Abstract
Signal amplification is ubiquitous in the control of physical systems, and the ultimate performance limit of amplifiers is set by quantum physics. Increasing the amplitude of an unknown quantum optical field, or any harmonic oscillator state, must introduce noise1. This linear amplification noise prevents perfect copying of the quantum state2, enforces quantum limits on communications and metrology3, and is the mechanism preventing the increase of entanglement via local operations. Non-deterministic versions of ideal cloning4 and local entanglement increase (distillation)5 are allowed, suggesting the possibility of non-deterministic noiseless linear amplification. Here we introduce, and experimentally demonstrate, such a noiseless linear amplifier for quantum states of the optical field, and use it for distillation of field-mode entanglement. This simple but powerful circuit enables practical devices for enhancing quantum technologies. The idea of noiseless amplification unifies approaches to cloning and distillation, and will find applications in quantum metrology and communications.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 12 print issues and online access
$209.00 per year
only $17.42 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Caves, C. M. Quantum-mechanical noise in an interferometer. Phys. Rev. D 23, 1693–1708 (1981).
Wootters, W. K. & Zurek, W. H. A single quantum cannot be cloned. Nature 299, 802–803 (1982).
Bachor, H.-A. & Ralph, T. C. A Guide to Experiments in Quantum Optics 2nd edn (Wiley-VCH, 2004).
Duan, L.-M. & Guo, G.-C. Probabilistic cloning and identification of linearly independent quantum states. Phys. Rev. Lett. 80, 4999–5002 (1998).
Bennett, C. H. et al. Purification of noisy entanglement and faithful teleportation via noisy channels. Phys. Rev. Lett. 76, 722–725 (1996).
Furusawa, A. et al. Unconditional quantum teleportation. Science, 282, 706–709 (1998).
Braunstein, S. L. & Kimble, H. J. Dense coding for continuous variables. Phys. Rev. A 61, 042302 (2000).
Ralph, T. C. & Huntington, E. H. Unconditional continuous variable dense coding. Phys. Rev. A 66, 042321 (2002).
Grosshans, F. Grangier, P. Continuous variable quantum cryptography using coherent states. Phys. Rev. Lett. 88, 057902 (2002).
Silberhorn, Ch., Ralph, T. C., Lütkenhaus, N. & Leuchs, G. Continuous variable key distribution—beating the 3 dB loss limit. Phys. Rev. Lett. 89, 167901 (2002).
Dowling, J. P. Quantum optical metrology—the lowdown on high-N00N states. Contemp. Phys. 49, 125143 (2008).
Pegg, D. T., Phillips, L. S. & Barnett S. M. Optical state truncation by projection synthesis. Phys. Rev. Lett. 81, 1604–1606 (1998).
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).
Mølmer, K. Optical coherence: a convenient fiction. Phys. Rev. A 55, 3195–3203 (1997).
Chou, C. W. et al. Measurement-induced entanglement for excitation stored in remote atomic ensembles. Nature 438, 828–832 (2005).
Ou, Z. Y., Pereira, S. F., Kimble, H. J. & Peng, K. C. Realization of the Einstein–Podolsky–Rosen paradox for continuous variables. Phys. Rev. Lett. 68, 3663–3666 (1992).
Ralph, T. C. & Lund, A. P. Nondeterministic noiseless linear amplification of quantum systems. in Proceedings of 9th International Conferenceon on Quantum Communication Measurement and Computing (ed. Lvovsky, A.) 155–160 (AIP, 2009).
Browne, D. E., Eisert, J., Scheel, S. & Plenio, M. B. Driving non-Gaussian to Gaussian states with linear optics. Phys. Rev. A 67, 062320 (2003).
Lund, A. P. & Ralph, T. C. Continuous-variable entanglement distillation over a general lossy channel. Phys. Rev. A 80, 032309 (2009).
Hage, B. et al. Preparation of distilled and purified continuous-variable entangled states. Nature Phys. 4, 915–918 (2008).
Dong, R. et al. Experimental entanglement distillation of mesoscopic quantum states. Nature Phys. 4, 919–923 (2008).
Takahashi, H. et al. Entanglement distillation from Gaussian input states. Nature Photon. 4, 178–181 (2010).
Andersen, U. L., Josse, V. & Leuchs, G. Unconditional quantum cloning of coherent states with linear optics. Phys. Rev. Lett. 94, 240503 (2005).
Higgins, B. L. et al. Entanglement-free Heisenberg-limited phase estimation. Nature 450, 393–396 (2007).
Acknowledgements
The authors thank E.H. Huntington and B.L. Higgins for useful discussions. This work was supported by the Australian Research Council.
Author information
Authors and Affiliations
Contributions
T.C.R. devised the protocol. T.C.R., A.P.L. and N.W. performed the theoretical calculations. G.J.P. and T.C.R. devised the experiment. G.J.P. and G.Y.X. designed the experiment. G.Y.X. built and characterized the experiment, and collected the data. G.Y.X. and G.J.P. analysed the data. All authors contributed substantially to the manuscript.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing financial interests.
Supplementary information
Supplementary information
Supplementary information (PDF 539 kb)
Rights and permissions
About this article
Cite this article
Xiang, G., Ralph, T., Lund, A. et al. Heralded noiseless linear amplification and distillation of entanglement. Nature Photon 4, 316–319 (2010). https://doi.org/10.1038/nphoton.2010.35
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/nphoton.2010.35
This article is cited by
-
Composable end-to-end security of Gaussian quantum networks with untrusted relays
npj Quantum Information (2022)
-
Quantum channel correction outperforming direct transmission
Nature Communications (2022)
-
Distillation of Gaussian Einstein-Podolsky-Rosen steering with noiseless linear amplification
npj Quantum Information (2022)
-
Sudden death and revival of Gaussian Einstein–Podolsky–Rosen steering in noisy channels
npj Quantum Information (2021)
-
Virtual zero-photon catalysis for improving continuous-variable quantum key distribution via Gaussian post-selection
Scientific Reports (2020)
