Abstract

Manipulating light by adding and subtracting individual photons is a powerful approach with a principal drawback: the operations are fundamentally probabilistic and the probability is often small. This limits not only the fundamental scalability but also the number of operations that can be applied in realistic experimental settings. We propose and analyze a loop-based technique which can significantly increase the probability of success while preserving the quality of the photon subtraction. We show the improvement both in single mode preparation and manipulation of non-Gaussian states with negative Wigner functions and in two-mode entanglement distillation protocol with Gaussian states of light.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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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] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  43. A. Tipsmark, R. Dong, A. Laghaout, P. Marek, M. Ježek, and U. L. Andersen, “Experimental demonstration of a hadamard gate for coherent state qubits,” Phys. Rev. A 84, 050301 (2011).
    [Crossref]
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    [Crossref] [PubMed]
  45. H. L. Jeannic, A. Cavaillès, K. Huang, R. Filip, and J. Laurat, “Slowing quantum decoherence by squeezing in phase space,” Phys. Rev. Lett. 120, 073603 (2018).
    [Crossref] [PubMed]
  46. C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722–725 (1996).
    [Crossref] [PubMed]
  47. T. Opatrný, G. Kurizki, and D.-G. Welsch, “Improvement on teleportation of continuous variables by photon subtraction via conditional measurement,” Phys. Rev. A 61, 032302 (2000).
    [Crossref]
  48. G. Adesso and F. Illuminati, “Entanglement in continuous-variable systems: recent advances and current perspectives,” J. Phys. A: Mathematical Theoretical 40, 7821–7880 (2007).
    [Crossref]
  49. K. Huang, H. L. Jeannic, J. Ruaudel, V. Verma, M. Shaw, F. Marsili, S. Nam, E. Wu, H. Zeng, Y.-C. Jeong, R. Filip, O. Morin, and J. Laurat, “Optical synthesis of large-amplitude squeezed coherent-state superpositions with minimal resources,” Phys. Rev. Lett. 115, 023602 (2015).
    [Crossref] [PubMed]
  50. V. B. Verma, A. E. Lita, M. J. Stevens, R. P. Mirin, and S. W. Nam, “Athermal avalanche in bilayer superconducting nanowire single-photon detectors,” Appl. Phys. Lett. 108, 131108 (2016).
    [Crossref]
  51. P. Marek and R. Filip, “Coherent-state phase concentration by quantum probabilistic amplification,” Phys. Rev. A 81, 022302 (2010).
    [Crossref]
  52. K. Park, P. Marek, and R. Filip, “Conditional nonlinear operations by sequential jaynes-cummings interactions,” Phys. Rev. A 94, 012332 (2016).
    [Crossref]

2018 (2)

2017 (4)

S. Takeda and A. Furusawa, “Universal quantum computing with measurement-induced continuous-variable gate sequence in a loop-based architecture,” Phys. Rev. Lett. 119, 120504 (2017).
[Crossref]

M. Walschaers, C. Fabre, V. Parigi, and N. Treps, “Entanglement and wigner function negativity of multimode non-gaussian states,” Phys. Rev. Lett. 119, 183601 (2017).
[Crossref] [PubMed]

Y.-S. Ra, C. Jacquard, A. Dufour, C. Fabre, and N. Treps, “Tomography of a mode-tunable coherent single-photon subtractor,” Phys. Rev. X 7, 031012 (2017).

J. Hloušek, M. Ježek, and R. Filip, “Work and information from thermal states after subtraction of energy quanta,” Sci. Rep. 713046 (2017).
[Crossref]

2016 (6)

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

G. Harder, T. J. Bartley, A. E. Lita, S. W. Nam, T. Gerrits, and C. Silberhorn, “Single-mode parametric-down-conversion states with 50 photons as a source for mesoscopic quantum optics,” Phys. Rev. Lett. 116, 143601 (2016).
[Crossref] [PubMed]

V. B. Verma, A. E. Lita, M. J. Stevens, R. P. Mirin, and S. W. Nam, “Athermal avalanche in bilayer superconducting nanowire single-photon detectors,” Appl. Phys. Lett. 108, 131108 (2016).
[Crossref]

K. Park, P. Marek, and R. Filip, “Conditional nonlinear operations by sequential jaynes-cummings interactions,” Phys. Rev. A 94, 012332 (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 (2016).
[Crossref] [PubMed]

H. L. Jeannic, V. B. Verma, A. Cavaillès, F. Marsili, M. D. Shaw, K. Huang, O. Morin, S. W. Nam, and J. Laurat, “High-efficiency WSi superconducting nanowire single-photon detectors for quantum state engineering in the near infrared,” Opt. Lett. 41, 5341 (2016).
[Crossref] [PubMed]

2015 (6)

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 (2015).
[Crossref]

K. Marshall, R. Pooser, G. Siopsis, and C. Weedbrook, “Repeat-until-success cubic phase gate for universal continuous-variable quantum computation,” Phys. Rev. A 91, 032321 (2015).
[Crossref]

R. J. Donaldson, R. J. Collins, E. Eleftheriadou, S. M. Barnett, J. Jeffers, and G. S. Buller, “Experimental implementation of a quantum optical state comparison amplifier,” Phys. Rev. Lett. 114, 120505 (2015).
[Crossref] [PubMed]

U. L. Andersen, J. S. Neergaard-Nielsen, P. van Loock, and A. Furusawa, “Hybrid discrete- and continuous-variable quantum information,” Nat. Phys. 11, 713–719 (2015).
[Crossref]

K. Huang, H. L. Jeannic, J. Ruaudel, V. Verma, M. Shaw, F. Marsili, S. Nam, E. Wu, H. Zeng, Y.-C. Jeong, R. Filip, O. Morin, and J. Laurat, “Optical synthesis of large-amplitude squeezed coherent-state superpositions with minimal resources,” Phys. Rev. Lett. 115, 023602 (2015).
[Crossref] [PubMed]

K. Huang, H. L. Jeannic, J. Ruaudel, V. Verma, M. Shaw, F. Marsili, S. Nam, E. Wu, H. Zeng, Y.-C. Jeong, R. Filip, O. Morin, and J. Laurat, “Optical synthesis of large-amplitude squeezed coherent-state superpositions with minimal resources,” Phys. Rev. Lett. 115, 023602 (2015).
[Crossref] [PubMed]

2014 (2)

M. Fuwa, S. Toba, S. Takeda, P. Marek, L. Mišta, R. Filip, P. van Loock, J. Yoshikawa, and A. Furusawa, “Noiseless conditional teleportation of a single photon,” Phys. Rev. Lett. 113, 223602 (2014).
[Crossref] [PubMed]

Y. Kurochkin, A. S. Prasad, and A. I. Lvovsky, “Distillation of the two-mode squeezed state,” Phys. Rev. Lett. 112, 070402 (2014).
[Crossref] [PubMed]

2013 (5)

S. Takeda, T. Mizuta, M. Fuwa, P. van Loock, and A. Furusawa, “Deterministic quantum teleportation of photonic quantum bits by a hybrid technique,” Nature 500, 315–318 (2013).
[Crossref] [PubMed]

J. Yoshikawa, K. Makino, S. Kurata, P. van Loock, and A. Furusawa, “Creation, storage, and on-demand release of optical quantum states with a negative wigner function,” Phys. Rev. X 3, 041028 (2013).

M. Cooper, L. J. Wright, C. Söller, and B. J. Smith, “Experimental generation of multi-photon fock states,” Opt. Express 21, 5309 (2013).
[Crossref] [PubMed]

M. Yukawa, K. Miyata, T. Mizuta, H. Yonezawa, P. Marek, R. Filip, and A. Furusawa, “Generating superposition of up-to three photons for continuous variable quantum information processing,” Opt. Express 21, 5529 (2013).
[Crossref] [PubMed]

M. Yukawa, K. Miyata, H. Yonezawa, P. Marek, R. Filip, and A. Furusawa, “Emulating quantum cubic nonlinearity,” Phys. Rev. A 88, 053816 (2013).
[Crossref]

2012 (2)

J. M. Raimond, P. Facchi, B. Peaudecerf, S. Pascazio, C. Sayrin, I. Dotsenko, S. Gleyzes, M. Brune, and S. Haroche, “Quantum zeno dynamics of a field in a cavity,” Phys. Rev. A 86, 032120 (2012).
[Crossref]

A. Mari and J. Eisert, “Positive wigner functions render classical simulation of quantum computation efficient,” Phys. Rev. Lett. 109, 230503 (2012).
[Crossref]

2011 (3)

A. Tipsmark, R. Dong, A. Laghaout, P. Marek, M. Ježek, and U. L. Andersen, “Experimental demonstration of a hadamard gate for coherent state qubits,” Phys. Rev. A 84, 050301 (2011).
[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] [PubMed]

P. Marek, R. Filip, and A. Furusawa, “Deterministic implementation of weak quantum cubic nonlinearity,” Phys. Rev. A 84, 053802 (2011).
[Crossref]

2010 (8)

P. Marek and R. Filip, “Coherent-state phase concentration by quantum probabilistic amplification,” Phys. Rev. A 81, 022302 (2010).
[Crossref]

P. Marek and J. Fiurášek, “Elementary gates for quantum information with superposed coherent states,” Physical Review A 82, 014304 (2010).
[Crossref]

E. Bimbard, N. Jain, A. MacRae, and A. I. Lvovsky, “Quantum-optical state engineering up to the two-photon level,” Nat. Photonics 4, 243–247 (2010).
[Crossref]

K. Park and H. Jeong, “Entangled coherent states versus entangled photon pairs for practical quantum-information processing,” Phys. Rev. A 82, 062325 (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]

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

2008 (1)

S. Deléglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J.-M. Raimond, and S. Haroche, “Reconstruction of non-classical cavity field states with snapshots of their decoherence,” Nature 455, 510–514 (2008).
[Crossref] [PubMed]

2007 (2)

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] [PubMed]

G. Adesso and F. Illuminati, “Entanglement in continuous-variable systems: recent advances and current perspectives,” J. Phys. A: Mathematical Theoretical 40, 7821–7880 (2007).
[Crossref]

2006 (1)

A. Ourjoumtsev, “Generating optical schrodinger kittens for quantum information processing,” Science 312, 83–86 (2006).
[Crossref] [PubMed]

2004 (1)

A. Zavatta, “Quantum-to-classical transition with single-photon-added coherent states of light,” Science 306, 660–662 (2004).
[Crossref] [PubMed]

2003 (1)

T. C. Ralph, A. Gilchrist, G. J. Milburn, W. J. Munro, and S. Glancy, “Quantum computation with optical coherent states,” Phys. Rev. A 68, 042319 (2003).
[Crossref]

2002 (2)

H. Jeong and M. S. Kim, “Efficient quantum computation using coherent states,” Phys. Rev. A 65, 042305 (2002).
[Crossref]

A. I. Lvovsky and J. Mlynek, “Quantum-optical catalysis: Generating nonclassical states of light by means of linear optics,” Phys. Rev. Lett. 88, 250401 (2002).
[Crossref] [PubMed]

2001 (1)

J. Calsamiglia, S. M. Barnett, N. Lütkenhaus, and K.-A. Suominen, “Removal of a single photon by adaptive absorption,” Phys. Rev. A 64, 043814 (2001).
[Crossref]

2000 (1)

T. Opatrný, G. Kurizki, and D.-G. Welsch, “Improvement on teleportation of continuous variables by photon subtraction via conditional measurement,” Phys. Rev. A 61, 032302 (2000).
[Crossref]

1996 (1)

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722–725 (1996).
[Crossref] [PubMed]

1991 (1)

C. T. Lee, “Measure of the nonclassicality of nonclassical states,” Phys. Rev. A 44, R2775–R2778 (1991).
[Crossref] [PubMed]

1974 (1)

R. Hudson, “When is the wigner quasi-probability density non-negative?” Rep. Mathe. Phys. 6, 249–252 (1974).
[Crossref]

Adesso, G.

G. Adesso and F. Illuminati, “Entanglement in continuous-variable systems: recent advances and current perspectives,” J. Phys. A: Mathematical Theoretical 40, 7821–7880 (2007).
[Crossref]

Andersen, U. L.

U. L. Andersen, J. S. Neergaard-Nielsen, P. van Loock, and A. Furusawa, “Hybrid discrete- and continuous-variable quantum information,” Nat. Phys. 11, 713–719 (2015).
[Crossref]

A. Tipsmark, R. Dong, A. Laghaout, P. Marek, M. Ježek, and U. L. Andersen, “Experimental demonstration of a hadamard gate for coherent state qubits,” Phys. Rev. A 84, 050301 (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]

Ansari, V.

Barbieri, M.

Barnett, S. M.

R. J. Donaldson, R. J. Collins, E. Eleftheriadou, S. M. Barnett, J. Jeffers, and G. S. Buller, “Experimental implementation of a quantum optical state comparison amplifier,” Phys. Rev. Lett. 114, 120505 (2015).
[Crossref] [PubMed]

J. Calsamiglia, S. M. Barnett, N. Lütkenhaus, and K.-A. Suominen, “Removal of a single photon by adaptive absorption,” Phys. Rev. A 64, 043814 (2001).
[Crossref]

Bartley, T. J.

G. Harder, T. J. Bartley, A. E. Lita, S. W. Nam, T. Gerrits, and C. Silberhorn, “Single-mode parametric-down-conversion states with 50 photons as a source for mesoscopic quantum optics,” Phys. Rev. Lett. 116, 143601 (2016).
[Crossref] [PubMed]

Bechler, O.

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 (2015).
[Crossref]

Bellini, M.

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 (2016).
[Crossref] [PubMed]

A. Zavatta, J. Fiurášek, and M. Bellini, “A high-fidelity noiseless amplifier for quantum light states,” Nat. Photonics 5, 52–60 (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).
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Figures (6)

Fig. 1
Fig. 1 (color online) Schematic representation of the adaptive photon subtraction. Part of the input signal is tapped off at the mostly transmissive beam splitter (BS) and directed towards avalanche photo-diode (APD). Positive detection event results in successfully transformed signal while negative one prompts the optical switches (S) to feed the signal back for the next attempt if a predetermined number of maximal steps was not reached yet.
Fig. 2
Fig. 2 Central negativity of non-Gaussian quantum state prepared from a pure state with 6dB of squeeezing relative to the achievable probability of success for (a) ideal and (b) contemporary detectors with quantum efficiency η = 0.8. The performance of the original single step subtraction protocol (black dotted) is significantly surpassed by taking as little as 10 steps (dashed blue) and which can be further improved by performing 100 steps (solid red). While the improvement is significant for both the ideal and the realistic detection, the losses due to quantum inefficincy make it impossible to attain maximal negativity with maximal probability of success.
Fig. 3
Fig. 3 The central negativity of the Wigner function (solid red line) and the achievable probability of success (dashed red line) in relation to the transmission coefficient of the tapping beam splitter for a photon subtracted impure squeezed state with 8 dB of squeezing and 10 dB of anti-squeezing. (a) ideal detector and N = 1. (b) ideal detector and N = 10. (c) ideal detector and N = 100. (d) realistic superconducting detector with currently available quantum efficiency η = 0.8 and N = 100. Where applicable, the black vertical lines mark the points in which the Wigner function negativity reaches the local minima even though the success probability is not saturated. The insets show the detail of these points.
Fig. 4
Fig. 4 Fidelity in respect to probability of success of the |+〉 ↦ |−〉transition facilitated by the subtraction procedure employing (a) ideal and (b) realistic superconducting detectors with detection efficiency η = 0.8. The superpositions |±〉 ∝ |α〉 ± |−α〉 are investigated for realistic α = 3 / 2 in both regimes of detection. Our procedure shows a significant improvement in success probability over the original subtraction protocol (dotted black) with as little as 10 steps (dashed blue). The maximal probability relative to desired fidelity of the transition can be further increased by taking, for example, 100 steps (solid red).
Fig. 5
Fig. 5 Schematic representation of the distillation of entanglement with help of the adaptive photon subtraction. Single photon subtractions (SPS, depicted in detail in Fig. 1) are attempted at both modes of the initial entangled state. If the subtraction was not successful and a predetermined number of steps was not reached yet, the optical switches are used for feeding the signal back for the next attempt.
Fig. 6
Fig. 6 Gaussaian logarithmic negativity in respect to success probability for distillation of entanglement from two mode uniformly squeezed vacuum state with 8 dB of generalised squeezing. The behaviour is investigated for ideal (solid curves) and realistic superconducting (dashed curves) detectors with quantum efficiency η = 0.8. Our procedure shows a significant improvement in terms of probability for as little as 10 allowed steps (blue). The attainable probability is roughly greater by an order of magnitude in comparison with the original procedure (black). Going to 75 steps (red) improves the probability even further, but the improvement rate steeply declines at that point.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

ρ ^ 0 , out Tr 1 [ U ^ 01 ρ ^ 0 , in | 0 1 0 | U ^ 0 , 1 Π ^ 1 ] ,
ρ ^ 0 , out κ 2 a ^ 0 ρ ^ 0 , i n a ^ 0 .
ρ ^ 0 , out ( n ) = Tr 1 , , n [ ( U ^ ( n ) ρ ^ 0 , in k = 1 n | 0 k 0 | U ^ ( n ) ) Π ^ ( n ) ] ,
U ^ ( n ) = k = 1 n U ^ 0 , k , Π ^ ( n ) = k = 1 n 1 Π ^ k Π ^ n
ρ ^ 0 , out = 1 P S n = 1 N ρ ^ 0 , out ( n ) ,
ρ ^ 0 , out 1 P S a ^ 0 [ ( 1 t 2 ) k = 0 N t k n ^ 0 ρ ^ 0 , in t k n ^ 0 ] a ^ 0 ,
P S ( 1 t 2 ) k = 0 N Tr [ ρ ^ 0 , in t 2 k n ^ 0 n ^ 0 ] ,
| ψ = 1 cosh r f = 0 ( tanh r ) f | f | f .
σ = ( α γ γ T β )
ν = 2 ( Δ Δ 2 4 det σ ) .

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