrits, B. Calkins, N. Tomlin, A. E. Lita, A. Migdall, S. W. Nam, and R. Mirin, “Extending single-photon optimized superconducting transition edge sensors beyond the single-photon counting regime,” presented at the Quantum Electronics and Laser Science Conference (2012).

Curves were classified as containing background photons if the initial or final voltage was above 16.8 mV, or if there was a peak of at least 16.8 mV after a time of 3.4 μs. The number of curves removed was consistent with the background rate given above.

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.

P. E. Black, “Greedy algorithm,” in Dictionary of Algorithms and Data Structures [online], P. E. Black, ed., U. S. National Institute of Standards and Technology (2February2005) (accessed March 5, 2012). Available from http://www.nist.gov/dads/HTML/greedyalgo.html .

S. V. Polyakov, A. Migdall, and S. W. Nam, “Real-time data-acquisition platform for pulsed measurements,” in Advances in Quantum Theory, AIP Conference Proceedings, Vol. 1327 (Växjö, 2010), pp. 505–519.

While always keeping in mind that this correspondence is never 100% assured, we refer to these as photon-number peaks.