Measurement-based noiseless linear amplification for quantum communication


Entanglement distillation is an indispensable ingredient in extended quantum communication networks. Distillation protocols are necessarily non-deterministic and require advanced experimental techniques such as noiseless amplification. Recently, it was shown that the benefits of noiseless amplification could be extracted by performing a post-selective filtering of the measurement record to improve the performance of quantum key distribution. We apply this protocol to entanglement degraded by transmission loss of up to the equivalent of 100 km of optical fibre. We measure an effective entangled resource stronger than that achievable by even a maximally entangled resource passively transmitted through the same channel. We also provide a proof-of-principle demonstration of secret key extraction from an otherwise insecure regime. The measurement-based noiseless linear amplifier offers two advantages over its physical counterpart: ease of implementation and near-optimal probability of success. It should provide an effective and versatile tool for a broad class of entanglement-based quantum communication protocols.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Schematic of equivalent methods of entanglement distillation with physical and measurement-based noiseless linear amplifiers.
Figure 3: Results of the measurement-based NLA implemented at the receiver (Bob) station.
Figure 2: Experimental set-up of the MB-NLA.
Figure 4: Improvement in the inseparability criterion of the two-mode EPR state for a series of lossy channels.
Figure 5: Application of MB-NLA to extract a positive key rate from an otherwise insecure regime in a CV-QKD system.


  1. 1

    Heisenberg, W. Über den anschaulichen inhalt der quantentheoretischen kinematik und mechanik. Z. Phys. 43, 172–198 (1927).

  2. 2

    Wootters, W. K. & Zurek, W. H. A single quantum cannot be cloned. Nature 299, 802–803 (1982).

  3. 3

    Giovannetti, V., Lloyd, S. & Maccone, L. Advances in quantum metrology. Nature Photon. 5, 222–229 (2011).

  4. 4

    Caves, C. M. Quantum limits on noise in linear amplifiers. Phys. Rev. D 26, 1817–1839 (1982).

  5. 5

    Caves, C. M., Combes, J., Jiang, Z. & Pandey, S. Quantum limits on phase-preserving linear amplifiers. Phys. Rev. A 86, 063802 (2012).

  6. 6

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

  7. 7

    Horodecki, M., Horodecki, P. & Horodecki, R. Inseparable two spin-1/2 density matrices can be distilled to a singlet form. Phys. Rev. Lett. 78, 574–577 (1997).

  8. 8

    Browne, D., Eisert, J., Scheel, S. & Plenio, M. Driving non-Gaussian to Gaussian states with linear optics. Phys. Rev. A 67, 062320 (2003).

  9. 9

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

  10. 10

    Kimble, H. J. The quantum internet. Nature 453, 1023–1030 (2008).

  11. 11

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

  12. 12

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

  13. 13

    Ralph, T. C. & Lund, A. P. Nondeterministic noiseless linear amplification of quantum systems in Proceedings of the 9th International Conference on Quantum Communication Measurement and Computing (ed. Lvovsky, A. I.) 155–160 (American Institute of Physics, 2009).

  14. 14

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

  15. 15

    Walk, N., Lund, A. P. & Ralph, T. C. Nondeterministic noiseless amplification via non-symplectic phase space transformations. New J. Phys. 15, 073014 (2013).

  16. 16

    Marek, P. & Filip, R. Coherent-state phase concentration by quantum probabilistic amplification. Phys. Rev. A 81, 022302 (2010).

  17. 17

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

  18. 18

    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).

  19. 19

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

  20. 20

    Ferreyrol, F., Blandino, R., Barbieri, M., Tualle-Brouri, R. & Grangier, P. Experimental realization of a nondeterministic optical noiseless amplifier. Phys. Rev. A 83, 063801 (2011).

  21. 21

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

  22. 22

    Osorio, C. I. et al. Heralded photon amplification for quantum communication. Phys. Rev. A 86, 023815 (2012).

  23. 23

    Kocsis, S., Xiang, G. Y., Ralph, T. C. & Pryde, G. J. Heralded noiseless amplification of a photon polarization qubit. Nature Phys. 9, 23–28 (2012).

  24. 24

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

  25. 25

    Usuga, M. A. et al. Noise-powered probabilistic concentration of phase information. Nature Phys. 6, 767–771 (2010).

  26. 26

    Reid, M. D. et al. Colloquium: the Einstein–Podolsky–Rosen paradox: from concepts to applications. Rev. Mod. Phys. 81, 1727–1751 (2009).

  27. 27

    Fiurášek, J. & Cerf, N. Gaussian postselection and virtual noiseless amplification in continuous-variable quantum key distribution. Phys. Rev. A 86, 060302 (2012).

  28. 28

    Walk, N., Ralph, T. C., Symul, T. & Lam, P. K. Security of continuous-variable quantum cryptography with Gaussian postselection. Phys. Rev. A 87, 020303 (2013).

  29. 29

    Hellwig, K. & Kraus, K. Operations and measurements. II. Commun. Math. Phys. 16, 142–147 (1970).

  30. 30

    Ferreyrol, F., Spagnolo, N., Blandino, R., Barbieri, M. & Tualle-Brouri, R. Heralded processes on continuous-variable spaces as quantum maps. Phys. Rev. A 86, 062327 (2012).

  31. 31

    Prugovečki, E. Information-theoretical aspects of quantum measurement. Int. J. Theor. Phys. 16, 321–331 (1977).

  32. 32

    Busch, P. & Lahti, P. J. The determination of the past and the future of a physical system in quantum mechanics. Found. Phys. 19, 633–678 (1989).

  33. 33

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

  34. 34

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

  35. 35

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

  36. 36

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

  37. 37

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

  38. 38

    Duan, L. M., Giedke, G., Cirac, J. I. & Zoller, P. Inseparability criterion for continuous variable systems. Phys. Rev. Lett. 84, 2722–2725 (2000).

  39. 39

    Reid, M. D. & Drummond, P. D. Quantum correlations of phase in nondegenerate parametric oscillation. Phys. Rev. Lett. 60, 2731–2733 (1988).

  40. 40

    Blandino, R. et al. Improving the maximum transmission distance of continuous-variable quantum key distribution using a noiseless amplifier. Phys. Rev. A 86, 012327 (2012).

  41. 41

    Lee, S.-Y., Ji, S.-W., Kim, H.-J. & Nha, H. Enhancing quantum entanglement for continuous variables by a coherent superposition of photon subtraction and addition. Phys. Rev. A 84, 012302 (2011).

  42. 42

    Kim, H.-J., Lee, S.-Y., Ji, S.-W. & Nha, H. Quantum linear amplifier enhanced by photon subtraction and addition. Phys. Rev. A 85, 013839 (2012).

  43. 43

    Barbieri, M. et al. Non-Gaussianity of quantum states: an experimental test on single-photon-added coherent states. Phys. Rev. A 82, 063833 (2010).

  44. 44

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

Download references


The authors thank S. Rahimi-Keshari, R. Blandino and A. P. Lund for helpful discussions. This research is supported by the Australian Research Council (ARC) under the Centre of Excellence for Quantum Computation and Communication Technology (CE110001027). P.K.L. is an ARC Future Fellow.

Author information

N.W. and T.C.R. developed the theory. H.M.C., S.M.A., J.J., S.H., T.S. and P.K.L. conceived and conducted the experiment. H.M.C., S.M.A. and N.W. analysed the data. H.M.C., N.W. and S.M.A. drafted the initial manuscript. P.K.L., T.C.R. and T.S. planned and supervised the entire project. All authors discussed the results and commented on the manuscript.

Correspondence to Ping Koy Lam.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 464 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

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

Download citation

Further reading