Abstract

Amplification of signals is an elemental function for many information processing systems and communication networks. However, optical quantum amplification has always been a technical challenge in both free space and fiber optics communication. Any phase-insensitive amplification of quantum light states would experience a degradation of signal-to-noise ratio as large as 3 dB for large gains. Fortunately, this degradation can be surmounted by probabilistic amplification processes. Here we experimentally demonstrate a linear amplification scheme for coherent input states that combines a heralded measurement-based noiseless linear amplifier and a deterministic linear amplifier. The amplifier is phase-insensitive and can enhance the signal-to-noise ratio of the incoming optical signal. By concatenating the two amplifiers, it introduces flexibility that allows one to tune between the regimes of high gain or high noise reduction and control the trade-off between these performances and a finite heralding probability. We demonstrate amplification with a signal transfer coefficient of Ts>1 with no statistical distortion of the output state. By partially relaxing the demand of output Gaussianity, we can obtain further improvement to achieve a Ts=2.55±0.08 with an amplification gain of 10.54. Since our amplification scheme only relies on linear optics and a post-selection algorithm, it has the potential of being used as a building block in extending the distance of quantum communication.

© 2017 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  29. R. Blandino, A. Leverrier, M. Barbieri, J. Etesse, P. Grangier, and R. Tualle-Brouri, “Improving the maximum transmission distance of continuous-variable quantum key distribution using a noiseless amplifier,” Phys. Rev. A 86, 012327 (2012).
    [Crossref]
  30. V. Josse, M. Sabuncu, N. Cerf, G. Leuchs, and U. Andersen, “Universal optical amplification without nonlinearity,” Phys. Rev. Lett. 96, 163602 (2006).
  31. J. Zhao, J. Y. Haw, T. Symul, P. K. Lam, and S. M. Assad, “Characterization of a measurement-based noiseless linear amplifier and its applications,” Phys. Rev. A 96, 012319 (2017).
    [Crossref]
  32. C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
    [Crossref]
  33. P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).
    [Crossref]
  34. T. C. Ralph, “Quantum error correction of continuous-variable states against Gaussian noise,” Phys. Rev. A 84, 022339 (2011).
    [Crossref]
  35. J. Dias and T. C. Ralph, “Quantum repeaters using continuous-variable teleportation,” Phys. Rev. A 95, 022312 (2017).
    [Crossref]
  36. P. Cochrane, T. C. Ralph, and A. Dolińska, “Optimal cloning for finite distributions of coherent states,” Phys. Rev. A 69, 042313 (2004).
    [Crossref]
  37. R. Blandino, N. Walk, A. P. Lund, and T. C. Ralph, “Channel purification via continuous-variable quantum teleportation with Gaussian postselection,” Phys. Rev. A 93, 012326 (2016).
    [Crossref]
  38. Q. He, L. Rosales-Zárate, G. Adesso, and M. D. Reid, “Secure continuous variable teleportation and Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 115, 180502 (2015).
    [Crossref]
  39. S. Makovejs, C. C. Roberts, F. Palacios, H. B. Matthews, D. A. Lewis, D. T. Smith, P. G. Diehl, J. J. Johnson, J. D. Patterson, C. R. Towery, and S. Y. Ten, “Record-low (0.1460  db/km) attenuation ultra-large Aeff optical fiber for submarine applications,” in Optical Fiber Communication Conference Post Deadline Papers, OSA Technical Digest (online) (Optical Society of America, 2015), paper . Th5A.2.

2017 (2)

J. Zhao, J. Y. Haw, T. Symul, P. K. Lam, and S. M. Assad, “Characterization of a measurement-based noiseless linear amplifier and its applications,” Phys. Rev. A 96, 012319 (2017).
[Crossref]

J. Dias and T. C. Ralph, “Quantum repeaters using continuous-variable teleportation,” Phys. Rev. A 95, 022312 (2017).
[Crossref]

2016 (3)

J. Y. Haw, J. Zhao, J. Dias, S. M. Assad, M. Bradshaw, R. Blandino, T. Symul, T. C. Ralph, and P. K. Lam, “Surpassing the no-cloning limit with a heralded hybrid linear amplifier for coherent states,” Nat. Commun. 7, 13222 (2016).
[Crossref]

J. Combes, N. Walk, A. P. Lund, T. C. Ralph, and C. M. Caves, “Models of reduced-noise, probabilistic linear amplifiers,” Phys. Rev. A 93, 052310 (2016).
[Crossref]

R. Blandino, N. Walk, A. P. Lund, and T. C. Ralph, “Channel purification via continuous-variable quantum teleportation with Gaussian postselection,” Phys. Rev. A 93, 012326 (2016).
[Crossref]

2015 (2)

Q. He, L. Rosales-Zárate, G. Adesso, and M. D. Reid, “Secure continuous variable teleportation and Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 115, 180502 (2015).
[Crossref]

A. E. Ulanov, I. A. Fedorov, A. A. Pushkina, Y. V. Kurochkin, T. C. Ralph, and A. I. Lvovsky, “Undoing the effect of loss on quantum entanglement,” Nat. Photonics 9, 764–768 (2015).
[Crossref]

2014 (2)

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5, 3049 (2014).
[Crossref]

H. M. Chrzanowski, N. Walk, S. M. Assad, J. Janousek, S. Hosseini, T. C. Ralph, T. Symul, and P. K. Lam, “Measurement-based noiseless linear amplification for quantum communication,” Nat. Photonics 8, 333–338 (2014).
[Crossref]

2013 (6)

J. Kong, F. Hudelist, Z. Y. Ou, and W. Zhang, “Cancellation of internal quantum noise of an amplifier by quantum correlation,” Phys. Rev. Lett. 111, 033608 (2013).
[Crossref]

N. Walk, A. P. Lund, and T. C. Ralph, “Nondeterministic noiseless amplification via non-symplectic phase space transformations,” New J. Phys. 15, 073014 (2013).
[Crossref]

S. Kocsis, G. Xiang, T. Ralph, and G. Pryde, “Heralded noiseless amplification of a photon polarization qubit,” Nat. Phys. 9, 23–28 (2013).
[Crossref]

S. Pandey, Z. Jiang, J. Combes, and C. M. Caves, “Quantum limits on probabilistic amplifiers,” Phys. Rev. A 88, 033852 (2013).
[Crossref]

N. Walk, T. C. Ralph, T. Symul, and P. K. Lam, “Security of continuous-variable quantum cryptography with Gaussian postselection,” Phys. Rev. A 87, 020303 (2013).
[Crossref]

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).
[Crossref]

2012 (4)

R. Blandino, A. Leverrier, M. Barbieri, J. Etesse, P. Grangier, and R. Tualle-Brouri, “Improving the maximum transmission distance of continuous-variable quantum key distribution using a noiseless amplifier,” Phys. Rev. A 86, 012327 (2012).
[Crossref]

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[Crossref]

J. Fiurśšek and N. J. Cerf, “Gaussian postselection and virtual noiseless amplification in continuous-variable quantum key distribution,” Phys. Rev. A 86, 060302 (2012).
[Crossref]

C. R. Müller, C. Wittmann, P. Marek, R. Filip, C. Marquardt, G. Leuchs, and U. L. Andersen, “Probabilistic cloning of coherent states without a phase reference,” Phys. Rev. A 86, 010305 (2012).
[Crossref]

2011 (3)

F. Ferreyrol, R. Blandino, M. Barbieri, R. Tualle-Brouri, and P. Grangier, “Experimental realization of a nondeterministic optical noiseless amplifier,” Phys. Rev. A 83, 063801 (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]

T. C. Ralph, “Quantum error correction of continuous-variable states against Gaussian noise,” Phys. Rev. A 84, 022339 (2011).
[Crossref]

2010 (3)

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]

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]

2009 (1)

T. C. Ralph and A. P. Lund, “Nondeterministic noiseless linear amplification of quantum systems,” AIP Conf. Proc. 1110, 155–160 (2009).

2006 (1)

V. Josse, M. Sabuncu, N. Cerf, G. Leuchs, and U. Andersen, “Universal optical amplification without nonlinearity,” Phys. Rev. Lett. 96, 163602 (2006).

2004 (2)

P. Cochrane, T. C. Ralph, and A. Dolińska, “Optimal cloning for finite distributions of coherent states,” Phys. Rev. A 69, 042313 (2004).
[Crossref]

J. Fiurášek, “Optimal probabilistic cloning and purification of quantum states,” Phys. Rev. A 70, 032308 (2004).
[Crossref]

1997 (1)

P. K. Lam, T. C. Ralph, E. H. Huntington, and H.-A. Bachor, “Noiseless signal amplification using positive electro-optic feedforward,” Phys. Rev. Lett. 79, 1471–1474 (1997).
[Crossref]

1993 (4)

J. A. Levenson, I. Abram, T. Rivera, and P. Grangier, “Reduction of quantum noise in optical parametric amplification,” J. Opt. Soc. Am. B 10, 2233–2238 (1993).
[Crossref]

J.-A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. Garreau, and P. Grangier, “Quantum optical cloning amplifier,” Phys. Rev. Lett. 70, 267–270 (1993).
[Crossref]

E. Goobar, A. Karlsson, G. Björk, and O. Nilsson, “Low-noise optoelectronic photon number amplifier and quantum-optical tap,” Opt. Lett. 18, 2138–2140 (1993).
[Crossref]

Z. Y. Ou, “Quantum amplification with correlated quantum fields,” Phys. Rev. A 48, R1761–R1764 (1993).
[Crossref]

1987 (1)

G. J. Milburn, M. L. Steyn-Ross, and D. F. Walls, “Linear amplifiers with phase-sensitive noise,” Phys. Rev. A 35, 4443–4445 (1987).
[Crossref]

1984 (1)

B. Yurke, “Use of cavities in squeezed-state generation,” Phys. Rev. A 29, 408–410 (1984).
[Crossref]

1982 (1)

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

1962 (1)

H. A. Haus and J. A. Mullen, “Quantum noise in linear amplifiers,” Phys. Rev. 128, 2407–2413 (1962).
[Crossref]

Abram, I.

J. A. Levenson, I. Abram, T. Rivera, and P. Grangier, “Reduction of quantum noise in optical parametric amplification,” J. Opt. Soc. Am. B 10, 2233–2238 (1993).
[Crossref]

J.-A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. Garreau, and P. Grangier, “Quantum optical cloning amplifier,” Phys. Rev. Lett. 70, 267–270 (1993).
[Crossref]

Adesso, G.

Q. He, L. Rosales-Zárate, G. Adesso, and M. D. Reid, “Secure continuous variable teleportation and Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 115, 180502 (2015).
[Crossref]

Andersen, U.

V. Josse, M. Sabuncu, N. Cerf, G. Leuchs, and U. Andersen, “Universal optical amplification without nonlinearity,” Phys. Rev. Lett. 96, 163602 (2006).

Andersen, U. L.

C. R. Müller, C. Wittmann, P. Marek, R. Filip, C. Marquardt, G. Leuchs, and U. L. Andersen, “Probabilistic cloning of coherent states without a phase reference,” Phys. Rev. A 86, 010305 (2012).
[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]

Assad, S. M.

J. Zhao, J. Y. Haw, T. Symul, P. K. Lam, and S. M. Assad, “Characterization of a measurement-based noiseless linear amplifier and its applications,” Phys. Rev. A 96, 012319 (2017).
[Crossref]

J. Y. Haw, J. Zhao, J. Dias, S. M. Assad, M. Bradshaw, R. Blandino, T. Symul, T. C. Ralph, and P. K. Lam, “Surpassing the no-cloning limit with a heralded hybrid linear amplifier for coherent states,” Nat. Commun. 7, 13222 (2016).
[Crossref]

H. M. Chrzanowski, N. Walk, S. M. Assad, J. Janousek, S. Hosseini, T. C. Ralph, T. Symul, and P. K. Lam, “Measurement-based noiseless linear amplification for quantum communication,” Nat. Photonics 8, 333–338 (2014).
[Crossref]

Bachor, H.-A.

P. K. Lam, T. C. Ralph, E. H. Huntington, and H.-A. Bachor, “Noiseless signal amplification using positive electro-optic feedforward,” Phys. Rev. Lett. 79, 1471–1474 (1997).
[Crossref]

Barbieri, M.

R. Blandino, A. Leverrier, M. Barbieri, J. Etesse, P. Grangier, and R. Tualle-Brouri, “Improving the maximum transmission distance of continuous-variable quantum key distribution using a noiseless amplifier,” Phys. Rev. A 86, 012327 (2012).
[Crossref]

F. Ferreyrol, R. Blandino, M. Barbieri, R. Tualle-Brouri, and P. Grangier, “Experimental realization of a nondeterministic optical noiseless amplifier,” Phys. Rev. A 83, 063801 (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]

Bellini, M.

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

Björk, G.

Blandino, R.

J. Y. Haw, J. Zhao, J. Dias, S. M. Assad, M. Bradshaw, R. Blandino, T. Symul, T. C. Ralph, and P. K. Lam, “Surpassing the no-cloning limit with a heralded hybrid linear amplifier for coherent states,” Nat. Commun. 7, 13222 (2016).
[Crossref]

R. Blandino, N. Walk, A. P. Lund, and T. C. Ralph, “Channel purification via continuous-variable quantum teleportation with Gaussian postselection,” Phys. Rev. A 93, 012326 (2016).
[Crossref]

R. Blandino, A. Leverrier, M. Barbieri, J. Etesse, P. Grangier, and R. Tualle-Brouri, “Improving the maximum transmission distance of continuous-variable quantum key distribution using a noiseless amplifier,” Phys. Rev. A 86, 012327 (2012).
[Crossref]

F. Ferreyrol, R. Blandino, M. Barbieri, R. Tualle-Brouri, and P. Grangier, “Experimental realization of a nondeterministic optical noiseless amplifier,” Phys. Rev. A 83, 063801 (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]

Bradshaw, M.

J. Y. Haw, J. Zhao, J. Dias, S. M. Assad, M. Bradshaw, R. Blandino, T. Symul, T. C. Ralph, and P. K. Lam, “Surpassing the no-cloning limit with a heralded hybrid linear amplifier for coherent states,” Nat. Commun. 7, 13222 (2016).
[Crossref]

Caves, C.

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

Caves, C. M.

J. Combes, N. Walk, A. P. Lund, T. C. Ralph, and C. M. Caves, “Models of reduced-noise, probabilistic linear amplifiers,” Phys. Rev. A 93, 052310 (2016).
[Crossref]

S. Pandey, Z. Jiang, J. Combes, and C. M. Caves, “Quantum limits on probabilistic amplifiers,” Phys. Rev. A 88, 033852 (2013).
[Crossref]

Cerf, N.

V. Josse, M. Sabuncu, N. Cerf, G. Leuchs, and U. Andersen, “Universal optical amplification without nonlinearity,” Phys. Rev. Lett. 96, 163602 (2006).

Cerf, N. J.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[Crossref]

J. Fiurśšek and N. J. Cerf, “Gaussian postselection and virtual noiseless amplification in continuous-variable quantum key distribution,” Phys. Rev. A 86, 060302 (2012).
[Crossref]

Chrzanowski, H. M.

H. M. Chrzanowski, N. Walk, S. M. Assad, J. Janousek, S. Hosseini, T. C. Ralph, T. Symul, and P. K. Lam, “Measurement-based noiseless linear amplification for quantum communication,” Nat. Photonics 8, 333–338 (2014).
[Crossref]

Cochrane, P.

P. Cochrane, T. C. Ralph, and A. Dolińska, “Optimal cloning for finite distributions of coherent states,” Phys. Rev. A 69, 042313 (2004).
[Crossref]

Combes, J.

J. Combes, N. Walk, A. P. Lund, T. C. Ralph, and C. M. Caves, “Models of reduced-noise, probabilistic linear amplifiers,” Phys. Rev. A 93, 052310 (2016).
[Crossref]

S. Pandey, Z. Jiang, J. Combes, and C. M. Caves, “Quantum limits on probabilistic amplifiers,” Phys. Rev. A 88, 033852 (2013).
[Crossref]

Diamanti, E.

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).
[Crossref]

Dias, J.

J. Dias and T. C. Ralph, “Quantum repeaters using continuous-variable teleportation,” Phys. Rev. A 95, 022312 (2017).
[Crossref]

J. Y. Haw, J. Zhao, J. Dias, S. M. Assad, M. Bradshaw, R. Blandino, T. Symul, T. C. Ralph, and P. K. Lam, “Surpassing the no-cloning limit with a heralded hybrid linear amplifier for coherent states,” Nat. Commun. 7, 13222 (2016).
[Crossref]

Diehl, P. G.

S. Makovejs, C. C. Roberts, F. Palacios, H. B. Matthews, D. A. Lewis, D. T. Smith, P. G. Diehl, J. J. Johnson, J. D. Patterson, C. R. Towery, and S. Y. Ten, “Record-low (0.1460  db/km) attenuation ultra-large Aeff optical fiber for submarine applications,” in Optical Fiber Communication Conference Post Deadline Papers, OSA Technical Digest (online) (Optical Society of America, 2015), paper . Th5A.2.

Dolinska, A.

P. Cochrane, T. C. Ralph, and A. Dolińska, “Optimal cloning for finite distributions of coherent states,” Phys. Rev. A 69, 042313 (2004).
[Crossref]

Etesse, J.

R. Blandino, A. Leverrier, M. Barbieri, J. Etesse, P. Grangier, and R. Tualle-Brouri, “Improving the maximum transmission distance of continuous-variable quantum key distribution using a noiseless amplifier,” Phys. Rev. A 86, 012327 (2012).
[Crossref]

Fayolle, P.

J.-A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. Garreau, and P. Grangier, “Quantum optical cloning amplifier,” Phys. Rev. Lett. 70, 267–270 (1993).
[Crossref]

Fedorov, I. A.

A. E. Ulanov, I. A. Fedorov, A. A. Pushkina, Y. V. Kurochkin, T. C. Ralph, and A. I. Lvovsky, “Undoing the effect of loss on quantum entanglement,” Nat. Photonics 9, 764–768 (2015).
[Crossref]

Ferreyrol, F.

F. Ferreyrol, R. Blandino, M. Barbieri, R. Tualle-Brouri, and P. Grangier, “Experimental realization of a nondeterministic optical noiseless amplifier,” Phys. Rev. A 83, 063801 (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]

Filip, R.

C. R. Müller, C. Wittmann, P. Marek, R. Filip, C. Marquardt, G. Leuchs, and U. L. Andersen, “Probabilistic cloning of coherent states without a phase reference,” Phys. Rev. A 86, 010305 (2012).
[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]

Fiurášek, J.

A. Zavatta, J. Fiurášek, and M. Bellini, “A high-fidelity noiseless amplifier for quantum light states,” Nat. Photonics 5, 52–60 (2011).
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J. Fiurášek, “Optimal probabilistic cloning and purification of quantum states,” Phys. Rev. A 70, 032308 (2004).
[Crossref]

Fiursšek, J.

J. Fiurśšek and N. J. Cerf, “Gaussian postselection and virtual noiseless amplification in continuous-variable quantum key distribution,” Phys. Rev. A 86, 060302 (2012).
[Crossref]

Fossier, S.

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]

García-Patrón, R.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[Crossref]

Garreau, J.

J.-A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. Garreau, and P. Grangier, “Quantum optical cloning amplifier,” Phys. Rev. Lett. 70, 267–270 (1993).
[Crossref]

Goobar, E.

Grangier, P.

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).
[Crossref]

R. Blandino, A. Leverrier, M. Barbieri, J. Etesse, P. Grangier, and R. Tualle-Brouri, “Improving the maximum transmission distance of continuous-variable quantum key distribution using a noiseless amplifier,” Phys. Rev. A 86, 012327 (2012).
[Crossref]

F. Ferreyrol, R. Blandino, M. Barbieri, R. Tualle-Brouri, and P. Grangier, “Experimental realization of a nondeterministic optical noiseless amplifier,” Phys. Rev. A 83, 063801 (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]

J.-A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. Garreau, and P. Grangier, “Quantum optical cloning amplifier,” Phys. Rev. Lett. 70, 267–270 (1993).
[Crossref]

J. A. Levenson, I. Abram, T. Rivera, and P. Grangier, “Reduction of quantum noise in optical parametric amplification,” J. Opt. Soc. Am. B 10, 2233–2238 (1993).
[Crossref]

Haus, H. A.

H. A. Haus and J. A. Mullen, “Quantum noise in linear amplifiers,” Phys. Rev. 128, 2407–2413 (1962).
[Crossref]

Haw, J. Y.

J. Zhao, J. Y. Haw, T. Symul, P. K. Lam, and S. M. Assad, “Characterization of a measurement-based noiseless linear amplifier and its applications,” Phys. Rev. A 96, 012319 (2017).
[Crossref]

J. Y. Haw, J. Zhao, J. Dias, S. M. Assad, M. Bradshaw, R. Blandino, T. Symul, T. C. Ralph, and P. K. Lam, “Surpassing the no-cloning limit with a heralded hybrid linear amplifier for coherent states,” Nat. Commun. 7, 13222 (2016).
[Crossref]

He, Q.

Q. He, L. Rosales-Zárate, G. Adesso, and M. D. Reid, “Secure continuous variable teleportation and Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 115, 180502 (2015).
[Crossref]

Hosseini, S.

H. M. Chrzanowski, N. Walk, S. M. Assad, J. Janousek, S. Hosseini, T. C. Ralph, T. Symul, and P. K. Lam, “Measurement-based noiseless linear amplification for quantum communication,” Nat. Photonics 8, 333–338 (2014).
[Crossref]

Hudelist, F.

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5, 3049 (2014).
[Crossref]

J. Kong, F. Hudelist, Z. Y. Ou, and W. Zhang, “Cancellation of internal quantum noise of an amplifier by quantum correlation,” Phys. Rev. Lett. 111, 033608 (2013).
[Crossref]

Huntington, E. H.

P. K. Lam, T. C. Ralph, E. H. Huntington, and H.-A. Bachor, “Noiseless signal amplification using positive electro-optic feedforward,” Phys. Rev. Lett. 79, 1471–1474 (1997).
[Crossref]

Janousek, J.

H. M. Chrzanowski, N. Walk, S. M. Assad, J. Janousek, S. Hosseini, T. C. Ralph, T. Symul, and P. K. Lam, “Measurement-based noiseless linear amplification for quantum communication,” Nat. Photonics 8, 333–338 (2014).
[Crossref]

Jiang, Z.

S. Pandey, Z. Jiang, J. Combes, and C. M. Caves, “Quantum limits on probabilistic amplifiers,” Phys. Rev. A 88, 033852 (2013).
[Crossref]

Jing, J.

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5, 3049 (2014).
[Crossref]

Johnson, J. J.

S. Makovejs, C. C. Roberts, F. Palacios, H. B. Matthews, D. A. Lewis, D. T. Smith, P. G. Diehl, J. J. Johnson, J. D. Patterson, C. R. Towery, and S. Y. Ten, “Record-low (0.1460  db/km) attenuation ultra-large Aeff optical fiber for submarine applications,” in Optical Fiber Communication Conference Post Deadline Papers, OSA Technical Digest (online) (Optical Society of America, 2015), paper . Th5A.2.

Josse, V.

V. Josse, M. Sabuncu, N. Cerf, G. Leuchs, and U. Andersen, “Universal optical amplification without nonlinearity,” Phys. Rev. Lett. 96, 163602 (2006).

Jouguet, P.

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).
[Crossref]

Karlsson, A.

Kocsis, S.

S. Kocsis, G. Xiang, T. Ralph, and G. Pryde, “Heralded noiseless amplification of a photon polarization qubit,” Nat. Phys. 9, 23–28 (2013).
[Crossref]

Kong, J.

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5, 3049 (2014).
[Crossref]

J. Kong, F. Hudelist, Z. Y. Ou, and W. Zhang, “Cancellation of internal quantum noise of an amplifier by quantum correlation,” Phys. Rev. Lett. 111, 033608 (2013).
[Crossref]

Kunz-Jacques, S.

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).
[Crossref]

Kurochkin, Y. V.

A. E. Ulanov, I. A. Fedorov, A. A. Pushkina, Y. V. Kurochkin, T. C. Ralph, and A. I. Lvovsky, “Undoing the effect of loss on quantum entanglement,” Nat. Photonics 9, 764–768 (2015).
[Crossref]

Lam, P. K.

J. Zhao, J. Y. Haw, T. Symul, P. K. Lam, and S. M. Assad, “Characterization of a measurement-based noiseless linear amplifier and its applications,” Phys. Rev. A 96, 012319 (2017).
[Crossref]

J. Y. Haw, J. Zhao, J. Dias, S. M. Assad, M. Bradshaw, R. Blandino, T. Symul, T. C. Ralph, and P. K. Lam, “Surpassing the no-cloning limit with a heralded hybrid linear amplifier for coherent states,” Nat. Commun. 7, 13222 (2016).
[Crossref]

H. M. Chrzanowski, N. Walk, S. M. Assad, J. Janousek, S. Hosseini, T. C. Ralph, T. Symul, and P. K. Lam, “Measurement-based noiseless linear amplification for quantum communication,” Nat. Photonics 8, 333–338 (2014).
[Crossref]

N. Walk, T. C. Ralph, T. Symul, and P. K. Lam, “Security of continuous-variable quantum cryptography with Gaussian postselection,” Phys. Rev. A 87, 020303 (2013).
[Crossref]

P. K. Lam, T. C. Ralph, E. H. Huntington, and H.-A. Bachor, “Noiseless signal amplification using positive electro-optic feedforward,” Phys. Rev. Lett. 79, 1471–1474 (1997).
[Crossref]

Leuchs, G.

C. R. Müller, C. Wittmann, P. Marek, R. Filip, C. Marquardt, G. Leuchs, and U. L. Andersen, “Probabilistic cloning of coherent states without a phase reference,” Phys. Rev. A 86, 010305 (2012).
[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]

V. Josse, M. Sabuncu, N. Cerf, G. Leuchs, and U. Andersen, “Universal optical amplification without nonlinearity,” Phys. Rev. Lett. 96, 163602 (2006).

Levenson, J. A.

Levenson, J.-A.

J.-A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. Garreau, and P. Grangier, “Quantum optical cloning amplifier,” Phys. Rev. Lett. 70, 267–270 (1993).
[Crossref]

Leverrier, A.

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).
[Crossref]

R. Blandino, A. Leverrier, M. Barbieri, J. Etesse, P. Grangier, and R. Tualle-Brouri, “Improving the maximum transmission distance of continuous-variable quantum key distribution using a noiseless amplifier,” Phys. Rev. A 86, 012327 (2012).
[Crossref]

Lewis, D. A.

S. Makovejs, C. C. Roberts, F. Palacios, H. B. Matthews, D. A. Lewis, D. T. Smith, P. G. Diehl, J. J. Johnson, J. D. Patterson, C. R. Towery, and S. Y. Ten, “Record-low (0.1460  db/km) attenuation ultra-large Aeff optical fiber for submarine applications,” in Optical Fiber Communication Conference Post Deadline Papers, OSA Technical Digest (online) (Optical Society of America, 2015), paper . Th5A.2.

Liu, C.

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5, 3049 (2014).
[Crossref]

Lloyd, S.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[Crossref]

Lund, A. P.

R. Blandino, N. Walk, A. P. Lund, and T. C. Ralph, “Channel purification via continuous-variable quantum teleportation with Gaussian postselection,” Phys. Rev. A 93, 012326 (2016).
[Crossref]

J. Combes, N. Walk, A. P. Lund, T. C. Ralph, and C. M. Caves, “Models of reduced-noise, probabilistic linear amplifiers,” Phys. Rev. A 93, 052310 (2016).
[Crossref]

N. Walk, A. P. Lund, and T. C. Ralph, “Nondeterministic noiseless amplification via non-symplectic phase space transformations,” New J. Phys. 15, 073014 (2013).
[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]

T. C. Ralph and A. P. Lund, “Nondeterministic noiseless linear amplification of quantum systems,” AIP Conf. Proc. 1110, 155–160 (2009).

Lvovsky, A. I.

A. E. Ulanov, I. A. Fedorov, A. A. Pushkina, Y. V. Kurochkin, T. C. Ralph, and A. I. Lvovsky, “Undoing the effect of loss on quantum entanglement,” Nat. Photonics 9, 764–768 (2015).
[Crossref]

Makovejs, S.

S. Makovejs, C. C. Roberts, F. Palacios, H. B. Matthews, D. A. Lewis, D. T. Smith, P. G. Diehl, J. J. Johnson, J. D. Patterson, C. R. Towery, and S. Y. Ten, “Record-low (0.1460  db/km) attenuation ultra-large Aeff optical fiber for submarine applications,” in Optical Fiber Communication Conference Post Deadline Papers, OSA Technical Digest (online) (Optical Society of America, 2015), paper . Th5A.2.

Marek, P.

C. R. Müller, C. Wittmann, P. Marek, R. Filip, C. Marquardt, G. Leuchs, and U. L. Andersen, “Probabilistic cloning of coherent states without a phase reference,” Phys. Rev. A 86, 010305 (2012).
[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]

Marquardt, C.

C. R. Müller, C. Wittmann, P. Marek, R. Filip, C. Marquardt, G. Leuchs, and U. L. Andersen, “Probabilistic cloning of coherent states without a phase reference,” Phys. Rev. A 86, 010305 (2012).
[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]

Matthews, H. B.

S. Makovejs, C. C. Roberts, F. Palacios, H. B. Matthews, D. A. Lewis, D. T. Smith, P. G. Diehl, J. J. Johnson, J. D. Patterson, C. R. Towery, and S. Y. Ten, “Record-low (0.1460  db/km) attenuation ultra-large Aeff optical fiber for submarine applications,” in Optical Fiber Communication Conference Post Deadline Papers, OSA Technical Digest (online) (Optical Society of America, 2015), paper . Th5A.2.

Milburn, G. J.

G. J. Milburn, M. L. Steyn-Ross, and D. F. Walls, “Linear amplifiers with phase-sensitive noise,” Phys. Rev. A 35, 4443–4445 (1987).
[Crossref]

Mullen, J. A.

H. A. Haus and J. A. Mullen, “Quantum noise in linear amplifiers,” Phys. Rev. 128, 2407–2413 (1962).
[Crossref]

Müller, C. R.

C. R. Müller, C. Wittmann, P. Marek, R. Filip, C. Marquardt, G. Leuchs, and U. L. Andersen, “Probabilistic cloning of coherent states without a phase reference,” Phys. Rev. A 86, 010305 (2012).
[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]

Nilsson, O.

Ou, Z.

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5, 3049 (2014).
[Crossref]

Ou, Z. Y.

J. Kong, F. Hudelist, Z. Y. Ou, and W. Zhang, “Cancellation of internal quantum noise of an amplifier by quantum correlation,” Phys. Rev. Lett. 111, 033608 (2013).
[Crossref]

Z. Y. Ou, “Quantum amplification with correlated quantum fields,” Phys. Rev. A 48, R1761–R1764 (1993).
[Crossref]

Palacios, F.

S. Makovejs, C. C. Roberts, F. Palacios, H. B. Matthews, D. A. Lewis, D. T. Smith, P. G. Diehl, J. J. Johnson, J. D. Patterson, C. R. Towery, and S. Y. Ten, “Record-low (0.1460  db/km) attenuation ultra-large Aeff optical fiber for submarine applications,” in Optical Fiber Communication Conference Post Deadline Papers, OSA Technical Digest (online) (Optical Society of America, 2015), paper . Th5A.2.

Pandey, S.

S. Pandey, Z. Jiang, J. Combes, and C. M. Caves, “Quantum limits on probabilistic amplifiers,” Phys. Rev. A 88, 033852 (2013).
[Crossref]

Patterson, J. D.

S. Makovejs, C. C. Roberts, F. Palacios, H. B. Matthews, D. A. Lewis, D. T. Smith, P. G. Diehl, J. J. Johnson, J. D. Patterson, C. R. Towery, and S. Y. Ten, “Record-low (0.1460  db/km) attenuation ultra-large Aeff optical fiber for submarine applications,” in Optical Fiber Communication Conference Post Deadline Papers, OSA Technical Digest (online) (Optical Society of America, 2015), paper . Th5A.2.

Pirandola, S.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[Crossref]

Pryde, G.

S. Kocsis, G. Xiang, T. Ralph, and G. Pryde, “Heralded noiseless amplification of a photon polarization qubit,” Nat. Phys. 9, 23–28 (2013).
[Crossref]

Pryde, G. J.

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]

Pushkina, A. A.

A. E. Ulanov, I. A. Fedorov, A. A. Pushkina, Y. V. Kurochkin, T. C. Ralph, and A. I. Lvovsky, “Undoing the effect of loss on quantum entanglement,” Nat. Photonics 9, 764–768 (2015).
[Crossref]

Ralph, T.

S. Kocsis, G. Xiang, T. Ralph, and G. Pryde, “Heralded noiseless amplification of a photon polarization qubit,” Nat. Phys. 9, 23–28 (2013).
[Crossref]

Ralph, T. C.

J. Dias and T. C. Ralph, “Quantum repeaters using continuous-variable teleportation,” Phys. Rev. A 95, 022312 (2017).
[Crossref]

R. Blandino, N. Walk, A. P. Lund, and T. C. Ralph, “Channel purification via continuous-variable quantum teleportation with Gaussian postselection,” Phys. Rev. A 93, 012326 (2016).
[Crossref]

J. Combes, N. Walk, A. P. Lund, T. C. Ralph, and C. M. Caves, “Models of reduced-noise, probabilistic linear amplifiers,” Phys. Rev. A 93, 052310 (2016).
[Crossref]

J. Y. Haw, J. Zhao, J. Dias, S. M. Assad, M. Bradshaw, R. Blandino, T. Symul, T. C. Ralph, and P. K. Lam, “Surpassing the no-cloning limit with a heralded hybrid linear amplifier for coherent states,” Nat. Commun. 7, 13222 (2016).
[Crossref]

A. E. Ulanov, I. A. Fedorov, A. A. Pushkina, Y. V. Kurochkin, T. C. Ralph, and A. I. Lvovsky, “Undoing the effect of loss on quantum entanglement,” Nat. Photonics 9, 764–768 (2015).
[Crossref]

H. M. Chrzanowski, N. Walk, S. M. Assad, J. Janousek, S. Hosseini, T. C. Ralph, T. Symul, and P. K. Lam, “Measurement-based noiseless linear amplification for quantum communication,” Nat. Photonics 8, 333–338 (2014).
[Crossref]

N. Walk, T. C. Ralph, T. Symul, and P. K. Lam, “Security of continuous-variable quantum cryptography with Gaussian postselection,” Phys. Rev. A 87, 020303 (2013).
[Crossref]

N. Walk, A. P. Lund, and T. C. Ralph, “Nondeterministic noiseless amplification via non-symplectic phase space transformations,” New J. Phys. 15, 073014 (2013).
[Crossref]

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[Crossref]

T. C. Ralph, “Quantum error correction of continuous-variable states against Gaussian noise,” Phys. Rev. A 84, 022339 (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]

T. C. Ralph and A. P. Lund, “Nondeterministic noiseless linear amplification of quantum systems,” AIP Conf. Proc. 1110, 155–160 (2009).

P. Cochrane, T. C. Ralph, and A. Dolińska, “Optimal cloning for finite distributions of coherent states,” Phys. Rev. A 69, 042313 (2004).
[Crossref]

P. K. Lam, T. C. Ralph, E. H. Huntington, and H.-A. Bachor, “Noiseless signal amplification using positive electro-optic feedforward,” Phys. Rev. Lett. 79, 1471–1474 (1997).
[Crossref]

Reid, M. D.

Q. He, L. Rosales-Zárate, G. Adesso, and M. D. Reid, “Secure continuous variable teleportation and Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 115, 180502 (2015).
[Crossref]

Rivera, T.

J.-A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. Garreau, and P. Grangier, “Quantum optical cloning amplifier,” Phys. Rev. Lett. 70, 267–270 (1993).
[Crossref]

J. A. Levenson, I. Abram, T. Rivera, and P. Grangier, “Reduction of quantum noise in optical parametric amplification,” J. Opt. Soc. Am. B 10, 2233–2238 (1993).
[Crossref]

Roberts, C. C.

S. Makovejs, C. C. Roberts, F. Palacios, H. B. Matthews, D. A. Lewis, D. T. Smith, P. G. Diehl, J. J. Johnson, J. D. Patterson, C. R. Towery, and S. Y. Ten, “Record-low (0.1460  db/km) attenuation ultra-large Aeff optical fiber for submarine applications,” in Optical Fiber Communication Conference Post Deadline Papers, OSA Technical Digest (online) (Optical Society of America, 2015), paper . Th5A.2.

Rosales-Zárate, L.

Q. He, L. Rosales-Zárate, G. Adesso, and M. D. Reid, “Secure continuous variable teleportation and Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 115, 180502 (2015).
[Crossref]

Sabuncu, M.

V. Josse, M. Sabuncu, N. Cerf, G. Leuchs, and U. Andersen, “Universal optical amplification without nonlinearity,” Phys. Rev. Lett. 96, 163602 (2006).

Shapiro, J. H.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[Crossref]

Smith, D. T.

S. Makovejs, C. C. Roberts, F. Palacios, H. B. Matthews, D. A. Lewis, D. T. Smith, P. G. Diehl, J. J. Johnson, J. D. Patterson, C. R. Towery, and S. Y. Ten, “Record-low (0.1460  db/km) attenuation ultra-large Aeff optical fiber for submarine applications,” in Optical Fiber Communication Conference Post Deadline Papers, OSA Technical Digest (online) (Optical Society of America, 2015), paper . Th5A.2.

Steyn-Ross, M. L.

G. J. Milburn, M. L. Steyn-Ross, and D. F. Walls, “Linear amplifiers with phase-sensitive noise,” Phys. Rev. A 35, 4443–4445 (1987).
[Crossref]

Symul, T.

J. Zhao, J. Y. Haw, T. Symul, P. K. Lam, and S. M. Assad, “Characterization of a measurement-based noiseless linear amplifier and its applications,” Phys. Rev. A 96, 012319 (2017).
[Crossref]

J. Y. Haw, J. Zhao, J. Dias, S. M. Assad, M. Bradshaw, R. Blandino, T. Symul, T. C. Ralph, and P. K. Lam, “Surpassing the no-cloning limit with a heralded hybrid linear amplifier for coherent states,” Nat. Commun. 7, 13222 (2016).
[Crossref]

H. M. Chrzanowski, N. Walk, S. M. Assad, J. Janousek, S. Hosseini, T. C. Ralph, T. Symul, and P. K. Lam, “Measurement-based noiseless linear amplification for quantum communication,” Nat. Photonics 8, 333–338 (2014).
[Crossref]

N. Walk, T. C. Ralph, T. Symul, and P. K. Lam, “Security of continuous-variable quantum cryptography with Gaussian postselection,” Phys. Rev. A 87, 020303 (2013).
[Crossref]

Ten, S. Y.

S. Makovejs, C. C. Roberts, F. Palacios, H. B. Matthews, D. A. Lewis, D. T. Smith, P. G. Diehl, J. J. Johnson, J. D. Patterson, C. R. Towery, and S. Y. Ten, “Record-low (0.1460  db/km) attenuation ultra-large Aeff optical fiber for submarine applications,” in Optical Fiber Communication Conference Post Deadline Papers, OSA Technical Digest (online) (Optical Society of America, 2015), paper . Th5A.2.

Towery, C. R.

S. Makovejs, C. C. Roberts, F. Palacios, H. B. Matthews, D. A. Lewis, D. T. Smith, P. G. Diehl, J. J. Johnson, J. D. Patterson, C. R. Towery, and S. Y. Ten, “Record-low (0.1460  db/km) attenuation ultra-large Aeff optical fiber for submarine applications,” in Optical Fiber Communication Conference Post Deadline Papers, OSA Technical Digest (online) (Optical Society of America, 2015), paper . Th5A.2.

Tualle-Brouri, R.

R. Blandino, A. Leverrier, M. Barbieri, J. Etesse, P. Grangier, and R. Tualle-Brouri, “Improving the maximum transmission distance of continuous-variable quantum key distribution using a noiseless amplifier,” Phys. Rev. A 86, 012327 (2012).
[Crossref]

F. Ferreyrol, R. Blandino, M. Barbieri, R. Tualle-Brouri, and P. Grangier, “Experimental realization of a nondeterministic optical noiseless amplifier,” Phys. Rev. A 83, 063801 (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]

Ulanov, A. E.

A. E. Ulanov, I. A. Fedorov, A. A. Pushkina, Y. V. Kurochkin, T. C. Ralph, and A. I. Lvovsky, “Undoing the effect of loss on quantum entanglement,” Nat. Photonics 9, 764–768 (2015).
[Crossref]

Usuga, M. A.

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]

Walk, N.

J. Combes, N. Walk, A. P. Lund, T. C. Ralph, and C. M. Caves, “Models of reduced-noise, probabilistic linear amplifiers,” Phys. Rev. A 93, 052310 (2016).
[Crossref]

R. Blandino, N. Walk, A. P. Lund, and T. C. Ralph, “Channel purification via continuous-variable quantum teleportation with Gaussian postselection,” Phys. Rev. A 93, 012326 (2016).
[Crossref]

H. M. Chrzanowski, N. Walk, S. M. Assad, J. Janousek, S. Hosseini, T. C. Ralph, T. Symul, and P. K. Lam, “Measurement-based noiseless linear amplification for quantum communication,” Nat. Photonics 8, 333–338 (2014).
[Crossref]

N. Walk, T. C. Ralph, T. Symul, and P. K. Lam, “Security of continuous-variable quantum cryptography with Gaussian postselection,” Phys. Rev. A 87, 020303 (2013).
[Crossref]

N. Walk, A. P. Lund, and T. C. Ralph, “Nondeterministic noiseless amplification via non-symplectic phase space transformations,” New J. Phys. 15, 073014 (2013).
[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]

Walls, D. F.

G. J. Milburn, M. L. Steyn-Ross, and D. F. Walls, “Linear amplifiers with phase-sensitive noise,” Phys. Rev. A 35, 4443–4445 (1987).
[Crossref]

Weedbrook, C.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[Crossref]

Wittmann, C.

C. R. Müller, C. Wittmann, P. Marek, R. Filip, C. Marquardt, G. Leuchs, and U. L. Andersen, “Probabilistic cloning of coherent states without a phase reference,” Phys. Rev. A 86, 010305 (2012).
[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]

Xiang, G.

S. Kocsis, G. Xiang, T. Ralph, and G. Pryde, “Heralded noiseless amplification of a photon polarization qubit,” Nat. Phys. 9, 23–28 (2013).
[Crossref]

Xiang, G. Y.

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]

Yurke, B.

B. Yurke, “Use of cavities in squeezed-state generation,” Phys. Rev. A 29, 408–410 (1984).
[Crossref]

Zavatta, A.

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

Zhang, W.

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5, 3049 (2014).
[Crossref]

J. Kong, F. Hudelist, Z. Y. Ou, and W. Zhang, “Cancellation of internal quantum noise of an amplifier by quantum correlation,” Phys. Rev. Lett. 111, 033608 (2013).
[Crossref]

Zhao, J.

J. Zhao, J. Y. Haw, T. Symul, P. K. Lam, and S. M. Assad, “Characterization of a measurement-based noiseless linear amplifier and its applications,” Phys. Rev. A 96, 012319 (2017).
[Crossref]

J. Y. Haw, J. Zhao, J. Dias, S. M. Assad, M. Bradshaw, R. Blandino, T. Symul, T. C. Ralph, and P. K. Lam, “Surpassing the no-cloning limit with a heralded hybrid linear amplifier for coherent states,” Nat. Commun. 7, 13222 (2016).
[Crossref]

AIP Conf. Proc. (1)

T. C. Ralph and A. P. Lund, “Nondeterministic noiseless linear amplification of quantum systems,” AIP Conf. Proc. 1110, 155–160 (2009).

J. Opt. Soc. Am. B (1)

Nat. Commun. (2)

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5, 3049 (2014).
[Crossref]

J. Y. Haw, J. Zhao, J. Dias, S. M. Assad, M. Bradshaw, R. Blandino, T. Symul, T. C. Ralph, and P. K. Lam, “Surpassing the no-cloning limit with a heralded hybrid linear amplifier for coherent states,” Nat. Commun. 7, 13222 (2016).
[Crossref]

Nat. Photonics (5)

H. M. Chrzanowski, N. Walk, S. M. Assad, J. Janousek, S. Hosseini, T. C. Ralph, T. Symul, and P. K. Lam, “Measurement-based noiseless linear amplification for quantum communication,” Nat. Photonics 8, 333–338 (2014).
[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. E. Ulanov, I. A. Fedorov, A. A. Pushkina, Y. V. Kurochkin, T. C. Ralph, and A. I. Lvovsky, “Undoing the effect of loss on quantum entanglement,” Nat. Photonics 9, 764–768 (2015).
[Crossref]

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).
[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]

Nat. Phys. (2)

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]

S. Kocsis, G. Xiang, T. Ralph, and G. Pryde, “Heralded noiseless amplification of a photon polarization qubit,” Nat. Phys. 9, 23–28 (2013).
[Crossref]

New J. Phys. (1)

N. Walk, A. P. Lund, and T. C. Ralph, “Nondeterministic noiseless amplification via non-symplectic phase space transformations,” New J. Phys. 15, 073014 (2013).
[Crossref]

Opt. Lett. (1)

Phys. Rev. (1)

H. A. Haus and J. A. Mullen, “Quantum noise in linear amplifiers,” Phys. Rev. 128, 2407–2413 (1962).
[Crossref]

Phys. Rev. A (16)

C. R. Müller, C. Wittmann, P. Marek, R. Filip, C. Marquardt, G. Leuchs, and U. L. Andersen, “Probabilistic cloning of coherent states without a phase reference,” Phys. Rev. A 86, 010305 (2012).
[Crossref]

B. Yurke, “Use of cavities in squeezed-state generation,” Phys. Rev. A 29, 408–410 (1984).
[Crossref]

G. J. Milburn, M. L. Steyn-Ross, and D. F. Walls, “Linear amplifiers with phase-sensitive noise,” Phys. Rev. A 35, 4443–4445 (1987).
[Crossref]

Z. Y. Ou, “Quantum amplification with correlated quantum fields,” Phys. Rev. A 48, R1761–R1764 (1993).
[Crossref]

J. Fiurášek, “Optimal probabilistic cloning and purification of quantum states,” Phys. Rev. A 70, 032308 (2004).
[Crossref]

F. Ferreyrol, R. Blandino, M. Barbieri, R. Tualle-Brouri, and P. Grangier, “Experimental realization of a nondeterministic optical noiseless amplifier,” Phys. Rev. A 83, 063801 (2011).
[Crossref]

R. Blandino, A. Leverrier, M. Barbieri, J. Etesse, P. Grangier, and R. Tualle-Brouri, “Improving the maximum transmission distance of continuous-variable quantum key distribution using a noiseless amplifier,” Phys. Rev. A 86, 012327 (2012).
[Crossref]

S. Pandey, Z. Jiang, J. Combes, and C. M. Caves, “Quantum limits on probabilistic amplifiers,” Phys. Rev. A 88, 033852 (2013).
[Crossref]

J. Combes, N. Walk, A. P. Lund, T. C. Ralph, and C. M. Caves, “Models of reduced-noise, probabilistic linear amplifiers,” Phys. Rev. A 93, 052310 (2016).
[Crossref]

J. Fiurśšek and N. J. Cerf, “Gaussian postselection and virtual noiseless amplification in continuous-variable quantum key distribution,” Phys. Rev. A 86, 060302 (2012).
[Crossref]

N. Walk, T. C. Ralph, T. Symul, and P. K. Lam, “Security of continuous-variable quantum cryptography with Gaussian postselection,” Phys. Rev. A 87, 020303 (2013).
[Crossref]

T. C. Ralph, “Quantum error correction of continuous-variable states against Gaussian noise,” Phys. Rev. A 84, 022339 (2011).
[Crossref]

J. Dias and T. C. Ralph, “Quantum repeaters using continuous-variable teleportation,” Phys. Rev. A 95, 022312 (2017).
[Crossref]

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[Crossref]

R. Blandino, N. Walk, A. P. Lund, and T. C. Ralph, “Channel purification via continuous-variable quantum teleportation with Gaussian postselection,” Phys. Rev. A 93, 012326 (2016).
[Crossref]

J. Zhao, J. Y. Haw, T. Symul, P. K. Lam, and S. M. Assad, “Characterization of a measurement-based noiseless linear amplifier and its applications,” Phys. Rev. A 96, 012319 (2017).
[Crossref]

Phys. Rev. D (1)

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

Phys. Rev. Lett. (6)

P. K. Lam, T. C. Ralph, E. H. Huntington, and H.-A. Bachor, “Noiseless signal amplification using positive electro-optic feedforward,” Phys. Rev. Lett. 79, 1471–1474 (1997).
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J.-A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. Garreau, and P. Grangier, “Quantum optical cloning amplifier,” Phys. Rev. Lett. 70, 267–270 (1993).
[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]

J. Kong, F. Hudelist, Z. Y. Ou, and W. Zhang, “Cancellation of internal quantum noise of an amplifier by quantum correlation,” Phys. Rev. Lett. 111, 033608 (2013).
[Crossref]

Q. He, L. Rosales-Zárate, G. Adesso, and M. D. Reid, “Secure continuous variable teleportation and Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 115, 180502 (2015).
[Crossref]

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Rev. Mod. Phys. (1)

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[Crossref]

Other (1)

S. Makovejs, C. C. Roberts, F. Palacios, H. B. Matthews, D. A. Lewis, D. T. Smith, P. G. Diehl, J. J. Johnson, J. D. Patterson, C. R. Towery, and S. Y. Ten, “Record-low (0.1460  db/km) attenuation ultra-large Aeff optical fiber for submarine applications,” in Optical Fiber Communication Conference Post Deadline Papers, OSA Technical Digest (online) (Optical Society of America, 2015), paper . Th5A.2.

Supplementary Material (1)

NameDescription
» Supplement 1       Supplemental document containing (1) our experimental scheme; (2) the derivation of the success probability; (3) the theoretical model that takes into account the experimental imperfections; and (4)Fig. S2, which plots the signal transfer coefficient as a function of power gain for two conjugate quadratures, as mentioned in Sec. 4B.

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Figures (6)

Fig. 1.
Fig. 1. Wigner function contours of input and output coherent states for a continuum of linear amplifiers. The green dashed circle here refers to the best possible deterministic linear amplifier, which adds the minimum amount of noise imposed by quantum mechanics; any amplifier that introduces less noise is necessarily probabilistic. One example of the probabilistic amplifiers is the perfect linear amplifier (PLA) that preserves the SNR of an incoming signal while amplifying its power. Amplifiers capable of enhancing SNR are called noise-reduced amplifiers (shaded area in orange, including the NLA) and the extreme case of the noise-reduced amplifier is an NLA that not only amplifies the amplitude of an input state, but also preserves its noise characteristics.
Fig. 2.
Fig. 2. Experimental schematic of our heralded noise-reduced linear amplifier achieved with a feed-forward loop. HD, homodyne measurement; EOM, electro-optic modulator.
Fig. 3.
Fig. 3. Tunability of the amplifier. Signal transfer coefficient (blue contours), various effective gains (red contours), and T (green lines) as the function of gNLA and gDLA. The blue-dotted line denotes the amplification process where the input SNR is preserved, while the enclosed shaded area refers to the region where additional noise is introduced. We note that, without a sufficiently high NLA gain, increasing gDLA alone would not suffice to approach the noise-reduced amplification.
Fig. 4.
Fig. 4. Linearity of the amplifier. (a) Amplification for coherent states with different amplitudes. Left panels: noise contours (one standard deviation width) of the amplified states, depicted in red. Right panels: normalized probability distribution for amplitude and phase quadratures of the output states. (b) Output magnitudes versus input magnitudes as we reduce the cutoff while maintaining the values of gNLA and gDLA. Inset: output magnitudes versus input magnitudes with cutoff αc=4.42 at different effective gains.
Fig. 5.
Fig. 5. Amplifier performance: noise properties and contour plot of the success probability PS in logarithmic scale as a function of Ts and geff. The success probability decreases as we increase the effective gain. The signal transfer coefficient for amplitude quadrature (blue symbols) is also superimposed as a function of geff2 for varying T: 0.6, 0.45. The theoretical prediction, assuming infinite cutoff, is depicted in crosses. It is clearly shown that the experimental Ts increases in compliance with the prediction, demonstrating that the cutoff (αc=4.3) selected is sufficient and no over- or underestimation of Ts appears. For the sake of comparison, the best achievable Ts of an optimal deterministic linear amplifier (also termed as the quantum noise limit) is shown in the orange solid line. This illustrates that our amplifier surpasses the quantum limit for a phase-insensitive amplifier, and this superiority becomes more distinguished as we increase the geff. Inset: the experimental data superimposed with its theoretical prediction for phase quadrature.
Fig. 6.
Fig. 6. Signal transfer coefficients in the large gain domain. (a) Ts exceeding 1 with increasing geff for αc=4.5 and a coherent state amplitude of |α|=0.5. The experimental Ts shows good agreement with the theory plot (in crosses) until around geff=6.5, where the data points start to depart, thereby indicating that the cutoff no long suffices to maintain the output Gaussianity. Inset: probability distribution of the amplified state labeled in red. (b) Probability distributions of the phase quadrature of the amplified state with cutoffs given by Eq.  (15). Data points are the post-selected ensemble out from 2.7×109 homodyne measurements, while the red curves indicate the corresponding best-fitted Gaussian distributions.

Equations (15)

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ρ^out=NTrv{U^gDLAgNLAn^ρ^in|00|vgNLAn^U^gDLA},
M^=Tr{M^ρ^out}=Tr{M^U^gDLAgNLAn^ρ^ingNLAn^U^gDLA}=Tr{M^DLAρ^NLA},
ρ^in(λ)=1π1λ2λ2d2αe1λ2λ2|α|2|αα|,
a^out=U^gDLAa^inU^gDLA=a^ingDLA+a^vgDLA21.
X^±out=gNLAgDLAX^±in.
(δX^±)2out=2gDLA21.
T=gNLA2/gDLA2.
P(αm)={exp(|αm|2|αc|2)(11(gNLA)2)if  |αm|αc1otherwise
X^±out=(1T2gDLAgNLA+T)X^±in,
(δX^±)2out=1+(gDLA)2.
Ts=SNRout/SNRin,
geff2/(2gDLA21)
Ts=(1T2gDLAgNLA+T)21+(gDLA)2.
Ts<geff22geff1
αc=(gNLA)2|αm|+β0.5gNLA.

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