S. Izumi, M. Takeoka, K. Wakui, M. Fujiwara, K. Ema, and M. Sasaki, “Optical phase estimation via coherent state and displaced photon counting,” Phys. Rev. A 94, 033842 (2016).

[Crossref]

M. Bina, A. Allevi, M. Bondani, and S. Olivares, “Phase-reference monitoring in coherent-state discrimination assisted by a photon-number resolving detector,” Sci. Rep. 6, 26025 (2016).

[Crossref]
[PubMed]

E. Diamanti, H.-K. Lo, B. Qi, and Z. Yuan, “Practical challenges in quantum key distribution,” npj Quantum Information 2, 16025 (2016).

[Crossref]

C. R. Müller and Ch. Marquardt, “A robust quantum receiver for phase shift keyed signals,” New J. Phys. 17, 032003 (2015).

[Crossref]

G. Donati, T. J. Bartley, X.-M. Jin, M.-D. Vidrighin, A. Datta, M. Barbieri, and I. A. Walmsley, “Observing optical coherence across Fock layers with weak-field homodyne detectors,” Nat. Commun. 5, 5584 (2014).

[Crossref]
[PubMed]

F. E. Becerra, J. Fan, G. Baumgartner, J. Goldhar, J. T. Kosloski, and A. Migdall, “Experimental demonstration of a receiver beating the standard quantum limit for multiple nonorthogonal state discrimination,” Nat. Photon. 7, 147–152 (2013).

[Crossref]

F. E. Becerra, J. Fan, and A. Migdall, “Implementation of generalized quantum measurements for unambiguous discrimination of multiple non-orthogonal coherent states,” Nat. Commun. 4, 2028 (2013).

[Crossref]
[PubMed]

S. Olivares, S. Cialdi, F. Castelli, and M. G. A. Paris, “Homodyne detection as a near-optimum receiver for phase-shift-keyed binary communication in the presence of phase diffusion,” Phys. Rev. A 87, 050303 (2013).

[Crossref]

L. Zhang, H. B. Coldenstrodt-Ronge, A. Datta, G. Puentes, J. S. Lundeen, X.-M. Jin, B. J. Smith, M. B. Plenio, and I. A. Walmsley, “Mapping coherence in measurement via full quantum tomography of a hybrid optical detector,” Nat. Photon. 6, 364–368 (2012).

[Crossref]

S. Izumi, M. Takeoka, M. Fujiwara, N. Dalla Pozza, A. Assalini, K. Ema, and M. Sasaki, “Displacement receiver for phase-shift-keyed coherent states,” Phys. Rev. A 86, 042328 (2012).

[Crossref]

A. Allevi, S. Olivares, and M. Bondani, “Measuring high-order photon-number correlations in experiments with multimode pulsed quantum states,” Phys. Rev. A 85, 063835 (2012).

[Crossref]

A. Allevi, S. Olivares, and M. Bondani, “Manipulating the non-Gaussianity of phase-randomized coherent states,” Opt. Express 20, 24850–24855 (2012).

[Crossref]
[PubMed]

A. Allevi, M. Bondani, and A. Andreoni, “Self-consistent phase determination for Wigner function reconstruction,” J. Opt. Soc. Am. B 27, 333–337 (2010).

[Crossref]

M. Ramilli, A. Allevi, V. Chmill, M. Bondani, M. Caccia, and A. Andreoni, “Photon-number statistics with silicon photomultipliers,” J. Opt. Soc. Am. B 27, 852–862 (2010).

[Crossref]

K. Laiho, K. N. Cassemiro, D. Gross, and C. Silberhorn, “Probing the negative Wigner function of a pulsed single photon point by point,” Phys. Rev. Lett. 105, 253603 (2010).

[Crossref]

G. Puentes, J. S. Lundeen, M. P. A. Branderhorst, H. B. Coldenstrodt-Ronge, B. J. Smith, and I. A. Walmsley, “Bridging particle and wave sensitivity in a configurable detector of positive operator-valued measures,” Phys. Rev. Lett. 102, 080404 (2009).

[Crossref]
[PubMed]

M. Bondani, A. Allevi, A. Agliati, and A. Andreoni, “Self- consistent characterization of light statistics,” J. Mod. Opt. 56, 226–231 (2009).

[Crossref]

A. Andreoni and M. Bondani, “Photon statistics in the macroscopic realm measured without photon counters,” Phys. Rev. A 80, 013819 (2009).

[Crossref]

M. Bondani, A. Allevi, and A. Andreoni, “Wigner function of pulsed fields by direct detection,” Opt. Lett. 34, 1444–1446 (2009).

[Crossref]
[PubMed]

K. Banaszek, A. Dragan, K. Wódkiewicz, and C. Radzewicz, “Direct measurement of optical quasi-distribution functions: Multimode theory and homodyne tests of Bell’s inequalities,” Phys. Rev. A 66, 043803 (2002).

[Crossref]

K. Banaszek, C. Radzewicz, K. Wódkiewicz, and J. S. Krasiński, “Direct measurement of the Wigner function by photon counting,” Phys. Rev. A 60, 674–677 (1999).

[Crossref]

S. Wallentowitz and W. Vogel, “Unbalanced homodyning for quantum state measurements,” Phys. Rev. A 53, 4528–4533 (1996).

[Crossref]
[PubMed]

B. Efron, “Bootstrap methods: another look at the jackknife,” Ann. Stat. 7, 1–26 (1979).

[Crossref]

J. G. Skellam, “The frequency distribution of the difference between two Poisson variates belonging to different populations,” J. Roy. Statist. Soc. (N. S.) 109, 296 (1946).

[Crossref]

M. Bondani, A. Allevi, A. Agliati, and A. Andreoni, “Self- consistent characterization of light statistics,” J. Mod. Opt. 56, 226–231 (2009).

[Crossref]

M. Bina, A. Allevi, M. Bondani, and S. Olivares, “Phase-reference monitoring in coherent-state discrimination assisted by a photon-number resolving detector,” Sci. Rep. 6, 26025 (2016).

[Crossref]
[PubMed]

A. Allevi, S. Olivares, and M. Bondani, “Manipulating the non-Gaussianity of phase-randomized coherent states,” Opt. Express 20, 24850–24855 (2012).

[Crossref]
[PubMed]

A. Allevi, S. Olivares, and M. Bondani, “Measuring high-order photon-number correlations in experiments with multimode pulsed quantum states,” Phys. Rev. A 85, 063835 (2012).

[Crossref]

A. Allevi, M. Bondani, and A. Andreoni, “Self-consistent phase determination for Wigner function reconstruction,” J. Opt. Soc. Am. B 27, 333–337 (2010).

[Crossref]

M. Ramilli, A. Allevi, V. Chmill, M. Bondani, M. Caccia, and A. Andreoni, “Photon-number statistics with silicon photomultipliers,” J. Opt. Soc. Am. B 27, 852–862 (2010).

[Crossref]

M. Bondani, A. Allevi, A. Agliati, and A. Andreoni, “Self- consistent characterization of light statistics,” J. Mod. Opt. 56, 226–231 (2009).

[Crossref]

M. Bondani, A. Allevi, and A. Andreoni, “Wigner function of pulsed fields by direct detection,” Opt. Lett. 34, 1444–1446 (2009).

[Crossref]
[PubMed]

A. Allevi, M. Bondani, and A. Andreoni, “Self-consistent phase determination for Wigner function reconstruction,” J. Opt. Soc. Am. B 27, 333–337 (2010).

[Crossref]

M. Ramilli, A. Allevi, V. Chmill, M. Bondani, M. Caccia, and A. Andreoni, “Photon-number statistics with silicon photomultipliers,” J. Opt. Soc. Am. B 27, 852–862 (2010).

[Crossref]

M. Bondani, A. Allevi, and A. Andreoni, “Wigner function of pulsed fields by direct detection,” Opt. Lett. 34, 1444–1446 (2009).

[Crossref]
[PubMed]

M. Bondani, A. Allevi, A. Agliati, and A. Andreoni, “Self- consistent characterization of light statistics,” J. Mod. Opt. 56, 226–231 (2009).

[Crossref]

A. Andreoni and M. Bondani, “Photon statistics in the macroscopic realm measured without photon counters,” Phys. Rev. A 80, 013819 (2009).

[Crossref]

S. Izumi, M. Takeoka, M. Fujiwara, N. Dalla Pozza, A. Assalini, K. Ema, and M. Sasaki, “Displacement receiver for phase-shift-keyed coherent states,” Phys. Rev. A 86, 042328 (2012).

[Crossref]

K. Banaszek, A. Dragan, K. Wódkiewicz, and C. Radzewicz, “Direct measurement of optical quasi-distribution functions: Multimode theory and homodyne tests of Bell’s inequalities,” Phys. Rev. A 66, 043803 (2002).

[Crossref]

K. Banaszek, C. Radzewicz, K. Wódkiewicz, and J. S. Krasiński, “Direct measurement of the Wigner function by photon counting,” Phys. Rev. A 60, 674–677 (1999).

[Crossref]

G. Donati, T. J. Bartley, X.-M. Jin, M.-D. Vidrighin, A. Datta, M. Barbieri, and I. A. Walmsley, “Observing optical coherence across Fock layers with weak-field homodyne detectors,” Nat. Commun. 5, 5584 (2014).

[Crossref]
[PubMed]

G. Donati, T. J. Bartley, X.-M. Jin, M.-D. Vidrighin, A. Datta, M. Barbieri, and I. A. Walmsley, “Observing optical coherence across Fock layers with weak-field homodyne detectors,” Nat. Commun. 5, 5584 (2014).

[Crossref]
[PubMed]

F. E. Becerra, J. Fan, G. Baumgartner, J. Goldhar, J. T. Kosloski, and A. Migdall, “Experimental demonstration of a receiver beating the standard quantum limit for multiple nonorthogonal state discrimination,” Nat. Photon. 7, 147–152 (2013).

[Crossref]

F. E. Becerra, J. Fan, G. Baumgartner, J. Goldhar, J. T. Kosloski, and A. Migdall, “Experimental demonstration of a receiver beating the standard quantum limit for multiple nonorthogonal state discrimination,” Nat. Photon. 7, 147–152 (2013).

[Crossref]

F. E. Becerra, J. Fan, and A. Migdall, “Implementation of generalized quantum measurements for unambiguous discrimination of multiple non-orthogonal coherent states,” Nat. Commun. 4, 2028 (2013).

[Crossref]
[PubMed]

M. Bina, A. Allevi, M. Bondani, and S. Olivares, “Phase-reference monitoring in coherent-state discrimination assisted by a photon-number resolving detector,” Sci. Rep. 6, 26025 (2016).

[Crossref]
[PubMed]

M. Bina, A. Allevi, M. Bondani, and S. Olivares, “Phase-reference monitoring in coherent-state discrimination assisted by a photon-number resolving detector,” Sci. Rep. 6, 26025 (2016).

[Crossref]
[PubMed]

A. Allevi, S. Olivares, and M. Bondani, “Manipulating the non-Gaussianity of phase-randomized coherent states,” Opt. Express 20, 24850–24855 (2012).

[Crossref]
[PubMed]

A. Allevi, S. Olivares, and M. Bondani, “Measuring high-order photon-number correlations in experiments with multimode pulsed quantum states,” Phys. Rev. A 85, 063835 (2012).

[Crossref]

A. Allevi, M. Bondani, and A. Andreoni, “Self-consistent phase determination for Wigner function reconstruction,” J. Opt. Soc. Am. B 27, 333–337 (2010).

[Crossref]

M. Ramilli, A. Allevi, V. Chmill, M. Bondani, M. Caccia, and A. Andreoni, “Photon-number statistics with silicon photomultipliers,” J. Opt. Soc. Am. B 27, 852–862 (2010).

[Crossref]

M. Bondani, A. Allevi, and A. Andreoni, “Wigner function of pulsed fields by direct detection,” Opt. Lett. 34, 1444–1446 (2009).

[Crossref]
[PubMed]

M. Bondani, A. Allevi, A. Agliati, and A. Andreoni, “Self- consistent characterization of light statistics,” J. Mod. Opt. 56, 226–231 (2009).

[Crossref]

A. Andreoni and M. Bondani, “Photon statistics in the macroscopic realm measured without photon counters,” Phys. Rev. A 80, 013819 (2009).

[Crossref]

G. Puentes, J. S. Lundeen, M. P. A. Branderhorst, H. B. Coldenstrodt-Ronge, B. J. Smith, and I. A. Walmsley, “Bridging particle and wave sensitivity in a configurable detector of positive operator-valued measures,” Phys. Rev. Lett. 102, 080404 (2009).

[Crossref]
[PubMed]

K. Laiho, K. N. Cassemiro, D. Gross, and C. Silberhorn, “Probing the negative Wigner function of a pulsed single photon point by point,” Phys. Rev. Lett. 105, 253603 (2010).

[Crossref]

S. Olivares, S. Cialdi, F. Castelli, and M. G. A. Paris, “Homodyne detection as a near-optimum receiver for phase-shift-keyed binary communication in the presence of phase diffusion,” Phys. Rev. A 87, 050303 (2013).

[Crossref]

S. Olivares, S. Cialdi, F. Castelli, and M. G. A. Paris, “Homodyne detection as a near-optimum receiver for phase-shift-keyed binary communication in the presence of phase diffusion,” Phys. Rev. A 87, 050303 (2013).

[Crossref]

L. Zhang, H. B. Coldenstrodt-Ronge, A. Datta, G. Puentes, J. S. Lundeen, X.-M. Jin, B. J. Smith, M. B. Plenio, and I. A. Walmsley, “Mapping coherence in measurement via full quantum tomography of a hybrid optical detector,” Nat. Photon. 6, 364–368 (2012).

[Crossref]

G. Puentes, J. S. Lundeen, M. P. A. Branderhorst, H. B. Coldenstrodt-Ronge, B. J. Smith, and I. A. Walmsley, “Bridging particle and wave sensitivity in a configurable detector of positive operator-valued measures,” Phys. Rev. Lett. 102, 080404 (2009).

[Crossref]
[PubMed]

S. Izumi, M. Takeoka, M. Fujiwara, N. Dalla Pozza, A. Assalini, K. Ema, and M. Sasaki, “Displacement receiver for phase-shift-keyed coherent states,” Phys. Rev. A 86, 042328 (2012).

[Crossref]

G. Donati, T. J. Bartley, X.-M. Jin, M.-D. Vidrighin, A. Datta, M. Barbieri, and I. A. Walmsley, “Observing optical coherence across Fock layers with weak-field homodyne detectors,” Nat. Commun. 5, 5584 (2014).

[Crossref]
[PubMed]

L. Zhang, H. B. Coldenstrodt-Ronge, A. Datta, G. Puentes, J. S. Lundeen, X.-M. Jin, B. J. Smith, M. B. Plenio, and I. A. Walmsley, “Mapping coherence in measurement via full quantum tomography of a hybrid optical detector,” Nat. Photon. 6, 364–368 (2012).

[Crossref]

E. Diamanti, H.-K. Lo, B. Qi, and Z. Yuan, “Practical challenges in quantum key distribution,” npj Quantum Information 2, 16025 (2016).

[Crossref]

G. Donati, T. J. Bartley, X.-M. Jin, M.-D. Vidrighin, A. Datta, M. Barbieri, and I. A. Walmsley, “Observing optical coherence across Fock layers with weak-field homodyne detectors,” Nat. Commun. 5, 5584 (2014).

[Crossref]
[PubMed]

K. Banaszek, A. Dragan, K. Wódkiewicz, and C. Radzewicz, “Direct measurement of optical quasi-distribution functions: Multimode theory and homodyne tests of Bell’s inequalities,” Phys. Rev. A 66, 043803 (2002).

[Crossref]

B. Efron, “Bootstrap methods: another look at the jackknife,” Ann. Stat. 7, 1–26 (1979).

[Crossref]

S. Izumi, M. Takeoka, K. Wakui, M. Fujiwara, K. Ema, and M. Sasaki, “Optical phase estimation via coherent state and displaced photon counting,” Phys. Rev. A 94, 033842 (2016).

[Crossref]

S. Izumi, M. Takeoka, M. Fujiwara, N. Dalla Pozza, A. Assalini, K. Ema, and M. Sasaki, “Displacement receiver for phase-shift-keyed coherent states,” Phys. Rev. A 86, 042328 (2012).

[Crossref]

F. E. Becerra, J. Fan, and A. Migdall, “Implementation of generalized quantum measurements for unambiguous discrimination of multiple non-orthogonal coherent states,” Nat. Commun. 4, 2028 (2013).

[Crossref]
[PubMed]

F. E. Becerra, J. Fan, G. Baumgartner, J. Goldhar, J. T. Kosloski, and A. Migdall, “Experimental demonstration of a receiver beating the standard quantum limit for multiple nonorthogonal state discrimination,” Nat. Photon. 7, 147–152 (2013).

[Crossref]

S. Izumi, M. Takeoka, K. Wakui, M. Fujiwara, K. Ema, and M. Sasaki, “Optical phase estimation via coherent state and displaced photon counting,” Phys. Rev. A 94, 033842 (2016).

[Crossref]

S. Izumi, M. Takeoka, M. Fujiwara, N. Dalla Pozza, A. Assalini, K. Ema, and M. Sasaki, “Displacement receiver for phase-shift-keyed coherent states,” Phys. Rev. A 86, 042328 (2012).

[Crossref]

F. E. Becerra, J. Fan, G. Baumgartner, J. Goldhar, J. T. Kosloski, and A. Migdall, “Experimental demonstration of a receiver beating the standard quantum limit for multiple nonorthogonal state discrimination,” Nat. Photon. 7, 147–152 (2013).

[Crossref]

K. Laiho, K. N. Cassemiro, D. Gross, and C. Silberhorn, “Probing the negative Wigner function of a pulsed single photon point by point,” Phys. Rev. Lett. 105, 253603 (2010).

[Crossref]

C. W. Helstrom, Quantum Detection and Estimation Theory (Academic, 1976).

S. Izumi, M. Takeoka, K. Wakui, M. Fujiwara, K. Ema, and M. Sasaki, “Optical phase estimation via coherent state and displaced photon counting,” Phys. Rev. A 94, 033842 (2016).

[Crossref]

S. Izumi, M. Takeoka, M. Fujiwara, N. Dalla Pozza, A. Assalini, K. Ema, and M. Sasaki, “Displacement receiver for phase-shift-keyed coherent states,” Phys. Rev. A 86, 042328 (2012).

[Crossref]

G. Donati, T. J. Bartley, X.-M. Jin, M.-D. Vidrighin, A. Datta, M. Barbieri, and I. A. Walmsley, “Observing optical coherence across Fock layers with weak-field homodyne detectors,” Nat. Commun. 5, 5584 (2014).

[Crossref]
[PubMed]

L. Zhang, H. B. Coldenstrodt-Ronge, A. Datta, G. Puentes, J. S. Lundeen, X.-M. Jin, B. J. Smith, M. B. Plenio, and I. A. Walmsley, “Mapping coherence in measurement via full quantum tomography of a hybrid optical detector,” Nat. Photon. 6, 364–368 (2012).

[Crossref]

F. E. Becerra, J. Fan, G. Baumgartner, J. Goldhar, J. T. Kosloski, and A. Migdall, “Experimental demonstration of a receiver beating the standard quantum limit for multiple nonorthogonal state discrimination,” Nat. Photon. 7, 147–152 (2013).

[Crossref]

K. Banaszek, C. Radzewicz, K. Wódkiewicz, and J. S. Krasiński, “Direct measurement of the Wigner function by photon counting,” Phys. Rev. A 60, 674–677 (1999).

[Crossref]

K. Laiho, K. N. Cassemiro, D. Gross, and C. Silberhorn, “Probing the negative Wigner function of a pulsed single photon point by point,” Phys. Rev. Lett. 105, 253603 (2010).

[Crossref]

E. Diamanti, H.-K. Lo, B. Qi, and Z. Yuan, “Practical challenges in quantum key distribution,” npj Quantum Information 2, 16025 (2016).

[Crossref]

L. Zhang, H. B. Coldenstrodt-Ronge, A. Datta, G. Puentes, J. S. Lundeen, X.-M. Jin, B. J. Smith, M. B. Plenio, and I. A. Walmsley, “Mapping coherence in measurement via full quantum tomography of a hybrid optical detector,” Nat. Photon. 6, 364–368 (2012).

[Crossref]

G. Puentes, J. S. Lundeen, M. P. A. Branderhorst, H. B. Coldenstrodt-Ronge, B. J. Smith, and I. A. Walmsley, “Bridging particle and wave sensitivity in a configurable detector of positive operator-valued measures,” Phys. Rev. Lett. 102, 080404 (2009).

[Crossref]
[PubMed]

C. R. Müller and Ch. Marquardt, “A robust quantum receiver for phase shift keyed signals,” New J. Phys. 17, 032003 (2015).

[Crossref]

F. E. Becerra, J. Fan, and A. Migdall, “Implementation of generalized quantum measurements for unambiguous discrimination of multiple non-orthogonal coherent states,” Nat. Commun. 4, 2028 (2013).

[Crossref]
[PubMed]

F. E. Becerra, J. Fan, G. Baumgartner, J. Goldhar, J. T. Kosloski, and A. Migdall, “Experimental demonstration of a receiver beating the standard quantum limit for multiple nonorthogonal state discrimination,” Nat. Photon. 7, 147–152 (2013).

[Crossref]

C. R. Müller and Ch. Marquardt, “A robust quantum receiver for phase shift keyed signals,” New J. Phys. 17, 032003 (2015).

[Crossref]

M. Bina, A. Allevi, M. Bondani, and S. Olivares, “Phase-reference monitoring in coherent-state discrimination assisted by a photon-number resolving detector,” Sci. Rep. 6, 26025 (2016).

[Crossref]
[PubMed]

S. Olivares, S. Cialdi, F. Castelli, and M. G. A. Paris, “Homodyne detection as a near-optimum receiver for phase-shift-keyed binary communication in the presence of phase diffusion,” Phys. Rev. A 87, 050303 (2013).

[Crossref]

A. Allevi, S. Olivares, and M. Bondani, “Manipulating the non-Gaussianity of phase-randomized coherent states,” Opt. Express 20, 24850–24855 (2012).

[Crossref]
[PubMed]

A. Allevi, S. Olivares, and M. Bondani, “Measuring high-order photon-number correlations in experiments with multimode pulsed quantum states,” Phys. Rev. A 85, 063835 (2012).

[Crossref]

S. Olivares, S. Cialdi, F. Castelli, and M. G. A. Paris, “Homodyne detection as a near-optimum receiver for phase-shift-keyed binary communication in the presence of phase diffusion,” Phys. Rev. A 87, 050303 (2013).

[Crossref]

L. Zhang, H. B. Coldenstrodt-Ronge, A. Datta, G. Puentes, J. S. Lundeen, X.-M. Jin, B. J. Smith, M. B. Plenio, and I. A. Walmsley, “Mapping coherence in measurement via full quantum tomography of a hybrid optical detector,” Nat. Photon. 6, 364–368 (2012).

[Crossref]

L. Zhang, H. B. Coldenstrodt-Ronge, A. Datta, G. Puentes, J. S. Lundeen, X.-M. Jin, B. J. Smith, M. B. Plenio, and I. A. Walmsley, “Mapping coherence in measurement via full quantum tomography of a hybrid optical detector,” Nat. Photon. 6, 364–368 (2012).

[Crossref]

G. Puentes, J. S. Lundeen, M. P. A. Branderhorst, H. B. Coldenstrodt-Ronge, B. J. Smith, and I. A. Walmsley, “Bridging particle and wave sensitivity in a configurable detector of positive operator-valued measures,” Phys. Rev. Lett. 102, 080404 (2009).

[Crossref]
[PubMed]

E. Diamanti, H.-K. Lo, B. Qi, and Z. Yuan, “Practical challenges in quantum key distribution,” npj Quantum Information 2, 16025 (2016).

[Crossref]

K. Banaszek, A. Dragan, K. Wódkiewicz, and C. Radzewicz, “Direct measurement of optical quasi-distribution functions: Multimode theory and homodyne tests of Bell’s inequalities,” Phys. Rev. A 66, 043803 (2002).

[Crossref]

K. Banaszek, C. Radzewicz, K. Wódkiewicz, and J. S. Krasiński, “Direct measurement of the Wigner function by photon counting,” Phys. Rev. A 60, 674–677 (1999).

[Crossref]

S. Izumi, M. Takeoka, K. Wakui, M. Fujiwara, K. Ema, and M. Sasaki, “Optical phase estimation via coherent state and displaced photon counting,” Phys. Rev. A 94, 033842 (2016).

[Crossref]

S. Izumi, M. Takeoka, M. Fujiwara, N. Dalla Pozza, A. Assalini, K. Ema, and M. Sasaki, “Displacement receiver for phase-shift-keyed coherent states,” Phys. Rev. A 86, 042328 (2012).

[Crossref]

K. Laiho, K. N. Cassemiro, D. Gross, and C. Silberhorn, “Probing the negative Wigner function of a pulsed single photon point by point,” Phys. Rev. Lett. 105, 253603 (2010).

[Crossref]

J. G. Skellam, “The frequency distribution of the difference between two Poisson variates belonging to different populations,” J. Roy. Statist. Soc. (N. S.) 109, 296 (1946).

[Crossref]

L. Zhang, H. B. Coldenstrodt-Ronge, A. Datta, G. Puentes, J. S. Lundeen, X.-M. Jin, B. J. Smith, M. B. Plenio, and I. A. Walmsley, “Mapping coherence in measurement via full quantum tomography of a hybrid optical detector,” Nat. Photon. 6, 364–368 (2012).

[Crossref]

G. Puentes, J. S. Lundeen, M. P. A. Branderhorst, H. B. Coldenstrodt-Ronge, B. J. Smith, and I. A. Walmsley, “Bridging particle and wave sensitivity in a configurable detector of positive operator-valued measures,” Phys. Rev. Lett. 102, 080404 (2009).

[Crossref]
[PubMed]

S. Izumi, M. Takeoka, K. Wakui, M. Fujiwara, K. Ema, and M. Sasaki, “Optical phase estimation via coherent state and displaced photon counting,” Phys. Rev. A 94, 033842 (2016).

[Crossref]

S. Izumi, M. Takeoka, M. Fujiwara, N. Dalla Pozza, A. Assalini, K. Ema, and M. Sasaki, “Displacement receiver for phase-shift-keyed coherent states,” Phys. Rev. A 86, 042328 (2012).

[Crossref]

G. Donati, T. J. Bartley, X.-M. Jin, M.-D. Vidrighin, A. Datta, M. Barbieri, and I. A. Walmsley, “Observing optical coherence across Fock layers with weak-field homodyne detectors,” Nat. Commun. 5, 5584 (2014).

[Crossref]
[PubMed]

S. Wallentowitz and W. Vogel, “Unbalanced homodyning for quantum state measurements,” Phys. Rev. A 53, 4528–4533 (1996).

[Crossref]
[PubMed]

S. Izumi, M. Takeoka, K. Wakui, M. Fujiwara, K. Ema, and M. Sasaki, “Optical phase estimation via coherent state and displaced photon counting,” Phys. Rev. A 94, 033842 (2016).

[Crossref]

S. Wallentowitz and W. Vogel, “Unbalanced homodyning for quantum state measurements,” Phys. Rev. A 53, 4528–4533 (1996).

[Crossref]
[PubMed]

G. Donati, T. J. Bartley, X.-M. Jin, M.-D. Vidrighin, A. Datta, M. Barbieri, and I. A. Walmsley, “Observing optical coherence across Fock layers with weak-field homodyne detectors,” Nat. Commun. 5, 5584 (2014).

[Crossref]
[PubMed]

L. Zhang, H. B. Coldenstrodt-Ronge, A. Datta, G. Puentes, J. S. Lundeen, X.-M. Jin, B. J. Smith, M. B. Plenio, and I. A. Walmsley, “Mapping coherence in measurement via full quantum tomography of a hybrid optical detector,” Nat. Photon. 6, 364–368 (2012).

[Crossref]

G. Puentes, J. S. Lundeen, M. P. A. Branderhorst, H. B. Coldenstrodt-Ronge, B. J. Smith, and I. A. Walmsley, “Bridging particle and wave sensitivity in a configurable detector of positive operator-valued measures,” Phys. Rev. Lett. 102, 080404 (2009).

[Crossref]
[PubMed]

K. Banaszek, A. Dragan, K. Wódkiewicz, and C. Radzewicz, “Direct measurement of optical quasi-distribution functions: Multimode theory and homodyne tests of Bell’s inequalities,” Phys. Rev. A 66, 043803 (2002).

[Crossref]

K. Banaszek, C. Radzewicz, K. Wódkiewicz, and J. S. Krasiński, “Direct measurement of the Wigner function by photon counting,” Phys. Rev. A 60, 674–677 (1999).

[Crossref]

E. Diamanti, H.-K. Lo, B. Qi, and Z. Yuan, “Practical challenges in quantum key distribution,” npj Quantum Information 2, 16025 (2016).

[Crossref]

L. Zhang, H. B. Coldenstrodt-Ronge, A. Datta, G. Puentes, J. S. Lundeen, X.-M. Jin, B. J. Smith, M. B. Plenio, and I. A. Walmsley, “Mapping coherence in measurement via full quantum tomography of a hybrid optical detector,” Nat. Photon. 6, 364–368 (2012).

[Crossref]

B. Efron, “Bootstrap methods: another look at the jackknife,” Ann. Stat. 7, 1–26 (1979).

[Crossref]

M. Bondani, A. Allevi, A. Agliati, and A. Andreoni, “Self- consistent characterization of light statistics,” J. Mod. Opt. 56, 226–231 (2009).

[Crossref]

A. Allevi, M. Bondani, and A. Andreoni, “Self-consistent phase determination for Wigner function reconstruction,” J. Opt. Soc. Am. B 27, 333–337 (2010).

[Crossref]

M. Ramilli, A. Allevi, V. Chmill, M. Bondani, M. Caccia, and A. Andreoni, “Photon-number statistics with silicon photomultipliers,” J. Opt. Soc. Am. B 27, 852–862 (2010).

[Crossref]

J. G. Skellam, “The frequency distribution of the difference between two Poisson variates belonging to different populations,” J. Roy. Statist. Soc. (N. S.) 109, 296 (1946).

[Crossref]

G. Donati, T. J. Bartley, X.-M. Jin, M.-D. Vidrighin, A. Datta, M. Barbieri, and I. A. Walmsley, “Observing optical coherence across Fock layers with weak-field homodyne detectors,” Nat. Commun. 5, 5584 (2014).

[Crossref]
[PubMed]

F. E. Becerra, J. Fan, and A. Migdall, “Implementation of generalized quantum measurements for unambiguous discrimination of multiple non-orthogonal coherent states,” Nat. Commun. 4, 2028 (2013).

[Crossref]
[PubMed]

F. E. Becerra, J. Fan, G. Baumgartner, J. Goldhar, J. T. Kosloski, and A. Migdall, “Experimental demonstration of a receiver beating the standard quantum limit for multiple nonorthogonal state discrimination,” Nat. Photon. 7, 147–152 (2013).

[Crossref]

L. Zhang, H. B. Coldenstrodt-Ronge, A. Datta, G. Puentes, J. S. Lundeen, X.-M. Jin, B. J. Smith, M. B. Plenio, and I. A. Walmsley, “Mapping coherence in measurement via full quantum tomography of a hybrid optical detector,” Nat. Photon. 6, 364–368 (2012).

[Crossref]

C. R. Müller and Ch. Marquardt, “A robust quantum receiver for phase shift keyed signals,” New J. Phys. 17, 032003 (2015).

[Crossref]

E. Diamanti, H.-K. Lo, B. Qi, and Z. Yuan, “Practical challenges in quantum key distribution,” npj Quantum Information 2, 16025 (2016).

[Crossref]

A. Allevi, S. Olivares, and M. Bondani, “Measuring high-order photon-number correlations in experiments with multimode pulsed quantum states,” Phys. Rev. A 85, 063835 (2012).

[Crossref]

A. Andreoni and M. Bondani, “Photon statistics in the macroscopic realm measured without photon counters,” Phys. Rev. A 80, 013819 (2009).

[Crossref]

S. Wallentowitz and W. Vogel, “Unbalanced homodyning for quantum state measurements,” Phys. Rev. A 53, 4528–4533 (1996).

[Crossref]
[PubMed]

K. Banaszek, C. Radzewicz, K. Wódkiewicz, and J. S. Krasiński, “Direct measurement of the Wigner function by photon counting,” Phys. Rev. A 60, 674–677 (1999).

[Crossref]

K. Banaszek, A. Dragan, K. Wódkiewicz, and C. Radzewicz, “Direct measurement of optical quasi-distribution functions: Multimode theory and homodyne tests of Bell’s inequalities,” Phys. Rev. A 66, 043803 (2002).

[Crossref]

S. Olivares, S. Cialdi, F. Castelli, and M. G. A. Paris, “Homodyne detection as a near-optimum receiver for phase-shift-keyed binary communication in the presence of phase diffusion,” Phys. Rev. A 87, 050303 (2013).

[Crossref]

S. Izumi, M. Takeoka, M. Fujiwara, N. Dalla Pozza, A. Assalini, K. Ema, and M. Sasaki, “Displacement receiver for phase-shift-keyed coherent states,” Phys. Rev. A 86, 042328 (2012).

[Crossref]

S. Izumi, M. Takeoka, K. Wakui, M. Fujiwara, K. Ema, and M. Sasaki, “Optical phase estimation via coherent state and displaced photon counting,” Phys. Rev. A 94, 033842 (2016).

[Crossref]

G. Puentes, J. S. Lundeen, M. P. A. Branderhorst, H. B. Coldenstrodt-Ronge, B. J. Smith, and I. A. Walmsley, “Bridging particle and wave sensitivity in a configurable detector of positive operator-valued measures,” Phys. Rev. Lett. 102, 080404 (2009).

[Crossref]
[PubMed]

K. Laiho, K. N. Cassemiro, D. Gross, and C. Silberhorn, “Probing the negative Wigner function of a pulsed single photon point by point,” Phys. Rev. Lett. 105, 253603 (2010).

[Crossref]

M. Bina, A. Allevi, M. Bondani, and S. Olivares, “Phase-reference monitoring in coherent-state discrimination assisted by a photon-number resolving detector,” Sci. Rep. 6, 26025 (2016).

[Crossref]
[PubMed]

C. W. Helstrom, Quantum Detection and Estimation Theory (Academic, 1976).

BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, and OIML, Evaluation of Measurement Data - Supplement 1 to the Guide to the Expression of Uncertainty in Measurement - Propagation of Distributions Using a Monte Carlo Method (JCGM 101, 2008), http://www.bipm.org/utils/common/documents/jcgm/JCGM_101_2008_E.pdf .