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.
This is a preview of subscription content
Subscribe to Journal
Get full journal access for 1 year
only $8.25 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Get time limited or full article access on ReadCube.
All prices are NET prices.
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).
Eisert, J., Scheel, S. & Plenio, M. B. Distilling Gaussian states with Gaussian operations is impossible. Phys. Rev. Lett. 89, 137903 (2002).
Fiurášek, J. Gaussian transformations and distillation of entangled Gaussian states. Phys. Rev. Lett. 89, 137904 (2002).
Giedke, G. & Cirac, J. I. Characterization of Gaussian operations and distillation of Gaussian states. Phys. Rev. A 66, 032316 (2002).
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).
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).
Nha, H. & Carmichael, H. J. Proposed test of quantum nonlocality for continuous variables. Phys. Rev. Lett. 93, 020401 (2004).
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).
Kwiat, P. G., Barraza-Lopez, S., Stefanov, A. & Gisin, N. Experimental entanglement distillation and ‘hidden’ non-locality. Nature 409, 1014–1017 (2001).
Pan, J.-W., Simon, C., Brukner, Č. & Zeilinger, A. Entanglement purification for quantum communication. Nature 410, 1067–1070 (2001).
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).
Reichle, R., Leibfried, D., Knill, E. et al. Experimental purification of two-atom entanglement. Nature 443, 838–841 (2006).
Braunstein, S. L. & van Loock, P. Quantum information with continuous variables. Rev. Mod. Phys. 77, 513–577 (2005).
Ferraro, A., Olivares, S. & Paris, M. G. A. Gaussian states in continuous variable quantum information. Preprint at <http://arXiv:quant-ph> 0503237 (2005).
Hage, B. Samblowski, A., Diguglielmo, J. et al. Preparation of distilled and purified continuous-variable entangled states. Nature Phys. 4, 915–918 (2008).
Dong, R., Lassen, M., Heersink, J. et al. Experimental entanglement distillation of mesoscopic quantum states. Nature Phys. 4, 919–923 (2008).
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).
Ourjoumtsev, A., Tualle-Brouri, R., Laurat, J. & Grangier, P. Generating optical Schrödinger kittens for quantum information processing. Science 312, 83–86 (2006).
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).
Wakui, K., Takahashi, H., Furusawa, A. & Sasaki, M. Photon subtracted squeezed states generated with periodically poled KTiOPO4 . Opt. Express 15, 3568–3574 (2007).
Ourjoumtsev, A., Dantan, A., Tualle-Brouri, R. & Grangier, P. Increasing entanglement between Gaussian states by coherent photon subtraction. Phys. Rev. Lett. 98, 030502 (2007).
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).
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).
Lvovsky, A. I. Iterative maximum-likelihood reconstruction in quantum homodyne tomography. J. Opt. B 6, 556–559 (2004).
Vidal, G. & Werner, R. F. Computable measure of entanglement. Phys. Rev. A 65, 032314 (2002).
Eisert, J., Browne, D., Scheel, S. & Plenio, M. B. Distillation of continuous-variable entanglement with optical means. Ann. Phys. 311, 431–458 (2004).
H.T. acknowledges financial support from the G-COE program, commissioned by the MEXT of Japan.
The authors declare no competing financial interests.
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
npj Quantum Information (2022)
npj Quantum Information (2022)
Nature Communications (2021)
Deterministic bidirectional communication and remote entanglement generation between superconducting qubits
npj Quantum Information (2019)