B. P. Abbott, et al., “Observation of gravitational waves from a binary black hole merger,” Phys. Rev. Lett. 116, 061102 (2016).

[Crossref]

J. Park, J. Joo, A. Zavatta, M. Bellini, and H. Jeong, “Efficient noiseless linear amplification for light fields with larger amplitudes,” Opt. Express 24, 1331–1346 (2016).

[Crossref]

S. Rosenblum, O. Bechler, I. Shomroni, Y. Lovsky, G. Guendelman, and B. Dayan, “Extraction of a single photon from an optical pulse,” Nat. Photonics 10, 19–22 (2016).

[Crossref]

M. D. Vidrighin, O. Dahlsten, M. Barbieri, M. S. Kim, V. Vedral, and I. A. Walmsley, “Photonic Maxwell’s demon,” Phys. Rev. Lett. 116, 050401 (2016).

[Crossref]

Y. Zhai, F. E. Becerra, B. L. Glebov, J. Wen, A. E. Lita, B. Calkins, T. Gerrits, J. Fan, S. W. Nam, and A. Migdall, “Photon-number-resolved detection of photon-subtracted thermal light,” Opt. Lett. 38, 2171–2173 (2013).

[Crossref]

R. Carranza and C. C. Gerry, “Photon-subtracted two-mode squeezed vacuum states and applications to quantum optical interferometry,” J. Opt. Soc. Am. B 29, 2581–2587 (2012).

[Crossref]

C. I. Osorio, N. Bruno, N. Sangouard, H. Zbinden, N. Gisin, and R. T. Thew, “Heralded photon amplification for quantum communication,” Phys. Rev. A 86, 023815 (2012).

[Crossref]

J. Honer, R. Löw, H. Weimer, T. Pfau, and H. P. Büchler, “Artificial atoms can do more than atoms: deterministic single photon subtraction from arbitrary light fields,” Phys. Rev. Lett. 107, 093601 (2011).

[Crossref]

A. Zavatta, J. Fiurášek, and M. Bellini, “A high-fidelity noiseless amplifier for quantum light states,” Nat. Photonics 5, 52–60 (2011).

[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5, 222–229 (2011).

[Crossref]

C. C. Gerry and J. Mimih, “The parity operator in quantum optical metrology,” Contemp. Phys. 51, 497–511 (2010).

[Crossref]

M. Kacprowicz, R. Demkowicz-Dobrzański, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Experimental quantum-enhanced estimation of a lossy phase shift,” Nat. Photonics 4, 357–360 (2010).

[Crossref]

M. A. Usuga, C. R. Müller, C. Wittmann, P. Marek, R. Filip, C. Marquardt, G. Leuchs, and U. L. Andersen, “Noise-powered probabilistic concentration of phase information,” Nat. Phys. 6, 767–771 (2010).

[Crossref]

F. Ferreyrol, M. Barbieri, R. Blandino, S. Fossier, R. Tualle-Brouri, and P. Grangier, “Implementation of a nondeterministic optical noiseless amplifier,” Phys. Rev. Lett. 104, 123603 (2010).

[Crossref]

G. Y. Xiang, T. C. Ralph, A. P. Lund, N. Walk, and G. J. Pryde, “Heralded noiseless linear amplification and distillation of entanglement,” Nat. Photonics 4, 316–319 (2010).

[Crossref]

H. Takahashi, J. S. Neergaard-Nielsen, M. Takeuchi, M. Takeoka, K. Hayasaka, A. Furusawa, and M. Sasaki, “Entanglement distillation from Gaussian input states,” Nat. Photonics 4, 178–181 (2010).

A. Zavatta, V. Parigi, M. S. Kim, H. Jeong, and M. Bellini, “Experimental demonstration of the bosonic commutation relation via superpositions of quantum operations on thermal light fields,” Phys. Rev. Lett. 103, 140406 (2009).

[Crossref]

A. Ourjoumtsev, F. Ferreyrol, R. Tualle-Brouri, and P. Grangier, “Preparation of non-local superpositions of quasi-classical light states,” Nat. Phys. 5, 189–192 (2009).

[Crossref]

V. Parigi, A. Zavatta, M. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890–1893 (2007).

[Crossref]

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316, 726–729 (2007).

[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).

[Crossref]

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating optical Schrödinger kittens for quantum information processing,” Science 312, 83–86 (2006).

[Crossref]

J. S. Neergaard-Nielsen, B. M. Nielsen, C. Hettich, K. Mølmer, and E. S. Polzik, “Generation of a superposition of odd photon number states for quantum information networks,” Phys. Rev. Lett. 97, 083604 (2006).

[Crossref]

J. Wenger, R. Tualle-Brouri, and P. Grangier, “Non-Gaussian statistics from individual pulses of squeezed light,” Phys. Rev. Lett. 92, 153601 (2004).

[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science 306, 1330–1336 (2004).

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature 429, 161–164 (2004).

[Crossref]

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature 429, 158–161 (2004).

[Crossref]

R. A. Campos, C. C. Gerry, and A. Benmoussa, “Optical interferometry at the Heisenberg limit with twin Fock states and parity measurements,” Phys. Rev. A 68, 023810 (2003).

[Crossref]

M. D’Angelo, M. V. Chekhova, and Y. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87, 013602 (2001).

[Crossref]

P. Grangier, R. E. Slusher, B. Yurke, and A. LaPorta, “Squeezed-light-enhanced polarization interferometer,” Phys. Rev. Lett. 59, 2153–2156 (1987).

[Crossref]

C. M. Caves, “Quantum limits on noise in linear-amplifiers,” Phys. Rev. D 26, 1817–1839 (1982).

[Crossref]

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981).

[Crossref]

F. T. Arecchi, “Measurement of the statistical distribution of Gaussian and laser sources,” Phys. Rev. Lett. 15, 912–916 (1965).

[Crossref]

B. P. Abbott, et al., “Observation of gravitational waves from a binary black hole merger,” Phys. Rev. Lett. 116, 061102 (2016).

[Crossref]

M. A. Usuga, C. R. Müller, C. Wittmann, P. Marek, R. Filip, C. Marquardt, G. Leuchs, and U. L. Andersen, “Noise-powered probabilistic concentration of phase information,” Nat. Phys. 6, 767–771 (2010).

[Crossref]

F. T. Arecchi, “Measurement of the statistical distribution of Gaussian and laser sources,” Phys. Rev. Lett. 15, 912–916 (1965).

[Crossref]

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature 429, 158–161 (2004).

[Crossref]

M. Kacprowicz, R. Demkowicz-Dobrzański, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Experimental quantum-enhanced estimation of a lossy phase shift,” Nat. Photonics 4, 357–360 (2010).

[Crossref]

M. D. Vidrighin, O. Dahlsten, M. Barbieri, M. S. Kim, V. Vedral, and I. A. Walmsley, “Photonic Maxwell’s demon,” Phys. Rev. Lett. 116, 050401 (2016).

[Crossref]

F. Ferreyrol, M. Barbieri, R. Blandino, S. Fossier, R. Tualle-Brouri, and P. Grangier, “Implementation of a nondeterministic optical noiseless amplifier,” Phys. Rev. Lett. 104, 123603 (2010).

[Crossref]

Y. Zhai, F. E. Becerra, B. L. Glebov, J. Wen, A. E. Lita, B. Calkins, T. Gerrits, J. Fan, S. W. Nam, and A. Migdall, “Photon-number-resolved detection of photon-subtracted thermal light,” Opt. Lett. 38, 2171–2173 (2013).

[Crossref]

S. Rosenblum, O. Bechler, I. Shomroni, Y. Lovsky, G. Guendelman, and B. Dayan, “Extraction of a single photon from an optical pulse,” Nat. Photonics 10, 19–22 (2016).

[Crossref]

J. Park, J. Joo, A. Zavatta, M. Bellini, and H. Jeong, “Efficient noiseless linear amplification for light fields with larger amplitudes,” Opt. Express 24, 1331–1346 (2016).

[Crossref]

A. Zavatta, J. Fiurášek, and M. Bellini, “A high-fidelity noiseless amplifier for quantum light states,” Nat. Photonics 5, 52–60 (2011).

[Crossref]

A. Zavatta, V. Parigi, M. S. Kim, H. Jeong, and M. Bellini, “Experimental demonstration of the bosonic commutation relation via superpositions of quantum operations on thermal light fields,” Phys. Rev. Lett. 103, 140406 (2009).

[Crossref]

V. Parigi, A. Zavatta, M. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890–1893 (2007).

[Crossref]

R. A. Campos, C. C. Gerry, and A. Benmoussa, “Optical interferometry at the Heisenberg limit with twin Fock states and parity measurements,” Phys. Rev. A 68, 023810 (2003).

[Crossref]

R. Birrittella and C. C. Gerry, “Quantum optical interferometry via the mixing of coherent and photon-subtracted squeezed vacuum states of light,” J. Opt. Soc. Am. B 31, 586–588 (2014).

[Crossref]

C. G. Parazzoli, B. E. Koltenbah, D. R. Gerwe, P. S. Idell, B. T. Gard, R. Birrittella, S. M. Hashemi Rafsanjani, M. Mirhosseini, O. S. Magana-Loaiza, J. P. Dowling, C. C. Gerry, R. W. Boyd, and B. C. Capron, “Enhanced thermal object imaging by photon addition and subtraction,” arXiv:1609:02780 (2016).

F. Ferreyrol, M. Barbieri, R. Blandino, S. Fossier, R. Tualle-Brouri, and P. Grangier, “Implementation of a nondeterministic optical noiseless amplifier,” Phys. Rev. Lett. 104, 123603 (2010).

[Crossref]

C. G. Parazzoli, B. E. Koltenbah, D. R. Gerwe, P. S. Idell, B. T. Gard, R. Birrittella, S. M. Hashemi Rafsanjani, M. Mirhosseini, O. S. Magana-Loaiza, J. P. Dowling, C. C. Gerry, R. W. Boyd, and B. C. Capron, “Enhanced thermal object imaging by photon addition and subtraction,” arXiv:1609:02780 (2016).

D. Braun, P. Jian, O. Pinel, and N. Treps, “Precision measurements with photon-subtracted or photon-added Gaussian states,” Phys. Rev. A 90, 013821 (2014).

[Crossref]

C. I. Osorio, N. Bruno, N. Sangouard, H. Zbinden, N. Gisin, and R. T. Thew, “Heralded photon amplification for quantum communication,” Phys. Rev. A 86, 023815 (2012).

[Crossref]

J. Honer, R. Löw, H. Weimer, T. Pfau, and H. P. Büchler, “Artificial atoms can do more than atoms: deterministic single photon subtraction from arbitrary light fields,” Phys. Rev. Lett. 107, 093601 (2011).

[Crossref]

Y. Zhai, F. E. Becerra, B. L. Glebov, J. Wen, A. E. Lita, B. Calkins, T. Gerrits, J. Fan, S. W. Nam, and A. Migdall, “Photon-number-resolved detection of photon-subtracted thermal light,” Opt. Lett. 38, 2171–2173 (2013).

[Crossref]

R. A. Campos, C. C. Gerry, and A. Benmoussa, “Optical interferometry at the Heisenberg limit with twin Fock states and parity measurements,” Phys. Rev. A 68, 023810 (2003).

[Crossref]

C. G. Parazzoli, B. E. Koltenbah, D. R. Gerwe, P. S. Idell, B. T. Gard, R. Birrittella, S. M. Hashemi Rafsanjani, M. Mirhosseini, O. S. Magana-Loaiza, J. P. Dowling, C. C. Gerry, R. W. Boyd, and B. C. Capron, “Enhanced thermal object imaging by photon addition and subtraction,” arXiv:1609:02780 (2016).

C. M. Caves, “Quantum limits on noise in linear-amplifiers,” Phys. Rev. D 26, 1817–1839 (1982).

[Crossref]

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981).

[Crossref]

M. D’Angelo, M. V. Chekhova, and Y. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87, 013602 (2001).

[Crossref]

M. D’Angelo, M. V. Chekhova, and Y. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87, 013602 (2001).

[Crossref]

M. D. Vidrighin, O. Dahlsten, M. Barbieri, M. S. Kim, V. Vedral, and I. A. Walmsley, “Photonic Maxwell’s demon,” Phys. Rev. Lett. 116, 050401 (2016).

[Crossref]

S. Rosenblum, O. Bechler, I. Shomroni, Y. Lovsky, G. Guendelman, and B. Dayan, “Extraction of a single photon from an optical pulse,” Nat. Photonics 10, 19–22 (2016).

[Crossref]

M. Kacprowicz, R. Demkowicz-Dobrzański, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Experimental quantum-enhanced estimation of a lossy phase shift,” Nat. Photonics 4, 357–360 (2010).

[Crossref]

C. G. Parazzoli, B. E. Koltenbah, D. R. Gerwe, P. S. Idell, B. T. Gard, R. Birrittella, S. M. Hashemi Rafsanjani, M. Mirhosseini, O. S. Magana-Loaiza, J. P. Dowling, C. C. Gerry, R. W. Boyd, and B. C. Capron, “Enhanced thermal object imaging by photon addition and subtraction,” arXiv:1609:02780 (2016).

Y. Zhai, F. E. Becerra, B. L. Glebov, J. Wen, A. E. Lita, B. Calkins, T. Gerrits, J. Fan, S. W. Nam, and A. Migdall, “Photon-number-resolved detection of photon-subtracted thermal light,” Opt. Lett. 38, 2171–2173 (2013).

[Crossref]

F. Ferreyrol, M. Barbieri, R. Blandino, S. Fossier, R. Tualle-Brouri, and P. Grangier, “Implementation of a nondeterministic optical noiseless amplifier,” Phys. Rev. Lett. 104, 123603 (2010).

[Crossref]

A. Ourjoumtsev, F. Ferreyrol, R. Tualle-Brouri, and P. Grangier, “Preparation of non-local superpositions of quasi-classical light states,” Nat. Phys. 5, 189–192 (2009).

[Crossref]

M. A. Usuga, C. R. Müller, C. Wittmann, P. Marek, R. Filip, C. Marquardt, G. Leuchs, and U. L. Andersen, “Noise-powered probabilistic concentration of phase information,” Nat. Phys. 6, 767–771 (2010).

[Crossref]

A. Zavatta, J. Fiurášek, and M. Bellini, “A high-fidelity noiseless amplifier for quantum light states,” Nat. Photonics 5, 52–60 (2011).

[Crossref]

F. Ferreyrol, M. Barbieri, R. Blandino, S. Fossier, R. Tualle-Brouri, and P. Grangier, “Implementation of a nondeterministic optical noiseless amplifier,” Phys. Rev. Lett. 104, 123603 (2010).

[Crossref]

H. Takahashi, J. S. Neergaard-Nielsen, M. Takeuchi, M. Takeoka, K. Hayasaka, A. Furusawa, and M. Sasaki, “Entanglement distillation from Gaussian input states,” Nat. Photonics 4, 178–181 (2010).

C. G. Parazzoli, B. E. Koltenbah, D. R. Gerwe, P. S. Idell, B. T. Gard, R. Birrittella, S. M. Hashemi Rafsanjani, M. Mirhosseini, O. S. Magana-Loaiza, J. P. Dowling, C. C. Gerry, R. W. Boyd, and B. C. Capron, “Enhanced thermal object imaging by photon addition and subtraction,” arXiv:1609:02780 (2016).

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature 429, 158–161 (2004).

[Crossref]

Y. Zhai, F. E. Becerra, B. L. Glebov, J. Wen, A. E. Lita, B. Calkins, T. Gerrits, J. Fan, S. W. Nam, and A. Migdall, “Photon-number-resolved detection of photon-subtracted thermal light,” Opt. Lett. 38, 2171–2173 (2013).

[Crossref]

R. Birrittella and C. C. Gerry, “Quantum optical interferometry via the mixing of coherent and photon-subtracted squeezed vacuum states of light,” J. Opt. Soc. Am. B 31, 586–588 (2014).

[Crossref]

R. Carranza and C. C. Gerry, “Photon-subtracted two-mode squeezed vacuum states and applications to quantum optical interferometry,” J. Opt. Soc. Am. B 29, 2581–2587 (2012).

[Crossref]

C. C. Gerry and J. Mimih, “The parity operator in quantum optical metrology,” Contemp. Phys. 51, 497–511 (2010).

[Crossref]

R. A. Campos, C. C. Gerry, and A. Benmoussa, “Optical interferometry at the Heisenberg limit with twin Fock states and parity measurements,” Phys. Rev. A 68, 023810 (2003).

[Crossref]

C. G. Parazzoli, B. E. Koltenbah, D. R. Gerwe, P. S. Idell, B. T. Gard, R. Birrittella, S. M. Hashemi Rafsanjani, M. Mirhosseini, O. S. Magana-Loaiza, J. P. Dowling, C. C. Gerry, R. W. Boyd, and B. C. Capron, “Enhanced thermal object imaging by photon addition and subtraction,” arXiv:1609:02780 (2016).

e.g., Eq. (2) can be derived using a procedure described in Chap. 6 of C. C. Gerry and P. Knight, Introductory Quantum Optics (Cambridge University, 2004).

C. G. Parazzoli, B. E. Koltenbah, D. R. Gerwe, P. S. Idell, B. T. Gard, R. Birrittella, S. M. Hashemi Rafsanjani, M. Mirhosseini, O. S. Magana-Loaiza, J. P. Dowling, C. C. Gerry, R. W. Boyd, and B. C. Capron, “Enhanced thermal object imaging by photon addition and subtraction,” arXiv:1609:02780 (2016).

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5, 222–229 (2011).

[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).

[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science 306, 1330–1336 (2004).

C. I. Osorio, N. Bruno, N. Sangouard, H. Zbinden, N. Gisin, and R. T. Thew, “Heralded photon amplification for quantum communication,” Phys. Rev. A 86, 023815 (2012).

[Crossref]

Y. Zhai, F. E. Becerra, B. L. Glebov, J. Wen, A. E. Lita, B. Calkins, T. Gerrits, J. Fan, S. W. Nam, and A. Migdall, “Photon-number-resolved detection of photon-subtracted thermal light,” Opt. Lett. 38, 2171–2173 (2013).

[Crossref]

F. Ferreyrol, M. Barbieri, R. Blandino, S. Fossier, R. Tualle-Brouri, and P. Grangier, “Implementation of a nondeterministic optical noiseless amplifier,” Phys. Rev. Lett. 104, 123603 (2010).

[Crossref]

A. Ourjoumtsev, F. Ferreyrol, R. Tualle-Brouri, and P. Grangier, “Preparation of non-local superpositions of quasi-classical light states,” Nat. Phys. 5, 189–192 (2009).

[Crossref]

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating optical Schrödinger kittens for quantum information processing,” Science 312, 83–86 (2006).

[Crossref]

J. Wenger, R. Tualle-Brouri, and P. Grangier, “Non-Gaussian statistics from individual pulses of squeezed light,” Phys. Rev. Lett. 92, 153601 (2004).

[Crossref]

P. Grangier, R. E. Slusher, B. Yurke, and A. LaPorta, “Squeezed-light-enhanced polarization interferometer,” Phys. Rev. Lett. 59, 2153–2156 (1987).

[Crossref]

S. Rosenblum, O. Bechler, I. Shomroni, Y. Lovsky, G. Guendelman, and B. Dayan, “Extraction of a single photon from an optical pulse,” Nat. Photonics 10, 19–22 (2016).

[Crossref]

C. G. Parazzoli, B. E. Koltenbah, D. R. Gerwe, P. S. Idell, B. T. Gard, R. Birrittella, S. M. Hashemi Rafsanjani, M. Mirhosseini, O. S. Magana-Loaiza, J. P. Dowling, C. C. Gerry, R. W. Boyd, and B. C. Capron, “Enhanced thermal object imaging by photon addition and subtraction,” arXiv:1609:02780 (2016).

H. Takahashi, J. S. Neergaard-Nielsen, M. Takeuchi, M. Takeoka, K. Hayasaka, A. Furusawa, and M. Sasaki, “Entanglement distillation from Gaussian input states,” Nat. Photonics 4, 178–181 (2010).

J. S. Neergaard-Nielsen, B. M. Nielsen, C. Hettich, K. Mølmer, and E. S. Polzik, “Generation of a superposition of odd photon number states for quantum information networks,” Phys. Rev. Lett. 97, 083604 (2006).

[Crossref]

J. Honer, R. Löw, H. Weimer, T. Pfau, and H. P. Büchler, “Artificial atoms can do more than atoms: deterministic single photon subtraction from arbitrary light fields,” Phys. Rev. Lett. 107, 093601 (2011).

[Crossref]

C. G. Parazzoli, B. E. Koltenbah, D. R. Gerwe, P. S. Idell, B. T. Gard, R. Birrittella, S. M. Hashemi Rafsanjani, M. Mirhosseini, O. S. Magana-Loaiza, J. P. Dowling, C. C. Gerry, R. W. Boyd, and B. C. Capron, “Enhanced thermal object imaging by photon addition and subtraction,” arXiv:1609:02780 (2016).

J. Park, J. Joo, A. Zavatta, M. Bellini, and H. Jeong, “Efficient noiseless linear amplification for light fields with larger amplitudes,” Opt. Express 24, 1331–1346 (2016).

[Crossref]

A. Zavatta, V. Parigi, M. S. Kim, H. Jeong, and M. Bellini, “Experimental demonstration of the bosonic commutation relation via superpositions of quantum operations on thermal light fields,” Phys. Rev. Lett. 103, 140406 (2009).

[Crossref]

D. Braun, P. Jian, O. Pinel, and N. Treps, “Precision measurements with photon-subtracted or photon-added Gaussian states,” Phys. Rev. A 90, 013821 (2014).

[Crossref]

M. Kacprowicz, R. Demkowicz-Dobrzański, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Experimental quantum-enhanced estimation of a lossy phase shift,” Nat. Photonics 4, 357–360 (2010).

[Crossref]

V. Parigi, A. Zavatta, M. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890–1893 (2007).

[Crossref]

M. D. Vidrighin, O. Dahlsten, M. Barbieri, M. S. Kim, V. Vedral, and I. A. Walmsley, “Photonic Maxwell’s demon,” Phys. Rev. Lett. 116, 050401 (2016).

[Crossref]

A. Zavatta, V. Parigi, M. S. Kim, H. Jeong, and M. Bellini, “Experimental demonstration of the bosonic commutation relation via superpositions of quantum operations on thermal light fields,” Phys. Rev. Lett. 103, 140406 (2009).

[Crossref]

e.g., Eq. (2) can be derived using a procedure described in Chap. 6 of C. C. Gerry and P. Knight, Introductory Quantum Optics (Cambridge University, 2004).

C. G. Parazzoli, B. E. Koltenbah, D. R. Gerwe, P. S. Idell, B. T. Gard, R. Birrittella, S. M. Hashemi Rafsanjani, M. Mirhosseini, O. S. Magana-Loaiza, J. P. Dowling, C. C. Gerry, R. W. Boyd, and B. C. Capron, “Enhanced thermal object imaging by photon addition and subtraction,” arXiv:1609:02780 (2016).

P. Grangier, R. E. Slusher, B. Yurke, and A. LaPorta, “Squeezed-light-enhanced polarization interferometer,” Phys. Rev. Lett. 59, 2153–2156 (1987).

[Crossref]

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating optical Schrödinger kittens for quantum information processing,” Science 312, 83–86 (2006).

[Crossref]

M. A. Usuga, C. R. Müller, C. Wittmann, P. Marek, R. Filip, C. Marquardt, G. Leuchs, and U. L. Andersen, “Noise-powered probabilistic concentration of phase information,” Nat. Phys. 6, 767–771 (2010).

[Crossref]

Y. Zhai, F. E. Becerra, B. L. Glebov, J. Wen, A. E. Lita, B. Calkins, T. Gerrits, J. Fan, S. W. Nam, and A. Migdall, “Photon-number-resolved detection of photon-subtracted thermal light,” Opt. Lett. 38, 2171–2173 (2013).

[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5, 222–229 (2011).

[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).

[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science 306, 1330–1336 (2004).

S. Rosenblum, O. Bechler, I. Shomroni, Y. Lovsky, G. Guendelman, and B. Dayan, “Extraction of a single photon from an optical pulse,” Nat. Photonics 10, 19–22 (2016).

[Crossref]

J. Honer, R. Löw, H. Weimer, T. Pfau, and H. P. Büchler, “Artificial atoms can do more than atoms: deterministic single photon subtraction from arbitrary light fields,” Phys. Rev. Lett. 107, 093601 (2011).

[Crossref]

G. Y. Xiang, T. C. Ralph, A. P. Lund, N. Walk, and G. J. Pryde, “Heralded noiseless linear amplification and distillation of entanglement,” Nat. Photonics 4, 316–319 (2010).

[Crossref]

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature 429, 161–164 (2004).

[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5, 222–229 (2011).

[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).

[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science 306, 1330–1336 (2004).

C. G. Parazzoli, B. E. Koltenbah, D. R. Gerwe, P. S. Idell, B. T. Gard, R. Birrittella, S. M. Hashemi Rafsanjani, M. Mirhosseini, O. S. Magana-Loaiza, J. P. Dowling, C. C. Gerry, R. W. Boyd, and B. C. Capron, “Enhanced thermal object imaging by photon addition and subtraction,” arXiv:1609:02780 (2016).

M. A. Usuga, C. R. Müller, C. Wittmann, P. Marek, R. Filip, C. Marquardt, G. Leuchs, and U. L. Andersen, “Noise-powered probabilistic concentration of phase information,” Nat. Phys. 6, 767–771 (2010).

[Crossref]

M. A. Usuga, C. R. Müller, C. Wittmann, P. Marek, R. Filip, C. Marquardt, G. Leuchs, and U. L. Andersen, “Noise-powered probabilistic concentration of phase information,” Nat. Phys. 6, 767–771 (2010).

[Crossref]

Y. Zhai, F. E. Becerra, B. L. Glebov, J. Wen, A. E. Lita, B. Calkins, T. Gerrits, J. Fan, S. W. Nam, and A. Migdall, “Photon-number-resolved detection of photon-subtracted thermal light,” Opt. Lett. 38, 2171–2173 (2013).

[Crossref]

C. C. Gerry and J. Mimih, “The parity operator in quantum optical metrology,” Contemp. Phys. 51, 497–511 (2010).

[Crossref]

C. G. Parazzoli, B. E. Koltenbah, D. R. Gerwe, P. S. Idell, B. T. Gard, R. Birrittella, S. M. Hashemi Rafsanjani, M. Mirhosseini, O. S. Magana-Loaiza, J. P. Dowling, C. C. Gerry, R. W. Boyd, and B. C. Capron, “Enhanced thermal object imaging by photon addition and subtraction,” arXiv:1609:02780 (2016).

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature 429, 161–164 (2004).

[Crossref]

J. S. Neergaard-Nielsen, B. M. Nielsen, C. Hettich, K. Mølmer, and E. S. Polzik, “Generation of a superposition of odd photon number states for quantum information networks,” Phys. Rev. Lett. 97, 083604 (2006).

[Crossref]

M. A. Usuga, C. R. Müller, C. Wittmann, P. Marek, R. Filip, C. Marquardt, G. Leuchs, and U. L. Andersen, “Noise-powered probabilistic concentration of phase information,” Nat. Phys. 6, 767–771 (2010).

[Crossref]

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316, 726–729 (2007).

[Crossref]

Y. Zhai, F. E. Becerra, B. L. Glebov, J. Wen, A. E. Lita, B. Calkins, T. Gerrits, J. Fan, S. W. Nam, and A. Migdall, “Photon-number-resolved detection of photon-subtracted thermal light,” Opt. Lett. 38, 2171–2173 (2013).

[Crossref]

H. Takahashi, J. S. Neergaard-Nielsen, M. Takeuchi, M. Takeoka, K. Hayasaka, A. Furusawa, and M. Sasaki, “Entanglement distillation from Gaussian input states,” Nat. Photonics 4, 178–181 (2010).

J. S. Neergaard-Nielsen, B. M. Nielsen, C. Hettich, K. Mølmer, and E. S. Polzik, “Generation of a superposition of odd photon number states for quantum information networks,” Phys. Rev. Lett. 97, 083604 (2006).

[Crossref]

J. S. Neergaard-Nielsen, B. M. Nielsen, C. Hettich, K. Mølmer, and E. S. Polzik, “Generation of a superposition of odd photon number states for quantum information networks,” Phys. Rev. Lett. 97, 083604 (2006).

[Crossref]

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316, 726–729 (2007).

[Crossref]

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316, 726–729 (2007).

[Crossref]

C. I. Osorio, N. Bruno, N. Sangouard, H. Zbinden, N. Gisin, and R. T. Thew, “Heralded photon amplification for quantum communication,” Phys. Rev. A 86, 023815 (2012).

[Crossref]

A. Ourjoumtsev, F. Ferreyrol, R. Tualle-Brouri, and P. Grangier, “Preparation of non-local superpositions of quasi-classical light states,” Nat. Phys. 5, 189–192 (2009).

[Crossref]

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating optical Schrödinger kittens for quantum information processing,” Science 312, 83–86 (2006).

[Crossref]

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature 429, 158–161 (2004).

[Crossref]

C. G. Parazzoli, B. E. Koltenbah, D. R. Gerwe, P. S. Idell, B. T. Gard, R. Birrittella, S. M. Hashemi Rafsanjani, M. Mirhosseini, O. S. Magana-Loaiza, J. P. Dowling, C. C. Gerry, R. W. Boyd, and B. C. Capron, “Enhanced thermal object imaging by photon addition and subtraction,” arXiv:1609:02780 (2016).

A. Zavatta, V. Parigi, M. S. Kim, H. Jeong, and M. Bellini, “Experimental demonstration of the bosonic commutation relation via superpositions of quantum operations on thermal light fields,” Phys. Rev. Lett. 103, 140406 (2009).

[Crossref]

V. Parigi, A. Zavatta, M. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890–1893 (2007).

[Crossref]

J. Honer, R. Löw, H. Weimer, T. Pfau, and H. P. Büchler, “Artificial atoms can do more than atoms: deterministic single photon subtraction from arbitrary light fields,” Phys. Rev. Lett. 107, 093601 (2011).

[Crossref]

D. Braun, P. Jian, O. Pinel, and N. Treps, “Precision measurements with photon-subtracted or photon-added Gaussian states,” Phys. Rev. A 90, 013821 (2014).

[Crossref]

J. S. Neergaard-Nielsen, B. M. Nielsen, C. Hettich, K. Mølmer, and E. S. Polzik, “Generation of a superposition of odd photon number states for quantum information networks,” Phys. Rev. Lett. 97, 083604 (2006).

[Crossref]

G. Y. Xiang, T. C. Ralph, A. P. Lund, N. Walk, and G. J. Pryde, “Heralded noiseless linear amplification and distillation of entanglement,” Nat. Photonics 4, 316–319 (2010).

[Crossref]

G. Y. Xiang, T. C. Ralph, A. P. Lund, N. Walk, and G. J. Pryde, “Heralded noiseless linear amplification and distillation of entanglement,” Nat. Photonics 4, 316–319 (2010).

[Crossref]

S. Rosenblum, O. Bechler, I. Shomroni, Y. Lovsky, G. Guendelman, and B. Dayan, “Extraction of a single photon from an optical pulse,” Nat. Photonics 10, 19–22 (2016).

[Crossref]

C. I. Osorio, N. Bruno, N. Sangouard, H. Zbinden, N. Gisin, and R. T. Thew, “Heralded photon amplification for quantum communication,” Phys. Rev. A 86, 023815 (2012).

[Crossref]

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316, 726–729 (2007).

[Crossref]

H. Takahashi, J. S. Neergaard-Nielsen, M. Takeuchi, M. Takeoka, K. Hayasaka, A. Furusawa, and M. Sasaki, “Entanglement distillation from Gaussian input states,” Nat. Photonics 4, 178–181 (2010).

M. D’Angelo, M. V. Chekhova, and Y. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87, 013602 (2001).

[Crossref]

S. Rosenblum, O. Bechler, I. Shomroni, Y. Lovsky, G. Guendelman, and B. Dayan, “Extraction of a single photon from an optical pulse,” Nat. Photonics 10, 19–22 (2016).

[Crossref]

P. Grangier, R. E. Slusher, B. Yurke, and A. LaPorta, “Squeezed-light-enhanced polarization interferometer,” Phys. Rev. Lett. 59, 2153–2156 (1987).

[Crossref]

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature 429, 161–164 (2004).

[Crossref]

H. Takahashi, J. S. Neergaard-Nielsen, M. Takeuchi, M. Takeoka, K. Hayasaka, A. Furusawa, and M. Sasaki, “Entanglement distillation from Gaussian input states,” Nat. Photonics 4, 178–181 (2010).

H. Takahashi, J. S. Neergaard-Nielsen, M. Takeuchi, M. Takeoka, K. Hayasaka, A. Furusawa, and M. Sasaki, “Entanglement distillation from Gaussian input states,” Nat. Photonics 4, 178–181 (2010).

H. Takahashi, J. S. Neergaard-Nielsen, M. Takeuchi, M. Takeoka, K. Hayasaka, A. Furusawa, and M. Sasaki, “Entanglement distillation from Gaussian input states,” Nat. Photonics 4, 178–181 (2010).

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316, 726–729 (2007).

[Crossref]

C. I. Osorio, N. Bruno, N. Sangouard, H. Zbinden, N. Gisin, and R. T. Thew, “Heralded photon amplification for quantum communication,” Phys. Rev. A 86, 023815 (2012).

[Crossref]

D. Braun, P. Jian, O. Pinel, and N. Treps, “Precision measurements with photon-subtracted or photon-added Gaussian states,” Phys. Rev. A 90, 013821 (2014).

[Crossref]

F. Ferreyrol, M. Barbieri, R. Blandino, S. Fossier, R. Tualle-Brouri, and P. Grangier, “Implementation of a nondeterministic optical noiseless amplifier,” Phys. Rev. Lett. 104, 123603 (2010).

[Crossref]

A. Ourjoumtsev, F. Ferreyrol, R. Tualle-Brouri, and P. Grangier, “Preparation of non-local superpositions of quasi-classical light states,” Nat. Phys. 5, 189–192 (2009).

[Crossref]

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating optical Schrödinger kittens for quantum information processing,” Science 312, 83–86 (2006).

[Crossref]

J. Wenger, R. Tualle-Brouri, and P. Grangier, “Non-Gaussian statistics from individual pulses of squeezed light,” Phys. Rev. Lett. 92, 153601 (2004).

[Crossref]

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature 429, 158–161 (2004).

[Crossref]

M. A. Usuga, C. R. Müller, C. Wittmann, P. Marek, R. Filip, C. Marquardt, G. Leuchs, and U. L. Andersen, “Noise-powered probabilistic concentration of phase information,” Nat. Phys. 6, 767–771 (2010).

[Crossref]

M. D. Vidrighin, O. Dahlsten, M. Barbieri, M. S. Kim, V. Vedral, and I. A. Walmsley, “Photonic Maxwell’s demon,” Phys. Rev. Lett. 116, 050401 (2016).

[Crossref]

M. D. Vidrighin, O. Dahlsten, M. Barbieri, M. S. Kim, V. Vedral, and I. A. Walmsley, “Photonic Maxwell’s demon,” Phys. Rev. Lett. 116, 050401 (2016).

[Crossref]

G. Y. Xiang, T. C. Ralph, A. P. Lund, N. Walk, and G. J. Pryde, “Heralded noiseless linear amplification and distillation of entanglement,” Nat. Photonics 4, 316–319 (2010).

[Crossref]

M. D. Vidrighin, O. Dahlsten, M. Barbieri, M. S. Kim, V. Vedral, and I. A. Walmsley, “Photonic Maxwell’s demon,” Phys. Rev. Lett. 116, 050401 (2016).

[Crossref]

M. Kacprowicz, R. Demkowicz-Dobrzański, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Experimental quantum-enhanced estimation of a lossy phase shift,” Nat. Photonics 4, 357–360 (2010).

[Crossref]

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature 429, 158–161 (2004).

[Crossref]

M. Kacprowicz, R. Demkowicz-Dobrzański, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Experimental quantum-enhanced estimation of a lossy phase shift,” Nat. Photonics 4, 357–360 (2010).

[Crossref]

J. Honer, R. Löw, H. Weimer, T. Pfau, and H. P. Büchler, “Artificial atoms can do more than atoms: deterministic single photon subtraction from arbitrary light fields,” Phys. Rev. Lett. 107, 093601 (2011).

[Crossref]

Y. Zhai, F. E. Becerra, B. L. Glebov, J. Wen, A. E. Lita, B. Calkins, T. Gerrits, J. Fan, S. W. Nam, and A. Migdall, “Photon-number-resolved detection of photon-subtracted thermal light,” Opt. Lett. 38, 2171–2173 (2013).

[Crossref]

J. Wenger, R. Tualle-Brouri, and P. Grangier, “Non-Gaussian statistics from individual pulses of squeezed light,” Phys. Rev. Lett. 92, 153601 (2004).

[Crossref]

M. A. Usuga, C. R. Müller, C. Wittmann, P. Marek, R. Filip, C. Marquardt, G. Leuchs, and U. L. Andersen, “Noise-powered probabilistic concentration of phase information,” Nat. Phys. 6, 767–771 (2010).

[Crossref]

G. Y. Xiang, T. C. Ralph, A. P. Lund, N. Walk, and G. J. Pryde, “Heralded noiseless linear amplification and distillation of entanglement,” Nat. Photonics 4, 316–319 (2010).

[Crossref]

P. Grangier, R. E. Slusher, B. Yurke, and A. LaPorta, “Squeezed-light-enhanced polarization interferometer,” Phys. Rev. Lett. 59, 2153–2156 (1987).

[Crossref]

J. Park, J. Joo, A. Zavatta, M. Bellini, and H. Jeong, “Efficient noiseless linear amplification for light fields with larger amplitudes,” Opt. Express 24, 1331–1346 (2016).

[Crossref]

A. Zavatta, J. Fiurášek, and M. Bellini, “A high-fidelity noiseless amplifier for quantum light states,” Nat. Photonics 5, 52–60 (2011).

[Crossref]

A. Zavatta, V. Parigi, M. S. Kim, H. Jeong, and M. Bellini, “Experimental demonstration of the bosonic commutation relation via superpositions of quantum operations on thermal light fields,” Phys. Rev. Lett. 103, 140406 (2009).

[Crossref]

V. Parigi, A. Zavatta, M. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890–1893 (2007).

[Crossref]

C. I. Osorio, N. Bruno, N. Sangouard, H. Zbinden, N. Gisin, and R. T. Thew, “Heralded photon amplification for quantum communication,” Phys. Rev. A 86, 023815 (2012).

[Crossref]

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature 429, 158–161 (2004).

[Crossref]

Y. Zhai, F. E. Becerra, B. L. Glebov, J. Wen, A. E. Lita, B. Calkins, T. Gerrits, J. Fan, S. W. Nam, and A. Migdall, “Photon-number-resolved detection of photon-subtracted thermal light,” Opt. Lett. 38, 2171–2173 (2013).

[Crossref]

C. C. Gerry and J. Mimih, “The parity operator in quantum optical metrology,” Contemp. Phys. 51, 497–511 (2010).

[Crossref]

H. Takahashi, J. S. Neergaard-Nielsen, M. Takeuchi, M. Takeoka, K. Hayasaka, A. Furusawa, and M. Sasaki, “Entanglement distillation from Gaussian input states,” Nat. Photonics 4, 178–181 (2010).

S. Rosenblum, O. Bechler, I. Shomroni, Y. Lovsky, G. Guendelman, and B. Dayan, “Extraction of a single photon from an optical pulse,” Nat. Photonics 10, 19–22 (2016).

[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5, 222–229 (2011).

[Crossref]

M. Kacprowicz, R. Demkowicz-Dobrzański, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Experimental quantum-enhanced estimation of a lossy phase shift,” Nat. Photonics 4, 357–360 (2010).

[Crossref]

G. Y. Xiang, T. C. Ralph, A. P. Lund, N. Walk, and G. J. Pryde, “Heralded noiseless linear amplification and distillation of entanglement,” Nat. Photonics 4, 316–319 (2010).

[Crossref]

A. Zavatta, J. Fiurášek, and M. Bellini, “A high-fidelity noiseless amplifier for quantum light states,” Nat. Photonics 5, 52–60 (2011).

[Crossref]

M. A. Usuga, C. R. Müller, C. Wittmann, P. Marek, R. Filip, C. Marquardt, G. Leuchs, and U. L. Andersen, “Noise-powered probabilistic concentration of phase information,” Nat. Phys. 6, 767–771 (2010).

[Crossref]

A. Ourjoumtsev, F. Ferreyrol, R. Tualle-Brouri, and P. Grangier, “Preparation of non-local superpositions of quasi-classical light states,” Nat. Phys. 5, 189–192 (2009).

[Crossref]

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature 429, 161–164 (2004).

[Crossref]

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature 429, 158–161 (2004).

[Crossref]

Y. Zhai, F. E. Becerra, B. L. Glebov, J. Wen, A. E. Lita, B. Calkins, T. Gerrits, J. Fan, S. W. Nam, and A. Migdall, “Photon-number-resolved detection of photon-subtracted thermal light,” Opt. Lett. 38, 2171–2173 (2013).

[Crossref]

R. A. Campos, C. C. Gerry, and A. Benmoussa, “Optical interferometry at the Heisenberg limit with twin Fock states and parity measurements,” Phys. Rev. A 68, 023810 (2003).

[Crossref]

D. Braun, P. Jian, O. Pinel, and N. Treps, “Precision measurements with photon-subtracted or photon-added Gaussian states,” Phys. Rev. A 90, 013821 (2014).

[Crossref]

C. I. Osorio, N. Bruno, N. Sangouard, H. Zbinden, N. Gisin, and R. T. Thew, “Heralded photon amplification for quantum communication,” Phys. Rev. A 86, 023815 (2012).

[Crossref]

C. M. Caves, “Quantum limits on noise in linear-amplifiers,” Phys. Rev. D 26, 1817–1839 (1982).

[Crossref]

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981).

[Crossref]

P. Grangier, R. E. Slusher, B. Yurke, and A. LaPorta, “Squeezed-light-enhanced polarization interferometer,” Phys. Rev. Lett. 59, 2153–2156 (1987).

[Crossref]

M. D’Angelo, M. V. Chekhova, and Y. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87, 013602 (2001).

[Crossref]

B. P. Abbott, et al., “Observation of gravitational waves from a binary black hole merger,” Phys. Rev. Lett. 116, 061102 (2016).

[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).

[Crossref]

F. Ferreyrol, M. Barbieri, R. Blandino, S. Fossier, R. Tualle-Brouri, and P. Grangier, “Implementation of a nondeterministic optical noiseless amplifier,” Phys. Rev. Lett. 104, 123603 (2010).

[Crossref]

F. T. Arecchi, “Measurement of the statistical distribution of Gaussian and laser sources,” Phys. Rev. Lett. 15, 912–916 (1965).

[Crossref]

J. Honer, R. Löw, H. Weimer, T. Pfau, and H. P. Büchler, “Artificial atoms can do more than atoms: deterministic single photon subtraction from arbitrary light fields,” Phys. Rev. Lett. 107, 093601 (2011).

[Crossref]

A. Zavatta, V. Parigi, M. S. Kim, H. Jeong, and M. Bellini, “Experimental demonstration of the bosonic commutation relation via superpositions of quantum operations on thermal light fields,” Phys. Rev. Lett. 103, 140406 (2009).

[Crossref]

M. D. Vidrighin, O. Dahlsten, M. Barbieri, M. S. Kim, V. Vedral, and I. A. Walmsley, “Photonic Maxwell’s demon,” Phys. Rev. Lett. 116, 050401 (2016).

[Crossref]

J. S. Neergaard-Nielsen, B. M. Nielsen, C. Hettich, K. Mølmer, and E. S. Polzik, “Generation of a superposition of odd photon number states for quantum information networks,” Phys. Rev. Lett. 97, 083604 (2006).

[Crossref]

J. Wenger, R. Tualle-Brouri, and P. Grangier, “Non-Gaussian statistics from individual pulses of squeezed light,” Phys. Rev. Lett. 92, 153601 (2004).

[Crossref]

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating optical Schrödinger kittens for quantum information processing,” Science 312, 83–86 (2006).

[Crossref]

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316, 726–729 (2007).

[Crossref]

V. Parigi, A. Zavatta, M. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890–1893 (2007).

[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science 306, 1330–1336 (2004).

e.g., Eq. (2) can be derived using a procedure described in Chap. 6 of C. C. Gerry and P. Knight, Introductory Quantum Optics (Cambridge University, 2004).

C. G. Parazzoli, B. E. Koltenbah, D. R. Gerwe, P. S. Idell, B. T. Gard, R. Birrittella, S. M. Hashemi Rafsanjani, M. Mirhosseini, O. S. Magana-Loaiza, J. P. Dowling, C. C. Gerry, R. W. Boyd, and B. C. Capron, “Enhanced thermal object imaging by photon addition and subtraction,” arXiv:1609:02780 (2016).