Abstract

We propose a homodyne-like detection scheme involving photon-number-resolving detectors to discriminate between two coherent states affected by either uniform or gaussian phase noise. A proof-of-principle experiment is performed employing two hybrid photodetectors, whose outputs are used in post processing to calculate the shot-by-shot photon-number differences. The performance of the strategy is quantified in terms of the error probability in discriminating the noisy coherent signals as a function of the characteristic noise parameters.

© 2017 Optical Society of America

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  1. S. Wallentowitz and W. Vogel, “Unbalanced homodyning for quantum state measurements,” Phys. Rev. A 53, 4528–4533 (1996).
    [Crossref] [PubMed]
  2. 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]
  3. M. Bondani, A. Allevi, and A. Andreoni, “Wigner function of pulsed fields by direct detection,” Opt. Lett. 34, 1444–1446 (2009).
    [Crossref] [PubMed]
  4. A. Allevi, S. Olivares, and M. Bondani, “Manipulating the non-Gaussianity of phase-randomized coherent states,” Opt. Express 20, 24850–24855 (2012).
    [Crossref] [PubMed]
  5. 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]
  6. 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]
  7. 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]
  8. 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]
  9. 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]
  10. 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]
  11. C. R. Müller and Ch. Marquardt, “A robust quantum receiver for phase shift keyed signals,” New J. Phys. 17, 032003 (2015).
    [Crossref]
  12. 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]
  13. 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]
  14. 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]
  15. 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]
  16. C. W. Helstrom, Quantum Detection and Estimation Theory (Academic, 1976).
  17. 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]
  18. M. Bondani, A. Allevi, A. Agliati, and A. Andreoni, “Self- consistent characterization of light statistics,” J. Mod. Opt. 56, 226–231 (2009).
    [Crossref]
  19. A. Andreoni and M. Bondani, “Photon statistics in the macroscopic realm measured without photon counters,” Phys. Rev. A 80, 013819 (2009).
    [Crossref]
  20. 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]
  21. 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]
  22. B. Efron, “Bootstrap methods: another look at the jackknife,” Ann. Stat. 7, 1–26 (1979).
    [Crossref]
  23. 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 .
  24. 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]
  25. E. Diamanti, H.-K. Lo, B. Qi, and Z. Yuan, “Practical challenges in quantum key distribution,” npj Quantum Information 2, 16025 (2016).
    [Crossref]
  26. 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]

2016 (3)

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]

2015 (1)

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

2014 (1)

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]

2013 (3)

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]

2012 (4)

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]

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]

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]

2010 (3)

2009 (4)

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, 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]

2002 (1)

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]

1999 (1)

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]

1996 (1)

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

1979 (1)

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

1946 (1)

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]

Agliati, A.

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

Allevi, A.

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, “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]

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]

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. 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]

Andreoni, A.

Assalini, A.

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]

Banaszek, K.

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]

Barbieri, M.

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]

Bartley, T. J.

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]

Baumgartner, G.

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]

Becerra, F. E.

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]

Bina, M.

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]

Bondani, M.

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, “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]

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]

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. 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]

Branderhorst, M. P. A.

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]

Caccia, M.

Cassemiro, K. N.

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]

Castelli, F.

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]

Chmill, V.

Cialdi, S.

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]

Coldenstrodt-Ronge, H. B.

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]

Dalla Pozza, N.

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]

Datta, A.

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]

Diamanti, E.

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

Donati, G.

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]

Dragan, A.

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]

Efron, B.

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

Ema, K.

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]

Fan, J.

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]

Fujiwara, M.

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]

Goldhar, J.

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]

Gross, D.

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]

Helstrom, C. W.

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

Izumi, S.

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]

Jin, X.-M.

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]

Kosloski, J. T.

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]

Krasinski, J. S.

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]

Laiho, K.

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]

Lo, H.-K.

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

Lundeen, J. S.

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]

Marquardt, Ch.

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

Migdall, A.

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]

Müller, C. R.

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

Olivares, S.

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, “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]

Paris, M. G. A.

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]

Plenio, M. B.

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]

Puentes, G.

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]

Qi, B.

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

Radzewicz, C.

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]

Ramilli, M.

Sasaki, M.

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]

Silberhorn, C.

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]

Skellam, J. G.

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]

Smith, B. J.

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]

Takeoka, M.

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]

Vidrighin, M.-D.

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]

Vogel, W.

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

Wakui, K.

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]

Wallentowitz, S.

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

Walmsley, I. A.

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]

Wódkiewicz, K.

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]

Yuan, Z.

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

Zhang, L.

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]

Ann. Stat. (1)

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

J. Mod. Opt. (1)

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

J. Opt. Soc. Am. B (2)

J. Roy. Statist. Soc. (N. S.) (1)

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]

Nat. Commun. (2)

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]

Nat. Photon. (2)

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]

New J. Phys. (1)

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

npj Quantum Information (1)

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

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (8)

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]

Phys. Rev. Lett. (2)

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]

Sci. Rep. (1)

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]

Other (2)

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 .

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Figures (5)

Fig. 1
Fig. 1

(a) Sketch of the experimental setup. (b) Two typical photon-number distributions measured by the HPDs: experimental histograms, theoretical Poisson distribution (black dots), with the same mean value of the data, and the corresponding fidelities. See the text for details.

Fig. 2
Fig. 2

Mean number of photons µc as a function of the step of (a) the piezoelectric movement and (b) of the relative phase ϕ (black dots). In both panels we use the same scale for vertical axis. We also report µc calculated according to Eq. (4) with τ = 0.5 and the amplitudes of the signal, b, and LO, a, measured separately (red circles). Data refer to Experiment #2. See the text for details.

Fig. 3
Fig. 3

Plots of SΔ (μc(0); μd(0)) as a function of Δ, for both Experiment #1 (a) and Experiment #2 (b), with the choice ϕ = 0, corresponding to the input |β〉. The fidelity between the data, averaged over M = 100 repetitions (dots), and the histograms, representing the theoretical previsions (3), are f = 99.89% for the Experiment #1 and f = 99.73% for the #2. For the sake of completeness, we also report the properly theoretical homodyne probability distribution (8) as a function of x = Δ / ( 2 α ) and suitably renormalized (green dashed line). See the text for details.

Fig. 4
Fig. 4

Error probability (in logarithmic scale) obtained by the experimental homodyne-like photocount differences Δ (black dots with error bars) as a function of the uniform phase-noise parameter γ (a)–(c) and gaussian phase-noise one σ (b)–(d) for the Experiment #1 (a)–(b) and #2 (c)–(d), where β and α are the amplitudes of signal and LO, respectively [see Eq. (4)]. We also plot the theoretical prediction using the Skellam distribution (solid red lines), the corresponding theoretical standard homodyne detection (green dotted lines), given by Eq. (7), and the Helstrom bound (black dashed lines).

Fig. 5
Fig. 5

Error probabilities P e ( H ) (a) and P e ( s k ) (b) for uniform (solid curves) and Gaussian (dashed curves) phase noise, in Experiment #2. For a fair comparison we set σ = γ / ( 2 3 ).

Equations (8)

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P e ( H ) = 1 2 [ 1 T r | η 1 ρ ^ 1 η 0 ρ ^ 0 | ] .
ρ ^ k ( ρ ^ k ) = d φ f ( φ ) U ^ ( φ ) ρ ^ k U ^ ( φ ) ,
S Δ ( μ c , μ d ) = e μ c μ d ( μ c μ d ) Δ 2 I Δ ( 2 μ c μ d ) , Δ ,
μ c ( ϕ ) = a c 2 + b c 2 + 2 a c b c cos ( ϕ ) and μ d ( ϕ ) = a d 2 + b d 2 2 a d b d cos ( ϕ ) ,
P e ( s k ) = d φ f ( φ ) p e ( s k ) ( φ ) ,
p e ( s k ) ( φ ) = 1 2 [ Δ = 1 S Δ ( μ c ( φ ) , μ d ( φ ) ) + Δ = 1 + S Δ ( μ c ( φ π ) , μ d ( φ π ) ) + S 0 ] ,
P e ( hd ) = 1 2 [ 0 d x d φ f ( φ ) p h d ( x ; β ; φ ) + 0 + d x d φ f ( φ ) p h d ( x ; β ; φ ) ] ,
p h d ( x ; ± β ; φ ) = 1 π e ( x 2 β cos φ ) 2 ,

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