Abstract

We present a proposal for entanglement purification of the continuous-variable quantum state of two propagating optical fields. The scheme is based on each field interacting with a local node-atomic ensemble whose internal collective excitation plays the role of an ancillary continuous-variable resource. Entanglement purification is achieved by a dichotomic measurement, representing the required non-Gaussian element, which consists of detecting the presence or absence of collective excitations in the atomic ensemble. This scheme can be extended to networks, where the nodes are single trapped atoms, and constitutes an important building block for the implementation of a continuous-variable quantum repeater.

© 2010 Optical Society of America

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    [CrossRef]
  2. S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005).
    [CrossRef]
  3. 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]
  4. J. Eisert, S. Scheel, and M. B. Plenio, “Distilling Gaussian states with Gaussian operations is impossible,” Phys. Rev. Lett. 89, 137903 (2002).
    [CrossRef] [PubMed]
  5. 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]
  6. H. Zeng and F. Lin, “Quantum conversion between the cavity fields and the center-of-mass motion of ions in a quantized trap,” Phys. Rev. A 50, R3589–R3592 (1994).
    [CrossRef] [PubMed]
  7. A. S. Parkins and H. J. Kimble, “Quantum state transfer between motion and light,” J. Opt. B: Quantum Semiclassical Opt. 1, 496–504 (1999).
    [CrossRef]
  8. G. Morigi, J. Eschner, S. Mancini, and D. Vitali, “Entangled light pulses from single cold atoms,” Phys. Rev. Lett. 96, 023601 (2006).
    [CrossRef] [PubMed]
  9. G. Morigi, J. Eschner, S. Mancini, and D. Vitali, “Coherent generation of EPR-entangled light pulses mediated by a single trapped atom,” Phys. Rev. A 73, 033822 (2006).
    [CrossRef]
  10. D. Vitali, P. Cañizares, J. Eschner, and G. Morigi, “Time-separated entangled light pulses from a single-atom emitter,” New J. Phys. 10, 033025 (2008).
    [CrossRef]
  11. J. Eschner, G. Morigi, F. Schmidt-Kaler, and R. Blatt, “Laser cooling of trapped ions,” J. Opt. Soc. Am. B 20, 1003–1015 (2003).
    [CrossRef]
  12. V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).
    [CrossRef] [PubMed]
  13. L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long- distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001).
    [CrossRef] [PubMed]
  14. L.-M. Duan, J. I. Cirac, and P. Zoller, “Three-dimensional theory for interaction between atomic ensembles and free-space light,” Phys. Rev. A 66, 023818 (2002).
    [CrossRef]
  15. T. Holstein and H. Primakoff, “Field dependence of the intrinsic domain magnetization of a ferromagnet,” Phys. Rev. 58, 1098–1113 (1940).
    [CrossRef]
  16. B. Julsgaard, A. Kozhekin, and E. S. Polzik, “Experimental long-lived entanglement of two macroscopic objects,” Nature 413, 400–403 (2001).
    [CrossRef] [PubMed]
  17. C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light,” Nature 409, 490–493 (2001).
    [CrossRef] [PubMed]
  18. D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
    [CrossRef] [PubMed]
  19. M. D. Lukin, S. F. Yelin, and M. Fleischhauer, “Entanglement of atomic ensembles by trapping correlated photon states,” Phys. Rev. Lett. 84, 4232–4235 (2000).
    [CrossRef] [PubMed]
  20. M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84, 5094–5097 (2000).
    [CrossRef] [PubMed]
  21. See, for instance, Ch. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kroll, J. H. Muller, J. Nunn, E. Polzik, J. Rarity, H. de Riedmatten, W. Rosenfeld, A. J. Shields, N. Skold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories: a review based on the European Integrated Project ‘Qubit Applications (QAP)’,” Eur. Phys. J. D 58, 1–22 (2010).
    [CrossRef]
  22. K. S. Choi, H. Deng, J. Laurat, and H. J. Kimble, “Mapping photonic entanglement into and out of a quantum memory,” Nature 452, 67–71 (2008).
    [CrossRef] [PubMed]
  23. D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, “Quantum dynamics of single trapped ions,” Rev. Mod. Phys. 75, 281–324 (2003).
    [CrossRef]
  24. A. Imamoglu, “High efficiency photon counting using stored light,” Phys. Rev. Lett. 89, 163602 (2002).
    [CrossRef] [PubMed]
  25. D. F. V. James and P. G. Kwiat, “Atomic vapor-based high efficiency optical detectors with photon number resolution,” Phys. Rev. Lett. 89, 183601 (2002).
    [CrossRef] [PubMed]
  26. S. Pirandola, S. Mancini, D. Vitali, and P. Tombesi, “Continuous-variable entanglement and quantum-state teleportation between optical and macroscopic vibrational modes through radiation pressure,” Phys. Rev. A 68, 062317 (2003).
    [CrossRef]
  27. D. F. Walls and G. J. Milburn, Quantum Optics, 2nd ed. (Springer, 2008).
    [CrossRef]
  28. S. Olivares, M. G. A. Paris, and R. Bonifacio, “Teleportation improvement by inconclusive photon subtraction,” Phys. Rev. A 67, 032314 (2003).
    [CrossRef]
  29. S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
    [CrossRef]
  30. A. Furusawa, J. Sorensen, S. L. Braunstein, C. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
    [CrossRef] [PubMed]
  31. S. Pirandola and S. Mancini, “Quantum teleportation with continuous variables: a survey,” Laser Phys. 16, 1418–1438 (2006).
    [CrossRef]
  32. K. E. Cahill and R. J. Glauber, “Density operators and quasiprobability distributions,” Phys. Rev. 177, 1882–1902 (1969).
    [CrossRef]
  33. G. Adesso and F. Illuminati, “Continuous variable tangle, monogamy inequality, and entanglement sharing in Gaussian states of continuous variable systems,” New J. Phys. 8, 15 (2006).
    [CrossRef]
  34. 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]
  35. 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]

2010 (2)

See, for instance, Ch. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kroll, J. H. Muller, J. Nunn, E. Polzik, J. Rarity, H. de Riedmatten, W. Rosenfeld, A. J. Shields, N. Skold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories: a review based on the European Integrated Project ‘Qubit Applications (QAP)’,” Eur. Phys. J. D 58, 1–22 (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]

2009 (1)

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev. Mod. Phys. 81, 865–942 (2009).
[CrossRef]

2008 (2)

D. Vitali, P. Cañizares, J. Eschner, and G. Morigi, “Time-separated entangled light pulses from a single-atom emitter,” New J. Phys. 10, 033025 (2008).
[CrossRef]

K. S. Choi, H. Deng, J. Laurat, and H. J. Kimble, “Mapping photonic entanglement into and out of a quantum memory,” Nature 452, 67–71 (2008).
[CrossRef] [PubMed]

2006 (6)

G. Adesso and F. Illuminati, “Continuous variable tangle, monogamy inequality, and entanglement sharing in Gaussian states of continuous variable systems,” New J. Phys. 8, 15 (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 73, 042310 (2006).
[CrossRef]

S. Pirandola and S. Mancini, “Quantum teleportation with continuous variables: a survey,” Laser Phys. 16, 1418–1438 (2006).
[CrossRef]

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

G. Morigi, J. Eschner, S. Mancini, and D. Vitali, “Entangled light pulses from single cold atoms,” Phys. Rev. Lett. 96, 023601 (2006).
[CrossRef] [PubMed]

G. Morigi, J. Eschner, S. Mancini, and D. Vitali, “Coherent generation of EPR-entangled light pulses mediated by a single trapped atom,” Phys. Rev. A 73, 033822 (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 (5)

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. Eschner, G. Morigi, F. Schmidt-Kaler, and R. Blatt, “Laser cooling of trapped ions,” J. Opt. Soc. Am. B 20, 1003–1015 (2003).
[CrossRef]

D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, “Quantum dynamics of single trapped ions,” Rev. Mod. Phys. 75, 281–324 (2003).
[CrossRef]

S. Pirandola, S. Mancini, D. Vitali, and P. Tombesi, “Continuous-variable entanglement and quantum-state teleportation between optical and macroscopic vibrational modes through radiation pressure,” Phys. Rev. A 68, 062317 (2003).
[CrossRef]

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

2002 (4)

A. Imamoglu, “High efficiency photon counting using stored light,” Phys. Rev. Lett. 89, 163602 (2002).
[CrossRef] [PubMed]

D. F. V. James and P. G. Kwiat, “Atomic vapor-based high efficiency optical detectors with photon number resolution,” Phys. Rev. Lett. 89, 183601 (2002).
[CrossRef] [PubMed]

L.-M. Duan, J. I. Cirac, and P. Zoller, “Three-dimensional theory for interaction between atomic ensembles and free-space light,” Phys. Rev. A 66, 023818 (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] [PubMed]

2001 (4)

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long- distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001).
[CrossRef] [PubMed]

B. Julsgaard, A. Kozhekin, and E. S. Polzik, “Experimental long-lived entanglement of two macroscopic objects,” Nature 413, 400–403 (2001).
[CrossRef] [PubMed]

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light,” Nature 409, 490–493 (2001).
[CrossRef] [PubMed]

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[CrossRef] [PubMed]

2000 (2)

M. D. Lukin, S. F. Yelin, and M. Fleischhauer, “Entanglement of atomic ensembles by trapping correlated photon states,” Phys. Rev. Lett. 84, 4232–4235 (2000).
[CrossRef] [PubMed]

M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84, 5094–5097 (2000).
[CrossRef] [PubMed]

1999 (1)

A. S. Parkins and H. J. Kimble, “Quantum state transfer between motion and light,” J. Opt. B: Quantum Semiclassical Opt. 1, 496–504 (1999).
[CrossRef]

1998 (2)

S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
[CrossRef]

A. Furusawa, J. Sorensen, S. L. Braunstein, C. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[CrossRef] [PubMed]

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]

1994 (1)

H. Zeng and F. Lin, “Quantum conversion between the cavity fields and the center-of-mass motion of ions in a quantized trap,” Phys. Rev. A 50, R3589–R3592 (1994).
[CrossRef] [PubMed]

1969 (1)

K. E. Cahill and R. J. Glauber, “Density operators and quasiprobability distributions,” Phys. Rev. 177, 1882–1902 (1969).
[CrossRef]

1940 (1)

T. Holstein and H. Primakoff, “Field dependence of the intrinsic domain magnetization of a ferromagnet,” Phys. Rev. 58, 1098–1113 (1940).
[CrossRef]

Adesso, G.

G. Adesso and F. Illuminati, “Continuous variable tangle, monogamy inequality, and entanglement sharing in Gaussian states of continuous variable systems,” New J. Phys. 8, 15 (2006).
[CrossRef]

Afzelius, M.

See, for instance, Ch. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kroll, J. H. Muller, J. Nunn, E. Polzik, J. Rarity, H. de Riedmatten, W. Rosenfeld, A. J. Shields, N. Skold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories: a review based on the European Integrated Project ‘Qubit Applications (QAP)’,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

Appel, J.

See, for instance, Ch. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kroll, J. H. Muller, J. Nunn, E. Polzik, J. Rarity, H. de Riedmatten, W. Rosenfeld, A. J. Shields, N. Skold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories: a review based on the European Integrated Project ‘Qubit Applications (QAP)’,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

Behroozi, C. H.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light,” Nature 409, 490–493 (2001).
[CrossRef] [PubMed]

Bennett, C. H.

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]

Blatt, R.

J. Eschner, G. Morigi, F. Schmidt-Kaler, and R. Blatt, “Laser cooling of trapped ions,” J. Opt. Soc. Am. B 20, 1003–1015 (2003).
[CrossRef]

D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, “Quantum dynamics of single trapped ions,” Rev. Mod. Phys. 75, 281–324 (2003).
[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]

Boyer de la Giroday, A.

See, for instance, Ch. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kroll, J. H. Muller, J. Nunn, E. Polzik, J. Rarity, H. de Riedmatten, W. Rosenfeld, A. J. Shields, N. Skold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories: a review based on the European Integrated Project ‘Qubit Applications (QAP)’,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

Brassard, G.

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]

Braunstein, S. L.

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

S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
[CrossRef]

A. Furusawa, J. Sorensen, S. L. Braunstein, C. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[CrossRef] [PubMed]

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]

Cahill, K. E.

K. E. Cahill and R. J. Glauber, “Density operators and quasiprobability distributions,” Phys. Rev. 177, 1882–1902 (1969).
[CrossRef]

Cañizares, P.

D. Vitali, P. Cañizares, J. Eschner, and G. Morigi, “Time-separated entangled light pulses from a single-atom emitter,” New J. Phys. 10, 033025 (2008).
[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]

Choi, K. S.

K. S. Choi, H. Deng, J. Laurat, and H. J. Kimble, “Mapping photonic entanglement into and out of a quantum memory,” Nature 452, 67–71 (2008).
[CrossRef] [PubMed]

Cirac, J. I.

L.-M. Duan, J. I. Cirac, and P. Zoller, “Three-dimensional theory for interaction between atomic ensembles and free-space light,” Phys. Rev. A 66, 023818 (2002).
[CrossRef]

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long- distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001).
[CrossRef] [PubMed]

de Riedmatten, H.

See, for instance, Ch. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kroll, J. H. Muller, J. Nunn, E. Polzik, J. Rarity, H. de Riedmatten, W. Rosenfeld, A. J. Shields, N. Skold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories: a review based on the European Integrated Project ‘Qubit Applications (QAP)’,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

Deng, H.

K. S. Choi, H. Deng, J. Laurat, and H. J. Kimble, “Mapping photonic entanglement into and out of a quantum memory,” Nature 452, 67–71 (2008).
[CrossRef] [PubMed]

Dewhurst, S. J.

See, for instance, Ch. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kroll, J. H. Muller, J. Nunn, E. Polzik, J. Rarity, H. de Riedmatten, W. Rosenfeld, A. J. Shields, N. Skold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories: a review based on the European Integrated Project ‘Qubit Applications (QAP)’,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

Duan, L. -M.

L.-M. Duan, J. I. Cirac, and P. Zoller, “Three-dimensional theory for interaction between atomic ensembles and free-space light,” Phys. Rev. A 66, 023818 (2002).
[CrossRef]

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long- distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001).
[CrossRef] [PubMed]

Dutton, Z.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light,” Nature 409, 490–493 (2001).
[CrossRef] [PubMed]

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] [PubMed]

Eschner, J.

D. Vitali, P. Cañizares, J. Eschner, and G. Morigi, “Time-separated entangled light pulses from a single-atom emitter,” New J. Phys. 10, 033025 (2008).
[CrossRef]

G. Morigi, J. Eschner, S. Mancini, and D. Vitali, “Coherent generation of EPR-entangled light pulses mediated by a single trapped atom,” Phys. Rev. A 73, 033822 (2006).
[CrossRef]

G. Morigi, J. Eschner, S. Mancini, and D. Vitali, “Entangled light pulses from single cold atoms,” Phys. Rev. Lett. 96, 023601 (2006).
[CrossRef] [PubMed]

J. Eschner, G. Morigi, F. Schmidt-Kaler, and R. Blatt, “Laser cooling of trapped ions,” J. Opt. Soc. Am. B 20, 1003–1015 (2003).
[CrossRef]

Fleischhauer, A.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[CrossRef] [PubMed]

Fleischhauer, M.

M. D. Lukin, S. F. Yelin, and M. Fleischhauer, “Entanglement of atomic ensembles by trapping correlated photon states,” Phys. Rev. Lett. 84, 4232–4235 (2000).
[CrossRef] [PubMed]

M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84, 5094–5097 (2000).
[CrossRef] [PubMed]

Fuchs, C.

A. Furusawa, J. Sorensen, S. L. Braunstein, C. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[CrossRef] [PubMed]

Furusawa, A.

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. Furusawa, J. Sorensen, S. L. Braunstein, C. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[CrossRef] [PubMed]

Giovannetti, V.

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

Gisin, N.

See, for instance, Ch. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kroll, J. H. Muller, J. Nunn, E. Polzik, J. Rarity, H. de Riedmatten, W. Rosenfeld, A. J. Shields, N. Skold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories: a review based on the European Integrated Project ‘Qubit Applications (QAP)’,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

Glauber, R. J.

K. E. Cahill and R. J. Glauber, “Density operators and quasiprobability distributions,” Phys. Rev. 177, 1882–1902 (1969).
[CrossRef]

Hau, L. V.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light,” Nature 409, 490–493 (2001).
[CrossRef] [PubMed]

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]

Holstein, T.

T. Holstein and H. Primakoff, “Field dependence of the intrinsic domain magnetization of a ferromagnet,” Phys. Rev. 58, 1098–1113 (1940).
[CrossRef]

Horodecki, K.

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev. Mod. Phys. 81, 865–942 (2009).
[CrossRef]

Horodecki, M.

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev. Mod. Phys. 81, 865–942 (2009).
[CrossRef]

Horodecki, P.

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev. Mod. Phys. 81, 865–942 (2009).
[CrossRef]

Horodecki, R.

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev. Mod. Phys. 81, 865–942 (2009).
[CrossRef]

Hu, C. Y.

See, for instance, Ch. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kroll, J. H. Muller, J. Nunn, E. Polzik, J. Rarity, H. de Riedmatten, W. Rosenfeld, A. J. Shields, N. Skold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories: a review based on the European Integrated Project ‘Qubit Applications (QAP)’,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

Illuminati, F.

G. Adesso and F. Illuminati, “Continuous variable tangle, monogamy inequality, and entanglement sharing in Gaussian states of continuous variable systems,” New J. Phys. 8, 15 (2006).
[CrossRef]

Imamoglu, A.

A. Imamoglu, “High efficiency photon counting using stored light,” Phys. Rev. Lett. 89, 163602 (2002).
[CrossRef] [PubMed]

James, D. F. V.

D. F. V. James and P. G. Kwiat, “Atomic vapor-based high efficiency optical detectors with photon number resolution,” Phys. Rev. Lett. 89, 183601 (2002).
[CrossRef] [PubMed]

Jelezko, F.

See, for instance, Ch. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kroll, J. H. Muller, J. Nunn, E. Polzik, J. Rarity, H. de Riedmatten, W. Rosenfeld, A. J. Shields, N. Skold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories: a review based on the European Integrated Project ‘Qubit Applications (QAP)’,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

Julsgaard, B.

B. Julsgaard, A. Kozhekin, and E. S. Polzik, “Experimental long-lived entanglement of two macroscopic objects,” Nature 413, 400–403 (2001).
[CrossRef] [PubMed]

Kimble, H. J.

K. S. Choi, H. Deng, J. Laurat, and H. J. Kimble, “Mapping photonic entanglement into and out of a quantum memory,” Nature 452, 67–71 (2008).
[CrossRef] [PubMed]

A. S. Parkins and H. J. Kimble, “Quantum state transfer between motion and light,” J. Opt. B: Quantum Semiclassical Opt. 1, 496–504 (1999).
[CrossRef]

A. Furusawa, J. Sorensen, S. L. Braunstein, C. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[CrossRef] [PubMed]

S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
[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]

Kozhekin, A.

B. Julsgaard, A. Kozhekin, and E. S. Polzik, “Experimental long-lived entanglement of two macroscopic objects,” Nature 413, 400–403 (2001).
[CrossRef] [PubMed]

Kroll, S.

See, for instance, Ch. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kroll, J. H. Muller, J. Nunn, E. Polzik, J. Rarity, H. de Riedmatten, W. Rosenfeld, A. J. Shields, N. Skold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories: a review based on the European Integrated Project ‘Qubit Applications (QAP)’,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

Kwiat, P. G.

D. F. V. James and P. G. Kwiat, “Atomic vapor-based high efficiency optical detectors with photon number resolution,” Phys. Rev. Lett. 89, 183601 (2002).
[CrossRef] [PubMed]

Laurat, J.

K. S. Choi, H. Deng, J. Laurat, and H. J. Kimble, “Mapping photonic entanglement into and out of a quantum memory,” Nature 452, 67–71 (2008).
[CrossRef] [PubMed]

Leibfried, D.

D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, “Quantum dynamics of single trapped ions,” Rev. Mod. Phys. 75, 281–324 (2003).
[CrossRef]

Lin, F.

H. Zeng and F. Lin, “Quantum conversion between the cavity fields and the center-of-mass motion of ions in a quantized trap,” Phys. Rev. A 50, R3589–R3592 (1994).
[CrossRef] [PubMed]

Liu, C.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light,” Nature 409, 490–493 (2001).
[CrossRef] [PubMed]

Lloyd, S.

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

Lukin, M. D.

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long- distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001).
[CrossRef] [PubMed]

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[CrossRef] [PubMed]

M. D. Lukin, S. F. Yelin, and M. Fleischhauer, “Entanglement of atomic ensembles by trapping correlated photon states,” Phys. Rev. Lett. 84, 4232–4235 (2000).
[CrossRef] [PubMed]

M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84, 5094–5097 (2000).
[CrossRef] [PubMed]

Maccone, L.

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

Mair, A.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[CrossRef] [PubMed]

Mancini, S.

G. Morigi, J. Eschner, S. Mancini, and D. Vitali, “Coherent generation of EPR-entangled light pulses mediated by a single trapped atom,” Phys. Rev. A 73, 033822 (2006).
[CrossRef]

G. Morigi, J. Eschner, S. Mancini, and D. Vitali, “Entangled light pulses from single cold atoms,” Phys. Rev. Lett. 96, 023601 (2006).
[CrossRef] [PubMed]

S. Pirandola and S. Mancini, “Quantum teleportation with continuous variables: a survey,” Laser Phys. 16, 1418–1438 (2006).
[CrossRef]

S. Pirandola, S. Mancini, D. Vitali, and P. Tombesi, “Continuous-variable entanglement and quantum-state teleportation between optical and macroscopic vibrational modes through radiation pressure,” Phys. Rev. A 68, 062317 (2003).
[CrossRef]

Milburn, G. J.

D. F. Walls and G. J. Milburn, Quantum Optics, 2nd ed. (Springer, 2008).
[CrossRef]

Monroe, C.

D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, “Quantum dynamics of single trapped ions,” Rev. Mod. Phys. 75, 281–324 (2003).
[CrossRef]

Morigi, G.

D. Vitali, P. Cañizares, J. Eschner, and G. Morigi, “Time-separated entangled light pulses from a single-atom emitter,” New J. Phys. 10, 033025 (2008).
[CrossRef]

G. Morigi, J. Eschner, S. Mancini, and D. Vitali, “Coherent generation of EPR-entangled light pulses mediated by a single trapped atom,” Phys. Rev. A 73, 033822 (2006).
[CrossRef]

G. Morigi, J. Eschner, S. Mancini, and D. Vitali, “Entangled light pulses from single cold atoms,” Phys. Rev. Lett. 96, 023601 (2006).
[CrossRef] [PubMed]

J. Eschner, G. Morigi, F. Schmidt-Kaler, and R. Blatt, “Laser cooling of trapped ions,” J. Opt. Soc. Am. B 20, 1003–1015 (2003).
[CrossRef]

Muller, J. H.

See, for instance, Ch. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kroll, J. H. Muller, J. Nunn, E. Polzik, J. Rarity, H. de Riedmatten, W. Rosenfeld, A. J. Shields, N. Skold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories: a review based on the European Integrated Project ‘Qubit Applications (QAP)’,” Eur. Phys. J. D 58, 1–22 (2010).
[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]

Nunn, J.

See, for instance, Ch. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kroll, J. H. Muller, J. Nunn, E. Polzik, J. Rarity, H. de Riedmatten, W. Rosenfeld, A. J. Shields, N. Skold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories: a review based on the European Integrated Project ‘Qubit Applications (QAP)’,” Eur. Phys. J. D 58, 1–22 (2010).
[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]

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]

Parkins, A. S.

A. S. Parkins and H. J. Kimble, “Quantum state transfer between motion and light,” J. Opt. B: Quantum Semiclassical Opt. 1, 496–504 (1999).
[CrossRef]

Phillips, D. F.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[CrossRef] [PubMed]

Pirandola, S.

S. Pirandola and S. Mancini, “Quantum teleportation with continuous variables: a survey,” Laser Phys. 16, 1418–1438 (2006).
[CrossRef]

S. Pirandola, S. Mancini, D. Vitali, and P. Tombesi, “Continuous-variable entanglement and quantum-state teleportation between optical and macroscopic vibrational modes through radiation pressure,” Phys. Rev. A 68, 062317 (2003).
[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] [PubMed]

Polzik, E.

See, for instance, Ch. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kroll, J. H. Muller, J. Nunn, E. Polzik, J. Rarity, H. de Riedmatten, W. Rosenfeld, A. J. Shields, N. Skold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories: a review based on the European Integrated Project ‘Qubit Applications (QAP)’,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

Polzik, E. S.

B. Julsgaard, A. Kozhekin, and E. S. Polzik, “Experimental long-lived entanglement of two macroscopic objects,” Nature 413, 400–403 (2001).
[CrossRef] [PubMed]

A. Furusawa, J. Sorensen, S. L. Braunstein, C. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[CrossRef] [PubMed]

Popescu, S.

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]

Primakoff, H.

T. Holstein and H. Primakoff, “Field dependence of the intrinsic domain magnetization of a ferromagnet,” Phys. Rev. 58, 1098–1113 (1940).
[CrossRef]

Rarity, J.

See, for instance, Ch. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kroll, J. H. Muller, J. Nunn, E. Polzik, J. Rarity, H. de Riedmatten, W. Rosenfeld, A. J. Shields, N. Skold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories: a review based on the European Integrated Project ‘Qubit Applications (QAP)’,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

Rosenfeld, W.

See, for instance, Ch. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kroll, J. H. Muller, J. Nunn, E. Polzik, J. Rarity, H. de Riedmatten, W. Rosenfeld, A. J. Shields, N. Skold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories: a review based on the European Integrated Project ‘Qubit Applications (QAP)’,” Eur. Phys. J. D 58, 1–22 (2010).
[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] [PubMed]

Schmidt-Kaler, F.

Schumacher, B.

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]

Shields, A. J.

See, for instance, Ch. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kroll, J. H. Muller, J. Nunn, E. Polzik, J. Rarity, H. de Riedmatten, W. Rosenfeld, A. J. Shields, N. Skold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories: a review based on the European Integrated Project ‘Qubit Applications (QAP)’,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

Simon, Ch.

See, for instance, Ch. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kroll, J. H. Muller, J. Nunn, E. Polzik, J. Rarity, H. de Riedmatten, W. Rosenfeld, A. J. Shields, N. Skold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories: a review based on the European Integrated Project ‘Qubit Applications (QAP)’,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

Skold, N.

See, for instance, Ch. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kroll, J. H. Muller, J. Nunn, E. Polzik, J. Rarity, H. de Riedmatten, W. Rosenfeld, A. J. Shields, N. Skold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories: a review based on the European Integrated Project ‘Qubit Applications (QAP)’,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

Smolin, J. A.

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]

Sorensen, J.

A. Furusawa, J. Sorensen, S. L. Braunstein, C. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[CrossRef] [PubMed]

Stevenson, R. M.

See, for instance, Ch. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kroll, J. H. Muller, J. Nunn, E. Polzik, J. Rarity, H. de Riedmatten, W. Rosenfeld, A. J. Shields, N. Skold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories: a review based on the European Integrated Project ‘Qubit Applications (QAP)’,” Eur. Phys. J. D 58, 1–22 (2010).
[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]

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]

Thew, R.

See, for instance, Ch. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kroll, J. H. Muller, J. Nunn, E. Polzik, J. Rarity, H. de Riedmatten, W. Rosenfeld, A. J. Shields, N. Skold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories: a review based on the European Integrated Project ‘Qubit Applications (QAP)’,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

Tombesi, P.

S. Pirandola, S. Mancini, D. Vitali, and P. Tombesi, “Continuous-variable entanglement and quantum-state teleportation between optical and macroscopic vibrational modes through radiation pressure,” Phys. Rev. A 68, 062317 (2003).
[CrossRef]

van Loock, P.

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

Vitali, D.

D. Vitali, P. Cañizares, J. Eschner, and G. Morigi, “Time-separated entangled light pulses from a single-atom emitter,” New J. Phys. 10, 033025 (2008).
[CrossRef]

G. Morigi, J. Eschner, S. Mancini, and D. Vitali, “Entangled light pulses from single cold atoms,” Phys. Rev. Lett. 96, 023601 (2006).
[CrossRef] [PubMed]

G. Morigi, J. Eschner, S. Mancini, and D. Vitali, “Coherent generation of EPR-entangled light pulses mediated by a single trapped atom,” Phys. Rev. A 73, 033822 (2006).
[CrossRef]

S. Pirandola, S. Mancini, D. Vitali, and P. Tombesi, “Continuous-variable entanglement and quantum-state teleportation between optical and macroscopic vibrational modes through radiation pressure,” Phys. Rev. A 68, 062317 (2003).
[CrossRef]

Walls, D. F.

D. F. Walls and G. J. Milburn, Quantum Optics, 2nd ed. (Springer, 2008).
[CrossRef]

Walmsley, I.

See, for instance, Ch. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kroll, J. H. Muller, J. Nunn, E. Polzik, J. Rarity, H. de Riedmatten, W. Rosenfeld, A. J. Shields, N. Skold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories: a review based on the European Integrated Project ‘Qubit Applications (QAP)’,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

Walsworth, R. L.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[CrossRef] [PubMed]

Weber, M.

See, for instance, Ch. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kroll, J. H. Muller, J. Nunn, E. Polzik, J. Rarity, H. de Riedmatten, W. Rosenfeld, A. J. Shields, N. Skold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories: a review based on the European Integrated Project ‘Qubit Applications (QAP)’,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

Weinfurter, H.

See, for instance, Ch. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kroll, J. H. Muller, J. Nunn, E. Polzik, J. Rarity, H. de Riedmatten, W. Rosenfeld, A. J. Shields, N. Skold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories: a review based on the European Integrated Project ‘Qubit Applications (QAP)’,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

Wineland, D.

D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, “Quantum dynamics of single trapped ions,” Rev. Mod. Phys. 75, 281–324 (2003).
[CrossRef]

Wootters, W. K.

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]

Wrachtrup, J.

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Figures (6)

Fig. 1
Fig. 1

Two entangled light fields—generated, for instance, by an optical parametric oscillator (OPO)—impinge each on one atomic ensemble. The light field couples to one dipolar transition of a Λ configuration of electronic levels (coupling strength g), while the second transition is driven by a laser (coupling strength Ω). The light fields are labeled here by the corresponding photon-annihilation operators a 1 and a 2 , while the involved atomic levels are | g and | e (stable states), with | i being the common excited state. Before the interaction the atoms are prepared in state | g . The effective interaction between fields and collective atomic excitations is parametric for the coupling scheme shown in (a), namely, photonic and atomic excitations are simultaneously created or annihilated. In (b) the interaction is beam-splitter-like, i.e., the total number of photonic and atomic excitations is conserved. After the interaction, the collective state of the atomic ensembles is measured. As a result the entanglement between fields a 1 and a 2 is expected to increase (see text for details).

Fig. 2
Fig. 2

Fidelities for the four conditional states, obtained after parametric interaction with the atomic ensemble from Eqs. (19) versus the interaction time t (in units of 1 / μ ). Here, λ = 0.5 and n t h = 0 . The curves correspond to F 00 (dotted-dashed line), F 01 = F 10 (dashed line), and F 11 (solid line). The initial teleportation fidelity F init (dotted line) is shown for comparison.

Fig. 3
Fig. 3

Fidelities for the beam-splitter interaction, as in Eqs. (19), as a function of λ, and for various values of n t h . The fidelities are evaluated at the optimal time t π / ν , where F 11 is maximal. The curves correspond to F 00 (dotted-dashed line), F 01 = F 10 (dashed line), and F 11 (solid line). The initial teleportation fidelity F init (dotted line) is shown for comparison.

Fig. 4
Fig. 4

Efficiency E [Eq. (21)] as a function of t (in units of 1 / ν ) and λ for the beam-splitter interaction and (a) n t h = 0 , (b) n t h = 0.05 .

Fig. 5
Fig. 5

Fidelities for entanglement swapping using the parametric interaction as a function of μ t for various values of λ and n t h . The curves correspond to F 00 (dotted-dashed line), F 01 = F 10 (dashed line), and F 11 (solid line). The initial teleportation fidelity F init (dotted line) is shown for comparison.

Fig. 6
Fig. 6

Fidelity for entanglement swapping using the parametric interaction as a function of μ t for various values of λ. This fidelity is compared with the entanglement stemming from a pure parametric interaction, F param = ( 1 + μ t ) / 2 .

Equations (70)

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ρ t = 1 i [ H , ρ ] ,
H = l = 1 , 2 ( g Ω l Δ N l S e g ( l ) a l + H .c . ) ,
H = l = 1 , 2 i μ l ( a l b l a l b l ) ,
H = l = 1 , 2 i ν l ( a l b l a l b l ) ,
{ E x 1 = 0 , E x 1 = 1 } { | 0 b 1 0 | , I b 1 | 0 b 1 0 | } ,
{ E x 2 = 0 , E x 2 = 1 } { | 0 b 2 0 | , I b 2 | 0 b 2 0 | } ,
ρ x = 1 p x Tr b 1 b 2 { ρ E x } ,
χ ( η , t ) = Tr { ρ ( t ) i e η i σ i i e η i σ i } ,
χ ( η , 0 ) = exp { ( λ 2 1 λ 2 + n t h ) ( | α 1 | 2 + | α 2 | 2 ) } exp { λ 1 λ 2 ( α 1 α 2 + α 1 α 2 ) } ,
χ par ( η , t ) t = μ ( α 1 β 1 + α 1 β 1 + α 2 β 2 + α 2 β 2 α 1 β 1 α 1 β 1 α 2 β 2 α 2 β 2 β 1 α 1 β 1 α 1 β 2 α 2 β 2 α 2 ) χ par ( η , t ) ,
χ BS ( η , t ) t = ν ( α 1 β 1 + α 1 β 1 + α 2 β 2 + α 2 β 2 β 1 α 1 β 1 α 1 β 2 α 2 β 2 α 2 ) χ BS ( η , t ) ,
ρ = d 2 α 1 π d 2 α 2 π d 2 β 1 π d 2 β 2 π χ ( α 1 , α 2 , β 1 , β 2 ) D ( α 1 ) D ( α 2 ) D ( β 1 ) D ( β 2 ) e ( | α 1 | 2 | α 2 | 2 | β 1 | 2 | β 2 | 2 ) / 2 ,
χ 00 ( α 1 , α 2 ) = 1 p 00 I ( α 1 , α 2 ; 1 , 1 ) ,
χ 01 ( α 1 , α 2 ) = 1 p 01 [ I ( α 1 , α 2 ; 1 , 0 ) I ( α 1 , α 2 ; 1 , 1 ) ] ,
χ 10 ( α 1 , α 2 ) = 1 p 10 [ I ( α 1 , α 2 ; 0 , 1 ) I ( α 1 , α 2 ; 1 , 1 ) ] ,
χ 11 ( α 1 , α 2 ) = 1 p 11 [ I ( α 1 , α 2 ; 0 , 0 ) I ( α 1 , α 2 ; 1 , 0 ) I ( α 1 , α 2 ; 0 , 1 ) + I ( α 1 , α 2 , 1 , 1 ) ] ,
χ x 1 x 2 ( α 1 = 0 , α 2 = 0 ) = 1.
I ( α 1 , α 2 ; u , v ) = d ( u β 1 ) d ( v β 2 ) χ ( α 1 , α 2 , β 1 , β 2 ) e | β 1 | 2 | β 2 | 2 ,
d ( u β 1 ) = { d 2 β 1 , u = 1 π δ 2 ( β 1 ) d 2 β 1 , u = 0 , }
d ( v β 2 ) = { d 2 β 2 , v = 1 π δ 2 ( β 2 ) d 2 β 2 , v = 0. }
F = d 2 ξ π | Φ i n ( ξ ) | 2 [ Φ c h ( ξ , ξ ) ] ,
Φ c h ( ξ , ξ ) = χ x 1 x 2 ( α 1 = ξ , α 2 = ξ ) exp ( | ξ | 2 ) ,
F x 1 x 2 = d 2 ξ π e 2 | ξ | 2 χ x 1 x 2 ( α 1 = ξ , α 2 = ξ ) .
F 00 = 1 p 00 1 ( B + 1 ) 2 B 12 2 1 2 + 2 A 2 A 12 2 ( C + D ) 2 B + 1 B 12 ,
F 01 = F 10 = 1 p 01 [ 1 B + 1 1 2 + 2 A 2 A 12 ( C + D ) 2 B + 1 1 ( B + 1 ) 2 B 12 2 1 2 + 2 A 2 A 12 2 ( C + D ) 2 B + 1 B 12 ] ,
F 11 = 1 p 11 [ 1 2 + 2 A 2 A 12 2 B + 1 1 2 + 2 A 2 A 12 ( C + D ) 2 B + 1 + 1 ( B + 1 ) 2 B 12 2 1 2 + 2 A 2 A 12 2 ( C + D ) 2 B + 1 B 12 ] ,
F init = 1 2 1 λ 2 1 λ + n t h ( 1 λ 2 ) .
E = { p 11 ( F 11 F init ) if   ( F 11 F init ) > 0 0 if   ( F 11 F init ) 0. }
χ par ( η , t ) = exp [ A ( | α 1 | 2 + | α 2 | 2 ) B ( | β 1 | 2 + | β 2 | 2 ) + A 12 ( α 1 α 2 + α 1 α 2 ) + B 12 ( β 1 β 2 + β 1 β 2 ) + C ( α 1 β 2 + α 1 β 2 + α 2 β 1 + α 2 β 1 ) + D ( α 1 β 1 + α 1 β 1 + α 2 β 2 + α 2 β 2 ) ] .
A ̇ = 2 μ D ,
B ̇ = 2 μ D ,
D ̇ = μ ( 1 + A + B ) ,
A ̇ 12 = 2 μ C ,
B ̇ 12 = 2 μ C ,
C ̇ = μ ( B 12 + A 12 ) ,
A ( t ) = [ 1 + n t h ( 1 λ 2 ) ] cosh 2 μ t 1 λ 2 1 ,
B ( t ) = [ 1 + n t h ( 1 λ 2 ) ] sinh 2 μ t 1 λ 2 ,
D ( t ) = 1 2 [ 1 + n t h ( 1 λ 2 ) ] sinh ( 2 μ t ) 1 λ 2 ,
C ( t ) = λ 2 sinh ( 2 μ t ) 1 λ 2 ,
A 12 ( t ) = λ cosh 2 μ t 1 λ 2 ,
B 12 ( t ) = λ sinh 2 μ t 1 λ 2 .
χ BS ( η , t ) = exp [ A ( | α 1 | 2 + | α 2 | 2 ) B ( | β 1 | 2 + | β 2 | 2 ) + A 12 ( α 1 α 2 + α 1 α 2 ) + B 12 ( β 1 β 2 + β 1 β 2 ) + D ( α 1 β 1 + α 1 β 1 + α 2 β 2 + α 2 β 2 ) + C ( α 1 β 2 + α 1 β 2 + α 2 β 1 + α 2 β 1 ) ] .
A ̇ = 2 ν D ,
B ̇ = 2 ν D ,
D ̇ = ν ( A B ) ,
A ̇ 12 = 2 ν C ,
B ̇ 12 = 2 ν C ,
C ̇ = ν ( A 12 B 12 ) ,
A ( t ) = [ λ 2 + n t h ( 1 λ 2 ) ] cos 2 ν t 1 λ 2 ,
B ( t ) = [ λ 2 + n t h ( 1 λ 2 ) ] sin 2 ν t 1 λ 2 ,
D ( t ) = 1 2 [ λ 2 + n t h ( 1 λ 2 ) ] sin ( 2 ν t ) 1 λ 2 ,
A 12 ( t ) = λ cos 2 ν t 1 λ 2 ,
B 12 ( t ) = λ sin 2 ν t 1 λ 2 ,
C ( t ) = λ 2 sin ( 2 ν t ) 1 λ 2 .
I ( α 1 , α 2 ; 0 , 0 ) = exp [ A ( | α 1 | 2 + | α 2 | 2 ) + A 12 ( α 1 α 2 + α 1 α 2 ) ] ,
I ( α 1 , α 2 ; 0 , 1 ) = 1 B + 1 exp [ ( A D 2 B + 1 ) | α 1 | 2 ( A C 2 B + 1 ) | α 2 | 2 + ( A 12 + C D B + 1 ) ( α 1 α 2 + α 1 α 2 ) ] ,
I ( α 1 , α 2 ; 1 , 0 ) = 1 B + 1 exp [ ( A C 2 B + 1 ) | α 1 | 2 ( A D 2 B + 1 ) | α 2 | 2 + ( A 12 + C D B + 1 ) ( α 1 α 2 + α 1 α 2 ) ] ,
I ( α 1 , α 2 ; 1 , 1 ) = 1 ( B + 1 ) 2 B 12 2 exp [ ( A ( B + 1 ) ( C 2 + D 2 ) + 2 B 12 C D ( B + 1 ) 2 B 12 2 ) ( | α 1 | 2 + | α 2 | 2 ) + ( A 12 + 2 ( B + 1 ) C D + B 12 ( C 2 + D 2 ) ( B + 1 ) 2 B 12 2 ) ( α 1 α 2 + α 1 α 2 ) ] .
p 00 = I ( 0 , 0 ; 1 , 1 ) = 1 ( B + 1 ) 2 B 12 2 ,
p 01 = I ( 0 , 0 ; 1 , 0 ) I ( 0 , 0 ; 1 , 1 ) = 1 B + 1 1 ( B + 1 ) 2 B 12 2 ,
p 10 = I ( 0 , 0 ; 0 , 1 ) I ( 0 , 0 ; 1 , 1 ) = 1 B + 1 1 ( B + 1 ) 2 B 12 2 ,
p 11 = I ( 0 , 0 ; 0 , 0 ) I ( 0 , 0 ; 1 , 0 ) I ( 0 , 0 ; 0 , 1 ) + I ( 0 , 0 ; 1 , 1 ) = 1 2 B + 1 + 1 ( B + 1 ) 2 B 12 2 .
I ( α 1 , α 2 ; 0 , 0 ) = exp [ A ( | α 1 | 2 + | α 2 | 2 ) + A 12 ( α 1 α 2 + α 1 α 2 ) ] ,
I ( α 1 , α 2 ; 0 , 1 ) = 1 B + 1 exp [ ( A C 2 B + 1 ) | α 1 | 2 ( A D 2 B + 1 ) | α 2 | 2 + ( A 12 + C D B + 1 ) ( α 1 α 2 + α 1 α 2 ) ] ,
I ( α 1 , α 2 ; 1 , 0 ) = 1 B + 1 exp [ ( A D 2 B + 1 ) | α 1 | 2 ( A C 2 B + 1 ) | α 2 | 2 + ( A 12 + C D B + 1 ) ( α 1 α 2 + α 1 α 2 ) ] ,
I ( α 1 , α 2 ; 1 , 1 ) = 1 ( B + 1 ) 2 B 12 2 exp [ ( A ( B + 1 ) ( D 2 + C 2 ) + 2 B 12 C D ( B + 1 ) 2 B 12 2 ) ( | α 1 | 2 + | α 2 | 2 ) + ( A 12 + 2 ( B + 1 ) C D + B 12 ( C 2 + D 2 ) ( B + 1 ) 2 B 12 2 ) ( α 1 α 2 + α 1 α 2 ) ] .
p 00 = I ( 0 , 0 ; 1 , 1 ) = 1 ( B + 1 ) 2 B 12 2 ,
p 01 = I ( 0 , 0 ; 1 , 0 ) I ( 0 , 0 ; 1 , 1 ) = 1 B + 1 1 ( B + 1 ) 2 B 12 2 ,
p 10 = I ( 0 , 0 ; 0 , 1 ) I ( 0 , 0 ; 1 , 1 ) = 1 B + 1 1 ( B + 1 ) 2 B 12 2 ,
p 11 = I ( 0 , 0 ; 0 , 0 ) I ( 0 , 0 ; 1 , 0 ) I ( 0 , 0 ; 0 , 1 ) + I ( 0 , 0 ; 1 , 1 ) = 1 2 B + 1 + 1 ( B + 1 ) 2 B 12 2 .

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