Entanglement distillation from Gaussian input states


Entanglement distillation is an essential protocol for long-distance quantum communications1, typically for extending the range of quantum key distribution. In the field of continuous variable quantum information processing, quantum as well as classical information is encoded in the light field quadratures, often in the form of Gaussian states. However, distillation from Gaussian input states has not yet been accomplished. It is made difficult by a prominent no-go theorem stating that no Gaussian operation can distill Gaussian states2,3,4. Here we demonstrate, for the first time, such distillation from Gaussian input states, realized by the implementation of non-Gaussian operations. By subtracting one or two photons, a large gain of entanglement was observed. For two photons, Gaussian-like entanglement was also improved. Other than quantum key distribution, this distilled entanglement can also be used for downstream applications such as high-fidelity quantum teleportation5 and a loophole-free Bell test6,7.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Schematic of the experiment.
Figure 2: Distillation results.
Figure 3: Squeezed variances of x (normalized by vacuum level).


  1. 1

    Briegel, H.-J., Dür, W., Cirac, J. I. & Zoller, P. Quantum repeaters: the role of imperfect local operations in quantum communication. Phys. Rev. Lett. 81, 5932–5935 (1998).

    ADS  Article  Google Scholar 

  2. 2

    Eisert, J., Scheel, S. & Plenio, M. B. Distilling Gaussian states with Gaussian operations is impossible. Phys. Rev. Lett. 89, 137903 (2002).

    ADS  MathSciNet  Article  Google Scholar 

  3. 3

    Fiurášek, J. Gaussian transformations and distillation of entangled Gaussian states. Phys. Rev. Lett. 89, 137904 (2002).

    ADS  MathSciNet  Article  Google Scholar 

  4. 4

    Giedke, G. & Cirac, J. I. Characterization of Gaussian operations and distillation of Gaussian states. Phys. Rev. A 66, 032316 (2002).

    ADS  Article  Google Scholar 

  5. 5

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

    ADS  Article  Google Scholar 

  6. 6

    García-Patrón, R., Fiurášek, J., Cerf, N. J. et al. Proposal for a loophole-free Bell test using homodyne detection. Phys. Rev. Lett. 93, 130409 (2004).

    ADS  Article  Google Scholar 

  7. 7

    Nha, H. & Carmichael, H. J. Proposed test of quantum nonlocality for continuous variables. Phys. Rev. Lett. 93, 020401 (2004).

    ADS  Article  Google Scholar 

  8. 8

    Bennett, C. H. Brassard, G., Popescu, S. et al. Purification of noisy entanglement and faithful teleportation via noisy channels. Phys. Rev. Lett. 76, 722–725 (1996).

    ADS  Article  Google Scholar 

  9. 9

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

    ADS  Article  Google Scholar 

  10. 10

    Pan, J.-W., Simon, C., Brukner, Č. & Zeilinger, A. Entanglement purification for quantum communication. Nature 410, 1067–1070 (2001).

    ADS  Article  Google Scholar 

  11. 11

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

    ADS  Article  Google Scholar 

  12. 12

    Reichle, R., Leibfried, D., Knill, E. et al. Experimental purification of two-atom entanglement. Nature 443, 838–841 (2006).

    ADS  Article  Google Scholar 

  13. 13

    Braunstein, S. L. & van Loock, P. Quantum information with continuous variables. Rev. Mod. Phys. 77, 513–577 (2005).

    ADS  MathSciNet  Article  Google Scholar 

  14. 14

    Ferraro, A., Olivares, S. & Paris, M. G. A. Gaussian states in continuous variable quantum information. Preprint at <http://arXiv:quant-ph> 0503237 (2005).

  15. 15

    Hage, B. Samblowski, A., Diguglielmo, J. et al. Preparation of distilled and purified continuous-variable entangled states. Nature Phys. 4, 915–918 (2008).

    ADS  Article  Google Scholar 

  16. 16

    Dong, R., Lassen, M., Heersink, J. et al. Experimental entanglement distillation of mesoscopic quantum states. Nature Phys. 4, 919–923 (2008).

    ADS  Article  Google Scholar 

  17. 17

    Bartlett, S. D., Sanders, B. C., Braunstein, S. L. & Nemoto, K. Efficient classical simulation of continuous variable quantum information processes. Phys. Rev. Lett. 88, 097904 (2002).

    ADS  Article  Google Scholar 

  18. 18

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

    ADS  Article  Google Scholar 

  19. 19

    Neergaard-Nielsen, J. S., Melholt Nielsen, B., Hettich, C., Mølmer, K. & Polzik, E. S. Generation of a superposition of odd photon number states for quantum information networks. Phys. Rev. Lett. 97, 083604 (2006).

    ADS  Article  Google Scholar 

  20. 20

    Wakui, K., Takahashi, H., Furusawa, A. & Sasaki, M. Photon subtracted squeezed states generated with periodically poled KTiOPO4 . Opt. Express 15, 3568–3574 (2007).

    ADS  Article  Google Scholar 

  21. 21

    Ourjoumtsev, A., Dantan, A., Tualle-Brouri, R. & Grangier, P. Increasing entanglement between Gaussian states by coherent photon subtraction. Phys. Rev. Lett. 98, 030502 (2007).

    ADS  Article  Google Scholar 

  22. 22

    Ourjoumtsev, A., Ferreyrol, F., Tualle-Brouri, R. & Grangier, P. Preparation of non-local superpositions of quasi-classical light states. Nature Phys. 5, 189–192 (2009).

    ADS  Article  Google Scholar 

  23. 23

    Takahashi, H., Wakui, K., Suzuki, S. et al. Generation of large-amplitude coherent-state superposition via ancilla-assisted photon subtraction. Phys. Rev. Lett. 101, 233605 (2008).

    ADS  Article  Google Scholar 

  24. 24

    Lvovsky, A. I. Iterative maximum-likelihood reconstruction in quantum homodyne tomography. J. Opt. B 6, 556–559 (2004).

    ADS  Article  Google Scholar 

  25. 25

    Vidal, G. & Werner, R. F. Computable measure of entanglement. Phys. Rev. A 65, 032314 (2002).

    ADS  Article  Google Scholar 

  26. 26

    Eisert, J., Browne, D., Scheel, S. & Plenio, M. B. Distillation of continuous-variable entanglement with optical means. Ann. Phys. 311, 431–458 (2004).

    ADS  MathSciNet  Article  Google Scholar 

Download references


H.T. acknowledges financial support from the G-COE program, commissioned by the MEXT of Japan.

Author information




H.T., M.Takeoka, A.F. and M.S. conceived the project. H.T., J.S.N-N. and M.Takeuchi carried out the experiment with assistance from K.H., and H.T., J.S.N-N. and M.Takeoka analysed the data. H.T., M.S., M.Takeoka and J.S.N-N. wrote the paper with discussions and input from all authors. The project was directed by M.S.

Corresponding author

Correspondence to Masahide Sasaki.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Takahashi, H., Neergaard-Nielsen, J., Takeuchi, M. et al. Entanglement distillation from Gaussian input states. Nature Photon 4, 178–181 (2010). https://doi.org/10.1038/nphoton.2010.1

Download citation

Further reading