Abstract

Entanglement distillation is a physically feasible operation which helps to partially or completely eliminate noise-induced decoherence in the distribution of entangled states. In this paper, we investigate the two-copy and single-copy distillation of an amplitude-damped continuous variable two-mode squeezed vacuum state. We consider local squeezing as one of the important tools [Phys. Rev. A 84, 062309 (2011)] to enhance distillation. Our result is twofold. First, we show that local squeezing is useful to improve the distillation of two-copy interference-based distillation. Second, we show single-copy photon subtraction-based distillation is more efficient in providing more entangled outputs. However, such an advantage would diminish and two-copy distillation could succeed with much higher probability of success for a fixed amount of distilled entanglement.

© 2014 Optical Society of America

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  1. 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]
  2. P. G. Kwiat, S. Barraza-Lopez, A. Stefanov, and N. Gisin, “Experimental entanglement distillation and ‘hidden’ non-locality,” Nature 409, 1014–1017 (2001).
    [CrossRef]
  3. J. W. Pan, C. Simon, Č. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature 410, 1067–1070 (2001).
    [CrossRef]
  4. T. Yamamoto, M. Koashi, Ş. K. Özdemir, and N. Imoto, “Experimental extraction of an entangled photon pair from two identically decohered pairs,” Nature 421, 343–346 (2003).
    [CrossRef]
  5. R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature 443, 838–841 (2006).
    [CrossRef]
  6. J. Eisert, S. Scheel, and M. B. Plenio, “Distilling Gaussian states with Gaussian operations is impossible,” Phys. Rev. Lett. 89, 137903 (2002).
    [CrossRef]
  7. J. Fiurášek, “Gaussian transformations and distillation of entangled Gaussian states,” Phys. Rev. Lett. 89, 137904 (2002).
    [CrossRef]
  8. G. Giedke and J. I. Cirac, “Characterization of Gaussian operations and distillation of Gaussian states,” Phys. Rev. A 66, 032316 (2002).
    [CrossRef]
  9. 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]
  10. A. P. Lund and T. C. Ralph, “Continuous-variable entanglement distillation over a general lossy channel,” Phys. Rev. A 80, 032309 (2009).
    [CrossRef]
  11. 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]
  12. 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]
  13. S. Olivares, M. G. A. Paris, and R. Bonifacio, “Teleportation improvement by inconclusive photon subtraction,” Phys. Rev. A 67, 032314 (2003).
    [CrossRef]
  14. 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 73, 042310 (2006).
    [CrossRef]
  15. 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]
  16. S. Zhang, Y. Dong, J. Shi, X. Zou, and G. Guo, “Roles of thermal noise and detector efficiency in distillation of continuous variable entanglement state,” J. Opt. Soc. Am. B 30, 2704–2709 (2013).
    [CrossRef]
  17. 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]
  18. B. Hage, A. Franzen, J. DiGuglielmo, P. Marek, J. Fiurášek, and R. Schnabel, “On the distillation and purification of phase-diffused squeezed states,” New J. Phys. 9, 227 (2007).
    [CrossRef]
  19. S. Zhang and P. van Loock, “Local Gaussian operations can enhance continuous-variable entanglement distillation,” Phys. Rev. A 84, 062309 (2011).
    [CrossRef]
  20. S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005).
    [CrossRef]
  21. G. Adesso and F. Illuminati, “Entanglement in continuous-variable systems: recent advances and current perspectives,” J. Phys. A 40, 7821–7880 (2007).
    [CrossRef]
  22. N. Lee, H. Benichi, Y. Takeno, S. Takeda, J. Webb, E. Huntington, and A. Furusawa, “Teleportation of nonclassical wave packets of light,” Science 332, 330–333 (2011).
    [CrossRef]
  23. G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A 65, 032314 (2002).
    [CrossRef]
  24. S. Yang, X. Zou, S. Zhang, B.-S. Shi, P. van Loock, and G. Guo, “Multipartite continuous-variable entanglement distillation using local squeezing and only one photon-subtraction operation,” Arxiv:1106.1536 (2011).
  25. W. J. Munro, “Optimal states for Bell-inequality violations using quadrature-phase homodyne measurements,” Phys. Rev. A 59, 4197–4201 (1999).
    [CrossRef]
  26. A. Acín, N. J. Cerf, A. Ferraro, and J. Niset, “Tests of multimode quantum nonlocality with homodyne measurement,” Phys. Rev. A 79, 012112 (2009).
    [CrossRef]

2013 (1)

2011 (2)

N. Lee, H. Benichi, Y. Takeno, S. Takeda, J. Webb, E. Huntington, and A. Furusawa, “Teleportation of nonclassical wave packets of light,” Science 332, 330–333 (2011).
[CrossRef]

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

2010 (1)

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]

2009 (2)

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

A. Acín, N. J. Cerf, A. Ferraro, and J. Niset, “Tests of multimode quantum nonlocality with homodyne measurement,” Phys. Rev. A 79, 012112 (2009).
[CrossRef]

2008 (2)

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 (2)

B. Hage, A. Franzen, J. DiGuglielmo, P. Marek, J. Fiurášek, and R. Schnabel, “On the distillation and purification of phase-diffused squeezed states,” New J. Phys. 9, 227 (2007).
[CrossRef]

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

2006 (2)

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 73, 042310 (2006).
[CrossRef]

R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature 443, 838–841 (2006).
[CrossRef]

2005 (1)

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005).
[CrossRef]

2003 (3)

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

T. Yamamoto, M. Koashi, Ş. K. Özdemir, and N. Imoto, “Experimental extraction of an entangled photon pair from two identically decohered pairs,” Nature 421, 343–346 (2003).
[CrossRef]

2002 (4)

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]

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

2001 (2)

P. G. Kwiat, S. Barraza-Lopez, A. Stefanov, and N. Gisin, “Experimental entanglement distillation and ‘hidden’ non-locality,” Nature 409, 1014–1017 (2001).
[CrossRef]

J. W. Pan, C. Simon, Č. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature 410, 1067–1070 (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]

1999 (1)

W. J. Munro, “Optimal states for Bell-inequality violations using quadrature-phase homodyne measurements,” Phys. Rev. A 59, 4197–4201 (1999).
[CrossRef]

1993 (1)

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]

Acín, A.

A. Acín, N. J. Cerf, A. Ferraro, and J. Niset, “Tests of multimode quantum nonlocality with homodyne measurement,” Phys. Rev. A 79, 012112 (2009).
[CrossRef]

Adesso, G.

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

Barraza-Lopez, S.

P. G. Kwiat, S. Barraza-Lopez, A. Stefanov, and N. Gisin, “Experimental entanglement distillation and ‘hidden’ non-locality,” Nature 409, 1014–1017 (2001).
[CrossRef]

Benichi, H.

N. Lee, H. Benichi, Y. Takeno, S. Takeda, J. Webb, E. Huntington, and A. Furusawa, “Teleportation of nonclassical wave packets of light,” Science 332, 330–333 (2011).
[CrossRef]

Bennett, C. H.

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]

Blakestad, R. B.

R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature 443, 838–841 (2006).
[CrossRef]

Bonifacio, R.

S. Olivares, M. G. A. Paris, and R. Bonifacio, “Teleportation 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]

Braunstein, S. L.

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005).
[CrossRef]

Britton, J.

R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature 443, 838–841 (2006).
[CrossRef]

Browne, D. E.

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]

Brukner, C.

J. W. Pan, C. Simon, Č. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature 410, 1067–1070 (2001).
[CrossRef]

Cerf, N. J.

A. Acín, N. J. Cerf, A. Ferraro, and J. Niset, “Tests of multimode quantum nonlocality with homodyne measurement,” Phys. Rev. A 79, 012112 (2009).
[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 73, 042310 (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]

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]

B. Hage, A. Franzen, J. DiGuglielmo, P. Marek, J. Fiurášek, and R. Schnabel, “On the distillation and purification of phase-diffused squeezed states,” New J. Phys. 9, 227 (2007).
[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]

Dong, Y.

Eisert, J.

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]

Ferraro, A.

A. Acín, N. J. Cerf, A. Ferraro, and J. Niset, “Tests of multimode quantum nonlocality with homodyne measurement,” Phys. Rev. A 79, 012112 (2009).
[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.

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]

B. Hage, A. Franzen, J. DiGuglielmo, P. Marek, J. Fiurášek, and R. Schnabel, “On the distillation and purification of phase-diffused squeezed states,” New J. Phys. 9, 227 (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]

B. Hage, A. Franzen, J. DiGuglielmo, P. Marek, J. Fiurášek, and R. Schnabel, “On the distillation and purification of phase-diffused squeezed states,” New J. Phys. 9, 227 (2007).
[CrossRef]

Furusawa, A.

N. Lee, H. Benichi, Y. Takeno, S. Takeda, J. Webb, E. Huntington, and A. Furusawa, “Teleportation of nonclassical wave packets of light,” Science 332, 330–333 (2011).
[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]

Giedke, G.

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

Gisin, N.

P. G. Kwiat, S. Barraza-Lopez, A. Stefanov, and N. Gisin, “Experimental entanglement distillation and ‘hidden’ non-locality,” Nature 409, 1014–1017 (2001).
[CrossRef]

Guo, G.

S. Zhang, Y. Dong, J. Shi, X. Zou, and G. Guo, “Roles of thermal noise and detector efficiency in distillation of continuous variable entanglement state,” J. Opt. Soc. Am. B 30, 2704–2709 (2013).
[CrossRef]

S. Yang, X. Zou, S. Zhang, B.-S. Shi, P. van Loock, and G. Guo, “Multipartite continuous-variable entanglement distillation using local squeezing and only one photon-subtraction operation,” Arxiv:1106.1536 (2011).

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]

B. Hage, A. Franzen, J. DiGuglielmo, P. Marek, J. Fiurášek, and R. Schnabel, “On the distillation and purification of phase-diffused squeezed states,” New J. Phys. 9, 227 (2007).
[CrossRef]

Hayasaka, K.

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]

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]

Huntington, E.

N. Lee, H. Benichi, Y. Takeno, S. Takeda, J. Webb, E. Huntington, and A. Furusawa, “Teleportation of nonclassical wave packets of light,” Science 332, 330–333 (2011).
[CrossRef]

Illuminati, F.

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

Imoto, N.

T. Yamamoto, M. Koashi, Ş. K. Özdemir, and N. Imoto, “Experimental extraction of an entangled photon pair from two identically decohered pairs,” Nature 421, 343–346 (2003).
[CrossRef]

Jost, J. D.

R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature 443, 838–841 (2006).
[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]

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 73, 042310 (2006).
[CrossRef]

Knill, E.

R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature 443, 838–841 (2006).
[CrossRef]

Koashi, M.

T. Yamamoto, M. Koashi, Ş. K. Özdemir, and N. Imoto, “Experimental extraction of an entangled photon pair from two identically decohered pairs,” Nature 421, 343–346 (2003).
[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]

Kwiat, P. G.

P. G. Kwiat, S. Barraza-Lopez, A. Stefanov, and N. Gisin, “Experimental entanglement distillation and ‘hidden’ non-locality,” Nature 409, 1014–1017 (2001).
[CrossRef]

Langer, C.

R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature 443, 838–841 (2006).
[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]

Lee, N.

N. Lee, H. Benichi, Y. Takeno, S. Takeda, J. Webb, E. Huntington, and A. Furusawa, “Teleportation of nonclassical wave packets of light,” Science 332, 330–333 (2011).
[CrossRef]

Leibfried, D.

R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature 443, 838–841 (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]

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]

Marek, P.

B. Hage, A. Franzen, J. DiGuglielmo, P. Marek, J. Fiurášek, and R. Schnabel, “On the distillation and purification of phase-diffused squeezed states,” New J. Phys. 9, 227 (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]

Munro, W. J.

W. J. Munro, “Optimal states for Bell-inequality violations using quadrature-phase homodyne measurements,” Phys. Rev. A 59, 4197–4201 (1999).
[CrossRef]

Neergaard-Nielsen, J. S.

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]

Niset, J.

A. Acín, N. J. Cerf, A. Ferraro, and J. Niset, “Tests of multimode quantum nonlocality with homodyne measurement,” Phys. Rev. A 79, 012112 (2009).
[CrossRef]

Olivares, S.

S. Olivares, M. G. A. Paris, and R. Bonifacio, “Teleportation 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]

Özdemir, S. K.

T. Yamamoto, M. Koashi, Ş. K. Özdemir, and N. Imoto, “Experimental extraction of an entangled photon pair from two identically decohered pairs,” Nature 421, 343–346 (2003).
[CrossRef]

Ozeri, R.

R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature 443, 838–841 (2006).
[CrossRef]

Pan, J. W.

J. W. Pan, C. Simon, Č. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature 410, 1067–1070 (2001).
[CrossRef]

Paris, M. G. A.

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

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]

Reichle, R.

R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature 443, 838–841 (2006).
[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]

Sasaki, M.

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]

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 73, 042310 (2006).
[CrossRef]

Scheel, S.

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]

B. Hage, A. Franzen, J. DiGuglielmo, P. Marek, J. Fiurášek, and R. Schnabel, “On the distillation and purification of phase-diffused squeezed states,” New J. Phys. 9, 227 (2007).
[CrossRef]

Seidelin, S.

R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature 443, 838–841 (2006).
[CrossRef]

Shi, B.-S.

S. Yang, X. Zou, S. Zhang, B.-S. Shi, P. van Loock, and G. Guo, “Multipartite continuous-variable entanglement distillation using local squeezing and only one photon-subtraction operation,” Arxiv:1106.1536 (2011).

Shi, J.

Simon, C.

J. W. Pan, C. Simon, Č. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature 410, 1067–1070 (2001).
[CrossRef]

Stefanov, A.

P. G. Kwiat, S. Barraza-Lopez, A. Stefanov, and N. Gisin, “Experimental entanglement distillation and ‘hidden’ non-locality,” Nature 409, 1014–1017 (2001).
[CrossRef]

Takahashi, H.

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]

Takeda, S.

N. Lee, H. Benichi, Y. Takeno, S. Takeda, J. Webb, E. Huntington, and A. Furusawa, “Teleportation of nonclassical wave packets of light,” Science 332, 330–333 (2011).
[CrossRef]

Takeno, Y.

N. Lee, H. Benichi, Y. Takeno, S. Takeda, J. Webb, E. Huntington, and A. Furusawa, “Teleportation of nonclassical wave packets of light,” Science 332, 330–333 (2011).
[CrossRef]

Takeoka, M.

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]

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 73, 042310 (2006).
[CrossRef]

Takeuchi, M.

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]

van Loock, P.

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

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005).
[CrossRef]

S. Yang, X. Zou, S. Zhang, B.-S. Shi, P. van Loock, and G. Guo, “Multipartite continuous-variable entanglement distillation using local squeezing and only one photon-subtraction operation,” Arxiv:1106.1536 (2011).

Vidal, G.

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

Webb, J.

N. Lee, H. Benichi, Y. Takeno, S. Takeda, J. Webb, E. Huntington, and A. Furusawa, “Teleportation of nonclassical wave packets of light,” Science 332, 330–333 (2011).
[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]

Wineland, D. J.

R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature 443, 838–841 (2006).
[CrossRef]

Wootters, W. K.

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]

Yamamoto, T.

T. Yamamoto, M. Koashi, Ş. K. Özdemir, and N. Imoto, “Experimental extraction of an entangled photon pair from two identically decohered pairs,” Nature 421, 343–346 (2003).
[CrossRef]

Yang, S.

S. Yang, X. Zou, S. Zhang, B.-S. Shi, P. van Loock, and G. Guo, “Multipartite continuous-variable entanglement distillation using local squeezing and only one photon-subtraction operation,” Arxiv:1106.1536 (2011).

Zeilinger, A.

J. W. Pan, C. Simon, Č. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature 410, 1067–1070 (2001).
[CrossRef]

Zhang, S.

S. Zhang, Y. Dong, J. Shi, X. Zou, and G. Guo, “Roles of thermal noise and detector efficiency in distillation of continuous variable entanglement state,” J. Opt. Soc. Am. B 30, 2704–2709 (2013).
[CrossRef]

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

S. Yang, X. Zou, S. Zhang, B.-S. Shi, P. van Loock, and G. Guo, “Multipartite continuous-variable entanglement distillation using local squeezing and only one photon-subtraction operation,” Arxiv:1106.1536 (2011).

Zou, X.

S. Zhang, Y. Dong, J. Shi, X. Zou, and G. Guo, “Roles of thermal noise and detector efficiency in distillation of continuous variable entanglement state,” J. Opt. Soc. Am. B 30, 2704–2709 (2013).
[CrossRef]

S. Yang, X. Zou, S. Zhang, B.-S. Shi, P. van Loock, and G. Guo, “Multipartite continuous-variable entanglement distillation using local squeezing and only one photon-subtraction operation,” Arxiv:1106.1536 (2011).

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

J. Phys. A (1)

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

Nat. Photonics (1)

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]

Nat. Phys. (2)

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]

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]

Nature (4)

P. G. Kwiat, S. Barraza-Lopez, A. Stefanov, and N. Gisin, “Experimental entanglement distillation and ‘hidden’ non-locality,” Nature 409, 1014–1017 (2001).
[CrossRef]

J. W. Pan, C. Simon, Č. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature 410, 1067–1070 (2001).
[CrossRef]

T. Yamamoto, M. Koashi, Ş. K. Özdemir, and N. Imoto, “Experimental extraction of an entangled photon pair from two identically decohered pairs,” Nature 421, 343–346 (2003).
[CrossRef]

R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature 443, 838–841 (2006).
[CrossRef]

New J. Phys. (1)

B. Hage, A. Franzen, J. DiGuglielmo, P. Marek, J. Fiurášek, and R. Schnabel, “On the distillation and purification of phase-diffused squeezed states,” New J. Phys. 9, 227 (2007).
[CrossRef]

Phys. Rev. A (10)

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

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

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

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]

S. Olivares, M. G. A. Paris, and R. Bonifacio, “Teleportation 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 73, 042310 (2006).
[CrossRef]

G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A 65, 032314 (2002).
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W. J. Munro, “Optimal states for Bell-inequality violations using quadrature-phase homodyne measurements,” Phys. Rev. A 59, 4197–4201 (1999).
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A. Acín, N. J. Cerf, A. Ferraro, and J. Niset, “Tests of multimode quantum nonlocality with homodyne measurement,” Phys. Rev. A 79, 012112 (2009).
[CrossRef]

Phys. Rev. Lett. (3)

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]

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]

Rev. Mod. Phys. (1)

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005).
[CrossRef]

Science (1)

N. Lee, H. Benichi, Y. Takeno, S. Takeda, J. Webb, E. Huntington, and A. Furusawa, “Teleportation of nonclassical wave packets of light,” Science 332, 330–333 (2011).
[CrossRef]

Other (1)

S. Yang, X. Zou, S. Zhang, B.-S. Shi, P. van Loock, and G. Guo, “Multipartite continuous-variable entanglement distillation using local squeezing and only one photon-subtraction operation,” Arxiv:1106.1536 (2011).

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Figures (5)

Fig. 1.
Fig. 1.

Two-copy interference-based distillation scheme. ρA1B1=ρA2B2 represent two identical copies of amplitude-damped TMSS. The circles denotes four local squeezing operators S^(ξ1) and S^(ξ2) applied to optical modes A1B1 and A2B2. After interference on bi-side 5050 beam splitters, modes A2 and B2 are measured with homodyne measurements. The whole distillation is successful when the results |xA2xB2|Q.

Fig. 2.
Fig. 2.

(a) Entanglement EN in distilled state as a function of squeezing parameter ξ1=ξ2=ξ. (b) Corresponding success probability. Other parameters: Q=0.05, η=0.5, r=0.33.

Fig. 3.
Fig. 3.

Single-copy PS-based distillation scheme. ρAB is the amplitude-damped TMSS. S^(ξ) represents squeezers. C, D are auxiliary vacuum state. Two beam splitters (with transmittance T) and two on–off detectors are utilized to implement the bi-side PS scheme. Successful distillation is heralded when two detectors register “on” results.

Fig. 4.
Fig. 4.

Comparison in weak squeezing scenario (r=0.33, ξ=0.50) of entanglement and distillation probability relation between single-copy strategy (ENTPsucc) and two-copy strategy (ENQPsucc). (a) Entanglement for single-copy distillation strategy (ENT) and two-copy distillation strategy (ENQ). (b) Threshold Q used for fixed probability of success PsuccQ. (c) Parameters of beam splitter for fixed probability of success PsuccT.

Fig. 5.
Fig. 5.

Comparison in strong squeezing scenario (r=0.33, ξ=1.0) of entanglement and distillation probability relation between single-copy strategy (ENTPsucc) and two-copy strategy (ENQPsucc). (a) Entanglement for single-copy distillation strategy (ENT) and two-copy distillation strategy (ENQ). (b) Threshold Q used for fixed probability of success PsuccQ. (c) Parameters of beam splitter for fixed probability of success PsuccT.

Equations (29)

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ρA1B1=m,n=0i=0nj=0mfnmij|niA1mi||njB1mj|,
X^=(x^1,p^1,x^2,p^2,,x^N,p^N),
x^k=a^k+a^k2,p^k=a^ka^ki2,k=1,,N,
χ(z)=Tr[ρexp[iX^zT]],zR2N.
Vm=12Tr[(X^X^m+X^mX^)ρ]Tr[X^ρ]Tr[X^mρ].
W(r)=R2Nd2Nz(2π)2Nexp[irzT]χ(z).
UρUSVST,
Vmix=1η+ηcosh(2r)2I4+ηsinh(2r)2(0110)(1001).
Vmixsqueeze=[S(ξ)S(ξ)]Vmix[S(ξ)S(ξ)]T.
x¯A1B1squeeze=x¯A1B1[S(ξ)S(ξ)]T.
W(r)=d8z(2π)8exp[irzT]exp[12zVtotzT],
Vtot=SA1,A2,A1,B2(VmixsqueezeVmixsqueeze)SA1,A2,B1,B2T,
SA1,A2,B1,B2=SA1,A2SB1B2,
SA1A2=12I4+12iσyI2.
x¯A1B1A2B2=(x¯A1B1squeezex¯A2B2squeeze)SA1A2B1B2T=(01×401×4)SA1A2B1B2T=01×8.
Psucc=dx1dp1dx2dp2dp3dp4|x3x4|Qdx3dx4Wtot(r).
Psucc=dp3dp4|x3x4|Qdx3dx4W(x3,p3,x4,p4),
Psucc=dp3dp4|x3x4|Qdx3dx4d4zR(2π)4ei(x3,p3,x4,p4)zRTe[12zRV2zRT]=|x3x4|Qdx3dx4d4zR(2π)2δz6,0δz8,0ei(x3,p3,x4,p4)zRTe[12zRV2zRT]=|x3x4|Qdx3dx4dz5dz7(2π)2ei(x3,x4)(z5,z7)Te12(z5,z7)Γ(z5,z7)T,
Γ=(Vtot(5,5)Vtot(5,7)Vtot(7,5)Vtot(7,7))
x3x42=y3,x3+x42=y4.
U=(12121212).
Psucc=|y3|Q2dy3dy4dz5dz7(2π)2ei(y3,y4)UT(z5,z7)Te12(z5,z7)Γ(z5,z7)T=|y3|Q2dy3dy4dζ5dζ7(2π)2ei(y3,y4)(ζ5,ζ7)Te12(ζ5,ζ7)ΓU(ζ5,ζ7)T,
Psucc=|y3|Q2dy3dζ52πeiy3ζ5e12(ζ5,0)ΓU(ζ5,0)T=|y3|Q2dy312πΓU(1,1)exp[y322ΓU(1,1)]
=Erf(Q2ΓU(1,1))
=Erf(Qeξ2(1η+ηcosh(2r)ηsinh(2r))),
ρA1B1A2B2=i1,j1,i2,j2=0D¯1m1,n1,m2,n2=0D¯1ρi1j1i2j2m1n1m2n2|i1j1A1B1m1n1||i2j2A2B2m2n2|,
Psucc·ρdistA1B1=|x3x4|QTr[ρA1B1A2B2IA1B1|x3x3||x4x4|]=i1j1m1n1=0D¯1Ci1j1m1n1|i1j1m1n1|,
Ci1j1m1n1=i2j2m2n2=0D¯1ρi1j1i2j2m1n1m2n2|x3x4|Qdx3dx4x3|i2m2|x3x4|j2n2|x4.
EN=log2(ρdistA1B1)TA1,

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