Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Measurement-based noiseless linear amplification for quantum communication

Abstract

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.

from$8.99

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.

References

  1. 1

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

    ADS  Article  Google Scholar 

  2. 2

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

    ADS  Article  Google Scholar 

  3. 3

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

    ADS  Article  Google Scholar 

  4. 4

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

    ADS  Article  Google Scholar 

  5. 5

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

    ADS  Article  Google Scholar 

  6. 6

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

    ADS  Article  Google Scholar 

  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).

    ADS  Article  Google Scholar 

  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).

    ADS  Article  Google Scholar 

  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).

    ADS  Article  Google Scholar 

  10. 10

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

    ADS  Article  Google Scholar 

  11. 11

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

    ADS  Article  Google Scholar 

  12. 12

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

    ADS  MathSciNet  Article  Google Scholar 

  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).

    Google Scholar 

  14. 14

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

    ADS  Article  Google Scholar 

  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).

    ADS  Article  Google Scholar 

  16. 16

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

    ADS  Article  Google Scholar 

  17. 17

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

    ADS  Article  Google Scholar 

  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).

    Article  Google Scholar 

  19. 19

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

    ADS  Article  Google Scholar 

  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).

    ADS  Article  Google Scholar 

  21. 21

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

    ADS  Article  Google Scholar 

  22. 22

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

    ADS  Article  Google Scholar 

  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).

    ADS  Article  Google Scholar 

  24. 24

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

    ADS  Article  Google Scholar 

  25. 25

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

    ADS  Article  Google Scholar 

  26. 26

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

    ADS  MathSciNet  Article  Google Scholar 

  27. 27

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

    ADS  Article  Google Scholar 

  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).

    ADS  Article  Google Scholar 

  29. 29

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

    ADS  MathSciNet  Article  Google Scholar 

  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).

    ADS  Article  Google Scholar 

  31. 31

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

    Article  Google Scholar 

  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).

    ADS  MathSciNet  Article  Google Scholar 

  33. 33

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

    ADS  MathSciNet  Article  Google Scholar 

  34. 34

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

    ADS  MathSciNet  Article  Google Scholar 

  35. 35

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

    ADS  Article  Google Scholar 

  36. 36

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

    ADS  Article  Google Scholar 

  37. 37

    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 

  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).

    ADS  Article  Google Scholar 

  39. 39

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

    ADS  Article  Google Scholar 

  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).

    ADS  Article  Google Scholar 

  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).

    ADS  Article  Google Scholar 

  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).

    ADS  Article  Google Scholar 

  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).

    ADS  Article  Google Scholar 

  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).

    ADS  Article  Google Scholar 

Download references

Acknowledgements

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

Affiliations

Authors

Contributions

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.

Corresponding author

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). https://doi.org/10.1038/nphoton.2014.49

Download citation

Further reading

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing