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Undoing the effect of loss on quantum entanglement


Entanglement distillation, the purpose of which is to probabilistically increase the strength and purity of quantum entanglement, is a primary element of many quantum communication and computation protocols. It is particularly necessary in quantum repeaters in order to counter the degradation of entanglement that inevitably occurs due to losses in communication lines. Here, we distil the Einstein–Podolsky–Rosen state of light, the workhorse of continuous-variable entanglement, using noiseless amplification. The advantage of our technique is that it permits recovering a macroscopic level of entanglement, however low the initial entanglement or however high the loss may be. Experimentally, we recover the original entanglement level after one of the Einstein–Podolsky–Rosen modes has experienced a loss factor of 20. The level of entanglement in our distilled state is higher than that achievable by direct transmission of any state through a similar loss channel. This is a key step towards realizing practical continuous-variable quantum communication protocols.

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Figure 1: Experimental set-up.
Figure 2: Experimental results.


  1. 1

    Nielsen, M. & Chuang, I. Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000).

    MATH  Google Scholar 

  2. 2

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

    ADS  Article  Google Scholar 

  3. 3

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

    ADS  MathSciNet  Article  Google Scholar 

  4. 4

    Reid, M. D. Demonstration of the Einstein–Podolsky–Rosen paradox using nondegenerate parametric amplification. Phys. Rev. A 40, 913–923 (1989).

    ADS  Article  Google Scholar 

  5. 5

    Weedbrook, C. et al. Gaussian quantum information. Rev. Mod. Phys. 84, 621–669 (2012).

    ADS  Article  Google Scholar 

  6. 6

    Ralph, T. C. & Lund, A. P. Nondeterministic noiseless linear amplifcation of quantum systems. AIP Conf. Proc. 1110, 155–160 (2009).

    ADS  Article  Google Scholar 

  7. 7

    Takahashi, H. et al. Entanglement distillation from Gaussian input states. Nature Photon. 4, 178–181 (2010).

    ADS  Article  Google Scholar 

  8. 8

    Kurochkin, Y., Prasad, A. S. & Lvovsky, A. I. Distillation of the two-mode squeezed state. Phys. Rev. Lett. 112, 070402 (2014).

    ADS  Article  Google Scholar 

  9. 9

    Bartley, T. J. & Walmsley, I. A. Directly comparing entanglement-enhancing non-Gaussian operations. New J. Phys. 17, 023038 (2015).

    ADS  Article  Google Scholar 

  10. 10

    Chrzanowski, H. M. et al. Measurement-based noiseless linear amplification for quantum communication. Nature Photon. 8, 333–338 (2014).

    ADS  Article  Google Scholar 

  11. 11

    Andersen, U. L., Neergaard-Nielsen, J. S., van Loock, P. & Furusawa, A. Hybrid discrete- and continuous-variable quantum information. Nature Phys. 11, 713–719 (2015).

    ADS  Article  Google Scholar 

  12. 12

    Xiang, G. Y., Ralph, T. C., Lund, A. P., Walk, N. & Pryde, G. J. Heralded noiseless linear amplification and distillation of entanglement. Nature Photon. 4, 316–319 (2010).

    Article  Google Scholar 

  13. 13

    Ferreyrol, F. et al. Implementation of a nondeterministic optical noiseless amplifier. Phys. Rev. Lett. 104, 123603 (2010).

    ADS  Article  Google Scholar 

  14. 14

    Zavatta, A., Fiurasek, J. & Bellini, M. A high-fidelity noiseless amplifier for quantum light states. Nature Photon. 5, 52–60 (2010).

    ADS  Article  Google Scholar 

  15. 15

    Kosis, S., Xiang, G. Y., Ralph, T. C. & Pryde, G. J. Heralded noiseless amplification of a photon polarization qubit. Nature Phys. 9, 23–28 (2013).

    ADS  Article  Google Scholar 

  16. 16

    Pegg, D., Phillips, L. & Barnett, S. Optical state truncation by projection synthesis. Phys. Rev. Lett. 81, 1604–1606 (1998).

    ADS  Article  Google Scholar 

  17. 17

    Babichev, S. A., Ries, J. & Lvovsky, A. I. Quantum scissors: teleportation of single-mode optical states by means of a nonlocal single photon. Europhys. Lett. 64, 1–7 (2003).

    ADS  Article  Google Scholar 

  18. 18

    Lvovsky, A. I. & Mlynek, J. Quantum-optical catalysis: generating nonclassical states of light by means of linear optics. Phys. Rev. Lett. 88, 250401 (2002).

    ADS  Article  Google Scholar 

  19. 19

    Mičuda, M. et al. Noiseless loss suppression in quantum optical communication. Phys. Rev. Lett. 109, 180503 (2012).

    ADS  Article  Google Scholar 

  20. 20

    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 

  21. 21

    Kumar, R. et al. Versatile wideband balanced detector for quantum optical homodyne tomography. Opt. Commun. 285, 5259–5267 (2012).

    ADS  Article  Google Scholar 

  22. 22

    Huisman, S. R. et al. Instant single-photon Fock state tomography. Opt. Lett. 34, 2739–2741 (2009).

    ADS  Article  Google Scholar 

  23. 23

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

    ADS  Article  Google Scholar 

  24. 24

    Pan, J. W., Gasparoni, S., Ursin, R., Weihs, G. & Zeilinger, A. Experimental entanglement purification of arbitrary unknown states. Nature 423, 417–422 (2003).

    ADS  Article  Google Scholar 

  25. 25

    Ralph, T. C. Quantum error correction of continuous-variable states against Gaussian noise. Phys. Rev. A 84, 022339 (2011).

    ADS  Article  Google Scholar 

  26. 26

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

    ADS  MathSciNet  Article  Google Scholar 

  27. 27

    Datta, A. et al. Compact continuous-variable entanglement distillation. Phys. Rev. Lett. 108, 060502 (2012).

    ADS  Article  Google Scholar 

  28. 28

    Berry, D. W. & Lvovsky, A. I. Linear-optical processing cannot increase photon efficiency. Phys. Rev. Lett. 105, 203601 (2010).

    ADS  Article  Google Scholar 

  29. 29

    Berry, D. W. & Lvovsky, A. I. Preservation of loss in linear-optical processing. Phys. Rev. A 84, 042304 (2011).

    ADS  Article  Google Scholar 

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The authors thank G. Adesso for discussions and the Russian Quantum Center for support. A.L. is supported by the National Science and Engineering Research Council of Canada and is a fellow of the Canadian Institute for Advanced Research. T.C.R.'s research is funded by the Australian Research Council Centre of Excellence for Quantum Computation and Communication Technology (project no. CE110001027).

Author information




The experiment was conceived and designed by A.E.U., I.F., Y.K., T.C.R. and A.L., and performed by A.E.U., I.F., Y.K., A.A.P. and A.L. The data were analysed by A.E.U., I.F. and A.L. A.E.U., I.F., Y.K., T.C.R. and A.L. contributed to writing the paper.

Corresponding author

Correspondence to A. I. Lvovsky.

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The authors declare no competing financial interests.

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Ulanov, A., Fedorov, I., Pushkina, A. et al. Undoing the effect of loss on quantum entanglement. Nature Photon 9, 764–768 (2015).

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