Abstract

We address the degradation of continuous variable (CV) entanglement distillation in the presence of thermal environment and nonunity detecting efficiency. We explore the logarithmic negativity as a criteria and compare the output entanglement between the schemes of single-photon subtraction (PS) and two-PS. The probability of success is also investigated. We show that compared with detector efficiency, thermal noise plays a more dominant role in Gaussian entanglement distillation. Our results shed more light on the noise mechanism that influences realistic CV entanglement distillation and is of experimental relevance in developing a more efficient entanglement distillation scheme.

© 2013 Optical Society of America

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  1. A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
    [CrossRef]
  2. C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
    [CrossRef]
  3. V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).
    [CrossRef]
  4. C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, “Mixed-state entanglement and quantum error correction,” Phys. Rev. A 54, 3824–3851 (1996).
    [CrossRef]
  5. J. Eisert, S. Scheel, and M. B. Plenio, “Distilling Gaussian states with Gaussian operations is impossible,” Phys. Rev. Lett. 89, 137903 (2002).
    [CrossRef]
  6. J. Fiurášek, “Gaussian transformations and distillation of entangled Gaussian states,” Phys. Rev. Lett. 89, 137904 (2002).
    [CrossRef]
  7. G. Giedke and J. I. Cirac, “Characterization of Gaussian operations and distillation of Gaussian states,” Phys. Rev. A 66, 032316 (2002).
    [CrossRef]
  8. 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]
  9. A. Zavatta, S. Viciani, and M. Bellini, “Quantum-to-classical transition with single-photon-added coherent states of light,” Science 306, 660–662 (2004).
    [CrossRef]
  10. J. Fiurášek, “Engineering quantum operations on traveling light beams by multiple photon addition and subtraction,” Phys. Rev. A 80, 053822 (2009).
    [CrossRef]
  11. C. Navarrete-Benlloch, R. García-Patrón, J. H. Shapiro, and N. J. Cerf, “Enhancing quantum entanglement by photon addition and subtraction,” Phys. Rev. A 86, 012328 (2012).
    [CrossRef]
  12. S. Zhang and P. van Loock, “Distillation of mixed-state continuous-variable entanglement by photon subtraction,” Phys. Rev. A 82, 062316 (2010).
    [CrossRef]
  13. D. E. Browne, J. Eisert, S. Scheel, and M. B. Plenio, “Driving non-Gaussian to Gaussian states with linear optics,” Phys. Rev. A 67, 062320 (2003).
    [CrossRef]
  14. J. Eisert, D. E. Browne, S. Scheel, and M. B. Plenio, “Distillation of continuous-variable entanglement with optical means,” Ann. Phys. 311, 431–458 (2004).
    [CrossRef]
  15. J. Eisert, M. B. Plenio, D. E. Browne, S. Scheel, and A. Feito, “On the experimental feasibility of continuous-variable optical entanglement distillation,” Opt. Spectrosc. 103, 173–177 (2007).
    [CrossRef]
  16. A. P. Lund and T. C. Ralph, “Continuous-variable entanglement distillation over a general lossy channel,” Phys. Rev. A 80, 032309 (2009).
    [CrossRef]
  17. J. Fiurášek, “Distillation and purification of symmetric entangled Gaussian states,” Phys. Rev. A 82, 042331 (2010).
    [CrossRef]
  18. E. T. Campbell and J. Eisert, “Gaussification and entanglement distillation of continuous-variable systems: a unifying picture,” Phys. Rev. Lett. 108, 020501 (2012).
    [CrossRef]
  19. B. Hage, A. Samblowski, J. Diguglielmo, A. Franzen, J. Fiurášek, and R. Schnabel, “Preparation of distilled and purified continuous-variable entangled states,” Nat. Phys. 4, 915–918 (2008).
    [CrossRef]
  20. R. Dong, M. Lassen, J. Heersink, C. Marquardt, R. Filip, G. Leuchs, and U. L. Andersen, “Experimental entanglement distillation of mesoscopic quantum states,” Nat. Phys. 4, 919–923 (2008).
    [CrossRef]
  21. P. van Loock, “Optical hybrid approaches to quantum information,” Laser Photon. Rev. 5, 167–200 (2011).
    [CrossRef]
  22. H. Takahashi, J. 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]
  23. 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]
  24. T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802 (2010).
    [CrossRef]
  25. S. Olivares, M. G. A. Paris, and R. Bonifacio, “Teleporation improvement by inconclusive photon subtraction,” Phys. Rev. A 67, 032314 (2003).
    [CrossRef]
  26. A. Kitagawa, M. Takeoka, M. Sasaki, and A. Chefles, “Entanglement evaluation of non-Gaussian states generated by photon subtraction from squeezed states,” Phys. Rev. A 73042310 (2006).
    [CrossRef]
  27. S. Zhang and P. van Loock, “Local Gaussian operations can enhance continuous-variable entanglement distillation,” Phys. Rev. A 84, 062309 (2011).
    [CrossRef]
  28. J. Fiurášek, “Improving entanglement concentration of Gaussian states by local displacements,” Phys. Rev. A 84, 012335 (2011).
    [CrossRef]
  29. P. Pearle, “Hidden-variable example based upon data rejection,” Phys. Rev. D 2, 1418–1425 (1970).
    [CrossRef]
  30. E. Santos, “Critical analysis of the empirical tests of local hidden-variable theories,” Phys. Rev. A 46, 3646–3656 (1992).
    [CrossRef]
  31. S. Yang, X. Zou, S. Zhang, B. Shi, P. van Loock, and G. Guo, “Multipartite continuous-variable entanglement distillation using local squeezing and only one photon-subtraction operation,” e-print arXiv:1106.1536v1.
  32. G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A 65, 032314 (2002).
    [CrossRef]
  33. G. Adesso, A. Serafini, and F. Illuminati, “Quantification and scaling of multipartite entanglement in continuous variable systems,” Phys. Rev. Lett. 93, 220504 (2004).
    [CrossRef]
  34. A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating optical Schrödinger kittens for quantum information processing,” Science 312, 83–86 (2006).
    [CrossRef]
  35. G. Lindblad, “Cloning the quantum oscillator,” J. Phys. A 33, 5059–5076 (2000).
    [CrossRef]
  36. P. Marek, J. Fiurášek, B. Hage, A. Franzen, J. DiGugliemo, and R. Schnabel, “Multiple-copy distillation and purification of phase-diffused squeezed states,” Phys. Rev. A 76, 053820 (2007).
    [CrossRef]

2012

C. Navarrete-Benlloch, R. García-Patrón, J. H. Shapiro, and N. J. Cerf, “Enhancing quantum entanglement by photon addition and subtraction,” Phys. Rev. A 86, 012328 (2012).
[CrossRef]

E. T. Campbell and J. Eisert, “Gaussification and entanglement distillation of continuous-variable systems: a unifying picture,” Phys. Rev. Lett. 108, 020501 (2012).
[CrossRef]

2011

P. van Loock, “Optical hybrid approaches to quantum information,” Laser Photon. Rev. 5, 167–200 (2011).
[CrossRef]

S. Zhang and P. van Loock, “Local Gaussian operations can enhance continuous-variable entanglement distillation,” Phys. Rev. A 84, 062309 (2011).
[CrossRef]

J. Fiurášek, “Improving entanglement concentration of Gaussian states by local displacements,” Phys. Rev. A 84, 012335 (2011).
[CrossRef]

2010

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802 (2010).
[CrossRef]

H. Takahashi, J. 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]

S. Zhang and P. van Loock, “Distillation of mixed-state continuous-variable entanglement by photon subtraction,” Phys. Rev. A 82, 062316 (2010).
[CrossRef]

J. Fiurášek, “Distillation and purification of symmetric entangled Gaussian states,” Phys. Rev. A 82, 042331 (2010).
[CrossRef]

2009

A. P. Lund and T. C. Ralph, “Continuous-variable entanglement distillation over a general lossy channel,” Phys. Rev. A 80, 032309 (2009).
[CrossRef]

J. Fiurášek, “Engineering quantum operations on traveling light beams by multiple photon addition and subtraction,” Phys. Rev. A 80, 053822 (2009).
[CrossRef]

2008

B. Hage, A. Samblowski, J. Diguglielmo, A. Franzen, J. Fiurášek, and R. Schnabel, “Preparation of distilled and purified continuous-variable entangled states,” Nat. Phys. 4, 915–918 (2008).
[CrossRef]

R. Dong, M. Lassen, J. Heersink, C. Marquardt, R. Filip, G. Leuchs, and U. L. Andersen, “Experimental entanglement distillation of mesoscopic quantum states,” Nat. Phys. 4, 919–923 (2008).
[CrossRef]

2007

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]

P. Marek, J. Fiurášek, B. Hage, A. Franzen, J. DiGugliemo, and R. Schnabel, “Multiple-copy distillation and purification of phase-diffused squeezed states,” Phys. Rev. A 76, 053820 (2007).
[CrossRef]

J. Eisert, M. B. Plenio, D. E. Browne, S. Scheel, and A. Feito, “On the experimental feasibility of continuous-variable optical entanglement distillation,” Opt. Spectrosc. 103, 173–177 (2007).
[CrossRef]

2006

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]

A. Kitagawa, M. Takeoka, M. Sasaki, and A. Chefles, “Entanglement evaluation of non-Gaussian states generated by photon subtraction from squeezed states,” Phys. Rev. A 73042310 (2006).
[CrossRef]

2004

G. Adesso, A. Serafini, and F. Illuminati, “Quantification and scaling of multipartite entanglement in continuous variable systems,” Phys. Rev. Lett. 93, 220504 (2004).
[CrossRef]

J. Eisert, D. E. Browne, S. Scheel, and M. B. Plenio, “Distillation of continuous-variable entanglement with optical means,” Ann. Phys. 311, 431–458 (2004).
[CrossRef]

A. Zavatta, S. Viciani, and M. Bellini, “Quantum-to-classical transition with single-photon-added coherent states of light,” Science 306, 660–662 (2004).
[CrossRef]

2003

D. E. Browne, J. Eisert, S. Scheel, and M. B. Plenio, “Driving non-Gaussian to Gaussian states with linear optics,” Phys. Rev. A 67, 062320 (2003).
[CrossRef]

S. Olivares, M. G. A. Paris, and R. Bonifacio, “Teleporation improvement by inconclusive photon subtraction,” Phys. Rev. A 67, 032314 (2003).
[CrossRef]

2002

G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A 65, 032314 (2002).
[CrossRef]

J. Eisert, S. Scheel, and M. B. Plenio, “Distilling Gaussian states with Gaussian operations is impossible,” Phys. Rev. Lett. 89, 137903 (2002).
[CrossRef]

J. Fiurášek, “Gaussian transformations and distillation of entangled Gaussian states,” Phys. Rev. Lett. 89, 137904 (2002).
[CrossRef]

G. Giedke and J. I. Cirac, “Characterization of Gaussian operations and distillation of Gaussian states,” Phys. Rev. A 66, 032316 (2002).
[CrossRef]

2000

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]

G. Lindblad, “Cloning the quantum oscillator,” J. Phys. A 33, 5059–5076 (2000).
[CrossRef]

1996

C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, “Mixed-state entanglement and quantum error correction,” Phys. Rev. A 54, 3824–3851 (1996).
[CrossRef]

1993

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef]

1992

E. Santos, “Critical analysis of the empirical tests of local hidden-variable theories,” Phys. Rev. A 46, 3646–3656 (1992).
[CrossRef]

1991

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
[CrossRef]

1970

P. Pearle, “Hidden-variable example based upon data rejection,” Phys. Rev. D 2, 1418–1425 (1970).
[CrossRef]

Adesso, G.

G. Adesso, A. Serafini, and F. Illuminati, “Quantification and scaling of multipartite entanglement in continuous variable systems,” Phys. Rev. Lett. 93, 220504 (2004).
[CrossRef]

Andersen, U. L.

R. Dong, M. Lassen, J. Heersink, C. Marquardt, R. Filip, G. Leuchs, and U. L. Andersen, “Experimental entanglement distillation of mesoscopic quantum states,” Nat. Phys. 4, 919–923 (2008).
[CrossRef]

Bellini, M.

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]

A. Zavatta, S. Viciani, and M. Bellini, “Quantum-to-classical transition with single-photon-added coherent states of light,” Science 306, 660–662 (2004).
[CrossRef]

Bennett, C. H.

C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, “Mixed-state entanglement and quantum error correction,” Phys. Rev. A 54, 3824–3851 (1996).
[CrossRef]

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef]

Bonifacio, R.

S. Olivares, M. G. A. Paris, and R. Bonifacio, “Teleporation improvement by inconclusive photon subtraction,” Phys. Rev. A 67, 032314 (2003).
[CrossRef]

Brassard, G.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef]

Browne, D. E.

J. Eisert, M. B. Plenio, D. E. Browne, S. Scheel, and A. Feito, “On the experimental feasibility of continuous-variable optical entanglement distillation,” Opt. Spectrosc. 103, 173–177 (2007).
[CrossRef]

J. Eisert, D. E. Browne, S. Scheel, and M. B. Plenio, “Distillation of continuous-variable entanglement with optical means,” Ann. Phys. 311, 431–458 (2004).
[CrossRef]

D. E. Browne, J. Eisert, S. Scheel, and M. B. Plenio, “Driving non-Gaussian to Gaussian states with linear optics,” Phys. Rev. A 67, 062320 (2003).
[CrossRef]

Calkins, B.

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802 (2010).
[CrossRef]

Campbell, E. T.

E. T. Campbell and J. Eisert, “Gaussification and entanglement distillation of continuous-variable systems: a unifying picture,” Phys. Rev. Lett. 108, 020501 (2012).
[CrossRef]

Cerf, N. J.

C. Navarrete-Benlloch, R. García-Patrón, J. H. Shapiro, and N. J. Cerf, “Enhancing quantum entanglement by photon addition and subtraction,” Phys. Rev. A 86, 012328 (2012).
[CrossRef]

Chefles, A.

A. Kitagawa, M. Takeoka, M. Sasaki, and A. Chefles, “Entanglement evaluation of non-Gaussian states generated by photon subtraction from squeezed states,” Phys. Rev. A 73042310 (2006).
[CrossRef]

Cirac, J. I.

G. Giedke and J. I. Cirac, “Characterization of Gaussian operations and distillation of Gaussian states,” Phys. Rev. A 66, 032316 (2002).
[CrossRef]

Clement, T. S.

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802 (2010).
[CrossRef]

Crépeau, C.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef]

Diguglielmo, J.

B. Hage, A. Samblowski, J. Diguglielmo, A. Franzen, J. Fiurášek, and R. Schnabel, “Preparation of distilled and purified continuous-variable entangled states,” Nat. Phys. 4, 915–918 (2008).
[CrossRef]

DiGugliemo, J.

P. Marek, J. Fiurášek, B. Hage, A. Franzen, J. DiGugliemo, and R. Schnabel, “Multiple-copy distillation and purification of phase-diffused squeezed states,” Phys. Rev. A 76, 053820 (2007).
[CrossRef]

DiVincenzo, D. P.

C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, “Mixed-state entanglement and quantum error correction,” Phys. Rev. A 54, 3824–3851 (1996).
[CrossRef]

Dong, R.

R. Dong, M. Lassen, J. Heersink, C. Marquardt, R. Filip, G. Leuchs, and U. L. Andersen, “Experimental entanglement distillation of mesoscopic quantum states,” Nat. Phys. 4, 919–923 (2008).
[CrossRef]

Eisert, J.

E. T. Campbell and J. Eisert, “Gaussification and entanglement distillation of continuous-variable systems: a unifying picture,” Phys. Rev. Lett. 108, 020501 (2012).
[CrossRef]

J. Eisert, M. B. Plenio, D. E. Browne, S. Scheel, and A. Feito, “On the experimental feasibility of continuous-variable optical entanglement distillation,” Opt. Spectrosc. 103, 173–177 (2007).
[CrossRef]

J. Eisert, D. E. Browne, S. Scheel, and M. B. Plenio, “Distillation of continuous-variable entanglement with optical means,” Ann. Phys. 311, 431–458 (2004).
[CrossRef]

D. E. Browne, J. Eisert, S. Scheel, and M. B. Plenio, “Driving non-Gaussian to Gaussian states with linear optics,” Phys. Rev. A 67, 062320 (2003).
[CrossRef]

J. Eisert, S. Scheel, and M. B. Plenio, “Distilling Gaussian states with Gaussian operations is impossible,” Phys. Rev. Lett. 89, 137903 (2002).
[CrossRef]

Ekert, A. K.

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
[CrossRef]

Feito, A.

J. Eisert, M. B. Plenio, D. E. Browne, S. Scheel, and A. Feito, “On the experimental feasibility of continuous-variable optical entanglement distillation,” Opt. Spectrosc. 103, 173–177 (2007).
[CrossRef]

Filip, R.

R. Dong, M. Lassen, J. Heersink, C. Marquardt, R. Filip, G. Leuchs, and U. L. Andersen, “Experimental entanglement distillation of mesoscopic quantum states,” Nat. Phys. 4, 919–923 (2008).
[CrossRef]

Fiurášek, J.

J. Fiurášek, “Improving entanglement concentration of Gaussian states by local displacements,” Phys. Rev. A 84, 012335 (2011).
[CrossRef]

J. Fiurášek, “Distillation and purification of symmetric entangled Gaussian states,” Phys. Rev. A 82, 042331 (2010).
[CrossRef]

J. Fiurášek, “Engineering quantum operations on traveling light beams by multiple photon addition and subtraction,” Phys. Rev. A 80, 053822 (2009).
[CrossRef]

B. Hage, A. Samblowski, J. Diguglielmo, A. Franzen, J. Fiurášek, and R. Schnabel, “Preparation of distilled and purified continuous-variable entangled states,” Nat. Phys. 4, 915–918 (2008).
[CrossRef]

P. Marek, J. Fiurášek, B. Hage, A. Franzen, J. DiGugliemo, and R. Schnabel, “Multiple-copy distillation and purification of phase-diffused squeezed states,” Phys. Rev. A 76, 053820 (2007).
[CrossRef]

J. Fiurášek, “Gaussian transformations and distillation of entangled Gaussian states,” Phys. Rev. Lett. 89, 137904 (2002).
[CrossRef]

Franzen, A.

B. Hage, A. Samblowski, J. Diguglielmo, A. Franzen, J. Fiurášek, and R. Schnabel, “Preparation of distilled and purified continuous-variable entangled states,” Nat. Phys. 4, 915–918 (2008).
[CrossRef]

P. Marek, J. Fiurášek, B. Hage, A. Franzen, J. DiGugliemo, and R. Schnabel, “Multiple-copy distillation and purification of phase-diffused squeezed states,” Phys. Rev. A 76, 053820 (2007).
[CrossRef]

Furusawa, A.

H. Takahashi, J. 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]

García-Patrón, R.

C. Navarrete-Benlloch, R. García-Patrón, J. H. Shapiro, and N. J. Cerf, “Enhancing quantum entanglement by photon addition and subtraction,” Phys. Rev. A 86, 012328 (2012).
[CrossRef]

Gerrits, T.

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802 (2010).
[CrossRef]

Giedke, G.

G. Giedke and J. I. Cirac, “Characterization of Gaussian operations and distillation of Gaussian states,” Phys. Rev. A 66, 032316 (2002).
[CrossRef]

Giovannetti, V.

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

Glancy, S.

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802 (2010).
[CrossRef]

Grangier, P.

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

Guo, G.

S. Yang, X. Zou, S. Zhang, B. Shi, P. van Loock, and G. Guo, “Multipartite continuous-variable entanglement distillation using local squeezing and only one photon-subtraction operation,” e-print arXiv:1106.1536v1.

Hage, B.

B. Hage, A. Samblowski, J. Diguglielmo, A. Franzen, J. Fiurášek, and R. Schnabel, “Preparation of distilled and purified continuous-variable entangled states,” Nat. Phys. 4, 915–918 (2008).
[CrossRef]

P. Marek, J. Fiurášek, B. Hage, A. Franzen, J. DiGugliemo, and R. Schnabel, “Multiple-copy distillation and purification of phase-diffused squeezed states,” Phys. Rev. A 76, 053820 (2007).
[CrossRef]

Hayasaka, K.

H. Takahashi, J. 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]

Heersink, J.

R. Dong, M. Lassen, J. Heersink, C. Marquardt, R. Filip, G. Leuchs, and U. L. Andersen, “Experimental entanglement distillation of mesoscopic quantum states,” Nat. Phys. 4, 919–923 (2008).
[CrossRef]

Illuminati, F.

G. Adesso, A. Serafini, and F. Illuminati, “Quantification and scaling of multipartite entanglement in continuous variable systems,” Phys. Rev. Lett. 93, 220504 (2004).
[CrossRef]

Jozsa, R.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef]

Kim, M.

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]

Kitagawa, A.

A. Kitagawa, M. Takeoka, M. Sasaki, and A. Chefles, “Entanglement evaluation of non-Gaussian states generated by photon subtraction from squeezed states,” Phys. Rev. A 73042310 (2006).
[CrossRef]

Knill, E.

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802 (2010).
[CrossRef]

Kurizki, G.

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]

Lassen, M.

R. Dong, M. Lassen, J. Heersink, C. Marquardt, R. Filip, G. Leuchs, and U. L. Andersen, “Experimental entanglement distillation of mesoscopic quantum states,” Nat. Phys. 4, 919–923 (2008).
[CrossRef]

Laurat, J.

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

Leuchs, G.

R. Dong, M. Lassen, J. Heersink, C. Marquardt, R. Filip, G. Leuchs, and U. L. Andersen, “Experimental entanglement distillation of mesoscopic quantum states,” Nat. Phys. 4, 919–923 (2008).
[CrossRef]

Lindblad, G.

G. Lindblad, “Cloning the quantum oscillator,” J. Phys. A 33, 5059–5076 (2000).
[CrossRef]

Lita, A. E.

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802 (2010).
[CrossRef]

Lloyd, S.

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

Lund, A. P.

A. P. Lund and T. C. Ralph, “Continuous-variable entanglement distillation over a general lossy channel,” Phys. Rev. A 80, 032309 (2009).
[CrossRef]

Maccone, L.

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

Marek, P.

P. Marek, J. Fiurášek, B. Hage, A. Franzen, J. DiGugliemo, and R. Schnabel, “Multiple-copy distillation and purification of phase-diffused squeezed states,” Phys. Rev. A 76, 053820 (2007).
[CrossRef]

Marquardt, C.

R. Dong, M. Lassen, J. Heersink, C. Marquardt, R. Filip, G. Leuchs, and U. L. Andersen, “Experimental entanglement distillation of mesoscopic quantum states,” Nat. Phys. 4, 919–923 (2008).
[CrossRef]

Migdall, A. L.

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802 (2010).
[CrossRef]

Miller, A.

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802 (2010).
[CrossRef]

Mirin, R. P.

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802 (2010).
[CrossRef]

Nam, S. W.

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802 (2010).
[CrossRef]

Navarrete-Benlloch, C.

C. Navarrete-Benlloch, R. García-Patrón, J. H. Shapiro, and N. J. Cerf, “Enhancing quantum entanglement by photon addition and subtraction,” Phys. Rev. A 86, 012328 (2012).
[CrossRef]

Neergaard-Nielsen, J.

H. Takahashi, J. 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]

Olivares, S.

S. Olivares, M. G. A. Paris, and R. Bonifacio, “Teleporation improvement by inconclusive photon subtraction,” Phys. Rev. A 67, 032314 (2003).
[CrossRef]

Opatrný, T.

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]

Ourjoumtsev, A.

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

Parigi, V.

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]

Paris, M. G. A.

S. Olivares, M. G. A. Paris, and R. Bonifacio, “Teleporation improvement by inconclusive photon subtraction,” Phys. Rev. A 67, 032314 (2003).
[CrossRef]

Pearle, P.

P. Pearle, “Hidden-variable example based upon data rejection,” Phys. Rev. D 2, 1418–1425 (1970).
[CrossRef]

Peres, A.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef]

Plenio, M. B.

J. Eisert, M. B. Plenio, D. E. Browne, S. Scheel, and A. Feito, “On the experimental feasibility of continuous-variable optical entanglement distillation,” Opt. Spectrosc. 103, 173–177 (2007).
[CrossRef]

J. Eisert, D. E. Browne, S. Scheel, and M. B. Plenio, “Distillation of continuous-variable entanglement with optical means,” Ann. Phys. 311, 431–458 (2004).
[CrossRef]

D. E. Browne, J. Eisert, S. Scheel, and M. B. Plenio, “Driving non-Gaussian to Gaussian states with linear optics,” Phys. Rev. A 67, 062320 (2003).
[CrossRef]

J. Eisert, S. Scheel, and M. B. Plenio, “Distilling Gaussian states with Gaussian operations is impossible,” Phys. Rev. Lett. 89, 137903 (2002).
[CrossRef]

Ralph, T. C.

A. P. Lund and T. C. Ralph, “Continuous-variable entanglement distillation over a general lossy channel,” Phys. Rev. A 80, 032309 (2009).
[CrossRef]

Samblowski, A.

B. Hage, A. Samblowski, J. Diguglielmo, A. Franzen, J. Fiurášek, and R. Schnabel, “Preparation of distilled and purified continuous-variable entangled states,” Nat. Phys. 4, 915–918 (2008).
[CrossRef]

Santos, E.

E. Santos, “Critical analysis of the empirical tests of local hidden-variable theories,” Phys. Rev. A 46, 3646–3656 (1992).
[CrossRef]

Sasaki, M.

H. Takahashi, J. 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]

A. Kitagawa, M. Takeoka, M. Sasaki, and A. Chefles, “Entanglement evaluation of non-Gaussian states generated by photon subtraction from squeezed states,” Phys. Rev. A 73042310 (2006).
[CrossRef]

Scheel, S.

J. Eisert, M. B. Plenio, D. E. Browne, S. Scheel, and A. Feito, “On the experimental feasibility of continuous-variable optical entanglement distillation,” Opt. Spectrosc. 103, 173–177 (2007).
[CrossRef]

J. Eisert, D. E. Browne, S. Scheel, and M. B. Plenio, “Distillation of continuous-variable entanglement with optical means,” Ann. Phys. 311, 431–458 (2004).
[CrossRef]

D. E. Browne, J. Eisert, S. Scheel, and M. B. Plenio, “Driving non-Gaussian to Gaussian states with linear optics,” Phys. Rev. A 67, 062320 (2003).
[CrossRef]

J. Eisert, S. Scheel, and M. B. Plenio, “Distilling Gaussian states with Gaussian operations is impossible,” Phys. Rev. Lett. 89, 137903 (2002).
[CrossRef]

Schnabel, R.

B. Hage, A. Samblowski, J. Diguglielmo, A. Franzen, J. Fiurášek, and R. Schnabel, “Preparation of distilled and purified continuous-variable entangled states,” Nat. Phys. 4, 915–918 (2008).
[CrossRef]

P. Marek, J. Fiurášek, B. Hage, A. Franzen, J. DiGugliemo, and R. Schnabel, “Multiple-copy distillation and purification of phase-diffused squeezed states,” Phys. Rev. A 76, 053820 (2007).
[CrossRef]

Serafini, A.

G. Adesso, A. Serafini, and F. Illuminati, “Quantification and scaling of multipartite entanglement in continuous variable systems,” Phys. Rev. Lett. 93, 220504 (2004).
[CrossRef]

Shapiro, J. H.

C. Navarrete-Benlloch, R. García-Patrón, J. H. Shapiro, and N. J. Cerf, “Enhancing quantum entanglement by photon addition and subtraction,” Phys. Rev. A 86, 012328 (2012).
[CrossRef]

Shi, B.

S. Yang, X. Zou, S. Zhang, B. Shi, P. van Loock, and G. Guo, “Multipartite continuous-variable entanglement distillation using local squeezing and only one photon-subtraction operation,” e-print arXiv:1106.1536v1.

Smolin, J. A.

C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, “Mixed-state entanglement and quantum error correction,” Phys. Rev. A 54, 3824–3851 (1996).
[CrossRef]

Takahashi, H.

H. Takahashi, J. 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]

Takeoka, M.

H. Takahashi, J. 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]

A. Kitagawa, M. Takeoka, M. Sasaki, and A. Chefles, “Entanglement evaluation of non-Gaussian states generated by photon subtraction from squeezed states,” Phys. Rev. A 73042310 (2006).
[CrossRef]

Takeuchi, M.

H. Takahashi, J. 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]

Tualle-Brouri, R.

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

van Loock, P.

P. van Loock, “Optical hybrid approaches to quantum information,” Laser Photon. Rev. 5, 167–200 (2011).
[CrossRef]

S. Zhang and P. van Loock, “Local Gaussian operations can enhance continuous-variable entanglement distillation,” Phys. Rev. A 84, 062309 (2011).
[CrossRef]

S. Zhang and P. van Loock, “Distillation of mixed-state continuous-variable entanglement by photon subtraction,” Phys. Rev. A 82, 062316 (2010).
[CrossRef]

S. Yang, X. Zou, S. Zhang, B. Shi, P. van Loock, and G. Guo, “Multipartite continuous-variable entanglement distillation using local squeezing and only one photon-subtraction operation,” e-print arXiv:1106.1536v1.

Viciani, S.

A. Zavatta, S. Viciani, and M. Bellini, “Quantum-to-classical transition with single-photon-added coherent states of light,” Science 306, 660–662 (2004).
[CrossRef]

Vidal, G.

G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A 65, 032314 (2002).
[CrossRef]

Welsch, D. G.

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]

Werner, R. F.

G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A 65, 032314 (2002).
[CrossRef]

Wootters, W. K.

C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, “Mixed-state entanglement and quantum error correction,” Phys. Rev. A 54, 3824–3851 (1996).
[CrossRef]

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef]

Yang, S.

S. Yang, X. Zou, S. Zhang, B. Shi, P. van Loock, and G. Guo, “Multipartite continuous-variable entanglement distillation using local squeezing and only one photon-subtraction operation,” e-print arXiv:1106.1536v1.

Zavatta, A.

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]

A. Zavatta, S. Viciani, and M. Bellini, “Quantum-to-classical transition with single-photon-added coherent states of light,” Science 306, 660–662 (2004).
[CrossRef]

Zhang, S.

S. Zhang and P. van Loock, “Local Gaussian operations can enhance continuous-variable entanglement distillation,” Phys. Rev. A 84, 062309 (2011).
[CrossRef]

S. Zhang and P. van Loock, “Distillation of mixed-state continuous-variable entanglement by photon subtraction,” Phys. Rev. A 82, 062316 (2010).
[CrossRef]

S. Yang, X. Zou, S. Zhang, B. Shi, P. van Loock, and G. Guo, “Multipartite continuous-variable entanglement distillation using local squeezing and only one photon-subtraction operation,” e-print arXiv:1106.1536v1.

Zou, X.

S. Yang, X. Zou, S. Zhang, B. Shi, P. van Loock, and G. Guo, “Multipartite continuous-variable entanglement distillation using local squeezing and only one photon-subtraction operation,” e-print arXiv:1106.1536v1.

Ann. Phys.

J. Eisert, D. E. Browne, S. Scheel, and M. B. Plenio, “Distillation of continuous-variable entanglement with optical means,” Ann. Phys. 311, 431–458 (2004).
[CrossRef]

J. Phys. A

G. Lindblad, “Cloning the quantum oscillator,” J. Phys. A 33, 5059–5076 (2000).
[CrossRef]

Laser Photon. Rev.

P. van Loock, “Optical hybrid approaches to quantum information,” Laser Photon. Rev. 5, 167–200 (2011).
[CrossRef]

Nat. Photonics

H. Takahashi, J. 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]

Nat. Phys.

B. Hage, A. Samblowski, J. Diguglielmo, A. Franzen, J. Fiurášek, and R. Schnabel, “Preparation of distilled and purified continuous-variable entangled states,” Nat. Phys. 4, 915–918 (2008).
[CrossRef]

R. Dong, M. Lassen, J. Heersink, C. Marquardt, R. Filip, G. Leuchs, and U. L. Andersen, “Experimental entanglement distillation of mesoscopic quantum states,” Nat. Phys. 4, 919–923 (2008).
[CrossRef]

Opt. Spectrosc.

J. Eisert, M. B. Plenio, D. E. Browne, S. Scheel, and A. Feito, “On the experimental feasibility of continuous-variable optical entanglement distillation,” Opt. Spectrosc. 103, 173–177 (2007).
[CrossRef]

Phys. Rev. A

A. P. Lund and T. C. Ralph, “Continuous-variable entanglement distillation over a general lossy channel,” Phys. Rev. A 80, 032309 (2009).
[CrossRef]

J. Fiurášek, “Distillation and purification of symmetric entangled Gaussian states,” Phys. Rev. A 82, 042331 (2010).
[CrossRef]

G. Giedke and J. I. Cirac, “Characterization of Gaussian operations and distillation of Gaussian states,” Phys. Rev. A 66, 032316 (2002).
[CrossRef]

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]

C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, “Mixed-state entanglement and quantum error correction,” Phys. Rev. A 54, 3824–3851 (1996).
[CrossRef]

J. Fiurášek, “Engineering quantum operations on traveling light beams by multiple photon addition and subtraction,” Phys. Rev. A 80, 053822 (2009).
[CrossRef]

C. Navarrete-Benlloch, R. García-Patrón, J. H. Shapiro, and N. J. Cerf, “Enhancing quantum entanglement by photon addition and subtraction,” Phys. Rev. A 86, 012328 (2012).
[CrossRef]

S. Zhang and P. van Loock, “Distillation of mixed-state continuous-variable entanglement by photon subtraction,” Phys. Rev. A 82, 062316 (2010).
[CrossRef]

D. E. Browne, J. Eisert, S. Scheel, and M. B. Plenio, “Driving non-Gaussian to Gaussian states with linear optics,” Phys. Rev. A 67, 062320 (2003).
[CrossRef]

E. Santos, “Critical analysis of the empirical tests of local hidden-variable theories,” Phys. Rev. A 46, 3646–3656 (1992).
[CrossRef]

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802 (2010).
[CrossRef]

S. Olivares, M. G. A. Paris, and R. Bonifacio, “Teleporation improvement by inconclusive photon subtraction,” Phys. Rev. A 67, 032314 (2003).
[CrossRef]

A. Kitagawa, M. Takeoka, M. Sasaki, and A. Chefles, “Entanglement evaluation of non-Gaussian states generated by photon subtraction from squeezed states,” Phys. Rev. A 73042310 (2006).
[CrossRef]

S. Zhang and P. van Loock, “Local Gaussian operations can enhance continuous-variable entanglement distillation,” Phys. Rev. A 84, 062309 (2011).
[CrossRef]

J. Fiurášek, “Improving entanglement concentration of Gaussian states by local displacements,” Phys. Rev. A 84, 012335 (2011).
[CrossRef]

P. Marek, J. Fiurášek, B. Hage, A. Franzen, J. DiGugliemo, and R. Schnabel, “Multiple-copy distillation and purification of phase-diffused squeezed states,” Phys. Rev. A 76, 053820 (2007).
[CrossRef]

G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A 65, 032314 (2002).
[CrossRef]

Phys. Rev. D

P. Pearle, “Hidden-variable example based upon data rejection,” Phys. Rev. D 2, 1418–1425 (1970).
[CrossRef]

Phys. Rev. Lett.

G. Adesso, A. Serafini, and F. Illuminati, “Quantification and scaling of multipartite entanglement in continuous variable systems,” Phys. Rev. Lett. 93, 220504 (2004).
[CrossRef]

J. Eisert, S. Scheel, and M. B. Plenio, “Distilling Gaussian states with Gaussian operations is impossible,” Phys. Rev. Lett. 89, 137903 (2002).
[CrossRef]

J. Fiurášek, “Gaussian transformations and distillation of entangled Gaussian states,” Phys. Rev. Lett. 89, 137904 (2002).
[CrossRef]

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
[CrossRef]

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef]

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

E. T. Campbell and J. Eisert, “Gaussification and entanglement distillation of continuous-variable systems: a unifying picture,” Phys. Rev. Lett. 108, 020501 (2012).
[CrossRef]

Science

A. Zavatta, S. Viciani, and M. Bellini, “Quantum-to-classical transition with single-photon-added coherent states of light,” Science 306, 660–662 (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]

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]

Other

S. Yang, X. Zou, S. Zhang, B. Shi, P. van Loock, and G. Guo, “Multipartite continuous-variable entanglement distillation using local squeezing and only one photon-subtraction operation,” e-print arXiv:1106.1536v1.

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Figures (4)

Fig. 1.
Fig. 1.

Entanglement distillation in presence of thermal noise. Single-mode-squeezed state |ξ and thermal noise ρth(Ns) are coupled with the 5050 beamsplitter, generating the mixed Gaussian entanglement that is to be distilled. Two more beamsplitters with transmittance coefficient T and photon “on–off” detectors D1 and D2 are used to implement the PS operations. We assume that the thermal noise level in the detecting zone is Nd.

Fig. 2.
Fig. 2.

Entanglement distillation with single-PS (open circles) and two-PS (open squares). Other parameters are chosen as Ns=Nd=N0, T=0.95. Photon number is truncated at D¯=10. The black solid lines in (a), (c), and (e) indicate the entanglement before distillation. (b), (d), and (f) The corresponding success probability (in logarithmic scale) as a function of log10N0.

Fig. 3.
Fig. 3.

Entanglement and success probability with detector efficiency η, for single-PS scheme (open circles) and two-PS scheme (open squares). Beamsplitter T=0.90 and D¯=7. The black solid lines in (a) and (c) indicate the entanglement before distillation. (b) and (d) The success probability as a function of thermal noise level log10N0.

Fig. 4.
Fig. 4.

(a) and (b) Entanglement and success probability of distilled state as a function of thermal noise level Nd after single-PS (open circles) and two-PS (open squares). Other parameters: σ=0.05, r=0.4, η=0.9, D¯=6. (c) and (d) Entanglement and success probability as a function of phase diffusion σ. Other parameters: η=0.90, Nd=106, r=0.4, D¯=6.

Equations (21)

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

|ξ=1coshrm=0(2m)!2mm!(tanhr)m|2m,
ρ^th(N)=1N+1m=0(NN+1)m|mm|.
ST(kl)=(T1TT1T1TT1TT).
VAB=S1/2(AB)(VAVB)S1/2(AB)T
VA=(Ns+1/2)I2,VB=diag(e2r/2,e2r/2)
VABCD=ST[VAB(Nd+12)I4]STT.
ρ^dist(2)·Psucc(2)=j=14Pjρ^(Λj)
P1=1,P2=[det(VC+I2/2)]1/2,P3=[det(VD+I2/2)]1/2,P4=[det(ΓCD+I4/2)]1/2,Λ1=ΓAB,Λ2=ΓABM1(VC+I2/2)1M1T,Λ3=ΓABM2(VD+I2/2)1M2T,Λ4=ΓABM(ΓCD+I4/2)1MT,
VABCD=(ΓABMMTΓCD),ΓCD=(VCςςTVD).
ρ^dist(1)·Psucc(1)=P2ρ^(Λ2)+P4ρ^(Λ4)
VABCDVABCD=XtotVABCDXtotT+Ntot
Xtot=I2I2ηI2ηI2,Ntot=0202(1η)I2/2(1η)I2/2,
ρmix=dϕΦ(ϕ)U(ϕ)|ξξ|U(ϕ)
Φ(ϕ)=12πσ2eϕ22σ2,
U(ϕ)=m,neinϕδmn|mn|.
ρmix=m,n=0(2m)!(2n)!2m+nm!n!(tanhr)m+ncoshre2(mn)2σ2|2m2n|.
ρAB=U(AB)(1/2)(ρmix|00|)U(AB)(1/2).
ρABCD=V(ρABρthC(Nd)ρthD(Nd))V,
V=U(AC)(T)U(BD)(T).
ρ˜TPS=Tr[ρABCDIABΠC(on)ΠD(on)]Psucc(2),
ρ˜SPS=Tr[ρABCDIAB|00|ΠD(on)]Psucc(1),

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