## Distilling single-photon entanglement from photon loss and decoherence |

JOSA B, Vol. 30, Issue 10, pp. 2737-2742 (2013)

http://dx.doi.org/10.1364/JOSAB.30.002737

Enhanced HTML Acrobat PDF (530 KB)

### Abstract

Single-photon entanglement (SPE) may be the simplest type of entanglement, but it is of major importance in quantum communication. Here we present a practical protocol for distilling the SPE from both photon loss and decoherence. With the help of some local single photons, the probability of single-photon loss can be decreased and the less-entangled state can also be recovered to the maximally entangled state simultaneously. It only requires some linear optical elements, which makes it feasible in current experiment conditions. This protocol might find applications in current quantum communications based on quantum repeaters.

© 2013 Optical Society of America

**OCIS Codes**

(270.0270) Quantum optics : Quantum optics

(270.5580) Quantum optics : Quantum electrodynamics

(270.5585) Quantum optics : Quantum information and processing

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: June 18, 2013

Manuscript Accepted: August 27, 2013

Published: September 26, 2013

**Citation**

Lan Zhou and Yu-Bo Sheng, "Distilling single-photon entanglement from photon loss and decoherence," J. Opt. Soc. Am. B **30**, 2737-2742 (2013)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-30-10-2737

Sort: Year | Journal | Reset

### References

- M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).
- N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002). [CrossRef]
- A. K. Ekert, “Quantum cryptography based on Bells theorem,” Phys. Rev. Lett. 67, 661–663 (1991). [CrossRef]
- G.-L. Long and X.-S. Liu, “Theoretically efficient high-capacity quantum-key-distribution scheme,” Phys. Rev. A 65, 032302 (2002). [CrossRef]
- C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993). [CrossRef]
- A. Karlsson and M. Bourennane, “Quantum teleportation using three-particle entanglement,” Phys. Rev. A 58, 4394–4400 (1998). [CrossRef]
- F. G. Deng, C. Y. Li, Y. S. Li, H. Y. Zhou, and Y. Wang, “Symmetric multiparty-controlled teleportation of an arbitrary two-particle entanglement,” Phys. Rev. A 72, 022338 (2005). [CrossRef]
- M. Hillery, V. Bužek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999). [CrossRef]
- A. Karlsson, M. Koashi, and N. Imoto, “Quantum entanglement for secret sharing and secret splitting,” Phys. Rev. A 59, 162–168 (1999). [CrossRef]
- L. Xiao, G.-L. Long, F.-G. Deng, and J.-W. Pan, “Efficient multiparty quantum-secret-sharing schemes,” Phys. Rev. A 69, 052307 (2004). [CrossRef]
- F.-G. Deng, G.-L. Long, and X.-S. Liu, “Two-step quantum direct communication protocol using the Einstein–Podolsky–Rosen pair block,” Phys. Rev. A 68, 042317 (2003). [CrossRef]
- C. Wang, F. G. Deng, Y. S. Li, X. S. Liu, and G. L. Long, “Quantum secure direct communication with high-dimension quantum superdense coding,” Phys. Rev. A 71, 044305 (2005). [CrossRef]
- R. Cleve, D. Gottesman, and H. K. Lo, “How to share a quantum secret,” Phys. Rev. Lett. 83, 648–651 (1999). [CrossRef]
- A. M. Lance, T. Symul, W. P. Bowen, B. C. Sanders, and P. K. Lam, “Tripartite quantum state sharing,” Phys. Rev. Lett. 92, 177903 (2004). [CrossRef]
- F. G. Deng, X. H. Li, C. Y. Li, P. Zhou, and H. Y. Zhou, “Multiparty quantum-state sharing of an arbitrary two-particle state with Einstein–Podolsky–Rosen pairs,” Phys. Rev. A 72, 044301 (2005). [CrossRef]
- S. M. Tan, D. F. Walls, and M. J. Collett, “Nonlocality of a single photon,” Phys. Rev. Lett. 66, 252–255 (1991). [CrossRef]
- L. Hardy, “Nonlocality of a single photon revisited,” Phys. Rev. Lett. 73, 2279–2283 (1994). [CrossRef]
- A. Peres, “Nonlocal effects in Fock space,” Phys. Rev. Lett. 74, 4571 (1995). [CrossRef]
- C. Silberhorn, T. C. Ralph, N. Lütkenhaus, and G. Leuchs, “Continuous variable quantum cryptography: beating the 3 dB loss limit,” Phys. Rev. Lett. 89, 167901 (2002). [CrossRef]
- C. Silberhorn, N. Korolkova, and G. Leuchs, “Quantum key distribution with bright entangled beams,” Phys. Rev. Lett. 88, 167902 (2002). [CrossRef]
- M. G. A. Paris, M. Cola, and R. Bonifacio, “Quantum state engineering assisted by entanglement,” Phys. Rev. A 67, 042104 (2003). [CrossRef]
- G. M. Ariano and P. Lo Presti, “Quantum tomography for measuring experimentally the matrix elements of an arbitrary quantum operation,” Phys. Rev. Lett. 86, 4195–4198 (2001). [CrossRef]
- G. M. Ariano, P. Lo Presti, and M. G. A. Paris, “Using entanglement improves the precision of quantum measurements,” Phys. Rev. Lett. 87, 270404 (2001). [CrossRef]
- L. M. Duan, M. D. Lukin, J. T. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001). [CrossRef]
- C. Simon, H. de Riedmatten, M. Afzelius, N. Sangouard, H. Zbinden, and N. Gisin, “Quantum repeaters with photon pair sources and multimode memories,” Phys. Rev. Lett. 98, 190503 (2007). [CrossRef]
- N. Sangouard, C. Simon, B. Zhao, Y. A. Chen, H. de Riedmatten, J. W. Pan, and N. Gisin, “Robust and efficient quantum repeaters with atomic ensembles and linear optics,” Phys. Rev. A 77, 062301 (2008). [CrossRef]
- N. Sangouard, C. Simon, H. de Riedmatten, and N. Gisin, “Quantum repeaters based on atomic ensembles and linear optics,” Rev. Mod. Phys. 83, 33–80 (2011). [CrossRef]
- N. Sangouard, C. Simon, T. Coudreau, and N. Gisin, “Purification of single-photon entanglement with linear optics,” Phys. Rev. A 78, 050301 (2008). [CrossRef]
- D. Salart, O. Landry, N. Sangouard, N. Gisin, H. Herrmann, B. Sanguinetti, C. Simon, W. Sohler, R. T. Thew, A. Thomas, and H. Zbinden, “Purification of single-photon entanglement,” Phys. Rev. Lett. 104, 180504 (2010). [CrossRef]
- Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Single-photon entanglement concentration for long-distance quantum communication,” Quantum Inf. Comput. 10, 272–281 (2010).
- L. Zhou, Y. B. Sheng, W. W. Cheng, L. Y. Gong, and S. M. Zhao, “Efficient entanglement concentration for arbitrary single-photon multimode W state,” J. Opt. Soc. Am. B 30, 71–78 (2013). [CrossRef]
- G. S. Paraoanu, “Partial measurements and the realization of quantum-mechanical counterfactuals,” Found. Phys. 41, 1214–1235 (2011). [CrossRef]
- G. S. Paraoanu, “Extraction of information from single quanta,” Phys. Rev. A 83, 044101 (2011). [CrossRef]
- G. S. Paraoanu, “Generalized partial measurements,” Europhys. Lett. 93, 64002 (2011). [CrossRef]
- T. C. Ralph and A. P. Lund, “Nondeterministic noiseless linear amplification of quantum systems,” in Proceedings of the 9th International Conference on Quantum Communication Measurement and Computing, A. lvovsky, ed. (AIP, 2009), pp. 155–160.
- N. Gisin, S. Pironio, and N. Sangouard, “Proposal for implementing device-independent quantum key distribution based on a heralded qubit amplifier,” Phys. Rev. Lett. 105, 070501 (2010). [CrossRef]
- G. Y. Xiang, T. C. Ralph, A. P. Lund, N. Walk, and G. J. Pryde, “Heralded noiseless linear amplification and distillation of entanglement,” Nat. Photonics 4, 316–319 (2010). [CrossRef]
- M. Curty and T. Moroder, “Heralded-qubit amplifiers for practical device-independent quantum key distribution,” Phys. Rev. A 84, 010304(R) (2011). [CrossRef]
- D. Pitkanen, X. Ma, R. Wickert, P. van Loock, and N. Lütkenhaus, “Efficient heralding of photonic qubits with applications to device-independent quantum key distribution,” Phys. Rev. A 84, 022325 (2011). [CrossRef]
- C. I. Osorio, N. Bruno, N. Sangouard, H. Zbinden, N. Gisin, and R. T. Thew, “Heralded photon amplification for quantum communication,” Phys. Rev. A 86, 023815 (2012). [CrossRef]
- S. Kocsis, G. Y. Xiang, T. C. Ralph, and G. J. Pryde, “Heralded noiseless amplification of a photon polarization qubit,” Nat. Phys. 9, 23–28 (2012). [CrossRef]
- S. L. Zhang, S. Yang, X. B. Zou, B. S. Shi, and G. C. Guo, “Protecting single-photon entangled state from photon loss with noiseless linear amplification,” Phys. Rev. A 86, 034302 (2012). [CrossRef]
- C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046–2052 (1996). [CrossRef]
- S. Bose, V. Vedral, and P. L. Knight, “Purification via entanglement swapping and conserved entanglement,” Phys. Rev. A 60, 194–197 (1999). [CrossRef]
- B. S. Shi, Y. K. Jiang, and G. C. Guo, “Optimal entanglement purification via entanglement swapping,” Phys. Rev. A 62, 054301 (2000). [CrossRef]
- Z. Zhao, J. W. Pan, and M. S. Zhan, “Practical scheme for entanglement concentration,” Phys. Rev. A 64, 014301 (2001). [CrossRef]
- T. Yamamoto, M. Koashi, and N. Imoto, “Concentration and purification scheme for two partially entangled photon pairs,” Phys. Rev. A 64, 012304 (2001). [CrossRef]
- Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics,” Phys. Rev. A 77, 062325 (2008). [CrossRef]
- Y. B. Sheng, L. Zhou, S. M. Zhao, and B. Y. Zheng, “Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs,” Phys. Rev. A 85, 012307 (2012). [CrossRef]
- F. G. Deng, “Optimal nonlocal multipartite entanglement concentration based on projection measurements,” Phys. Rev. A 85, 022311 (2012). [CrossRef]
- H. F. Wang, S. Zhang, and K. H. Yeon, “Linear-optics-based entanglement concentration of unknown partially entangled three photon W states,” J. Opt. Soc. Am. B 27, 2159–2164 (2010). [CrossRef]
- W. Xiong and L. Ye, “Schemes for entanglement concentration of two unknown partially entangled states with cross-Kerr nonlinearity,” J. Opt. Soc. Am. B 28, 2030–2037 (2011). [CrossRef]
- L. Zhou, Y. B. Sheng, W. W. Cheng, G. L. Yan, and S. M. Zhao, “Efficient entanglement concentration for arbitrary less-entangled NOON states,” Quant. Info. Proc. 12, 1307–1320 (2013). [CrossRef]
- Y. B. Sheng, L. Zhou, and S. M. Zhao, “Efficient two-step entanglement concentration for arbitrary W states,” Phys. Rev. A 85, 042302 (2012). [CrossRef]
- B. Gu, “Single-photon-assisted entanglement concentration of partially entangled multiphoton W states with linear optics,” J. Opt. Soc. Am. B 29, 1685–1689 (2012). [CrossRef]
- B. Gu, D. H. Quan, and S. R. Xiao, “Multi-photon entanglement concentration protocol for partially entangled W states with projection measurement,” Int. J. Theor. Phys. 51, 2966–2973 (2012). [CrossRef]
- F. F. Du, T. Li, B. C. Ren, H. R. Wei, and F. G. Deng, “Single-photon-assisted entanglement concentration of a multi-photon system in a partially entangled W state with weak cross-Kerr nonlinearity,” J. Opt. Soc. Am. B 29, 1399–1405 (2012). [CrossRef]
- Y. B. Sheng and L. Zhou, “Quantum entanglement concentration based on nonlinear optics for quantum communications,” Entropy 15, 1776–1820 (2013). [CrossRef]
- L. Zhou, “Efficient entanglement concentration for electron-spin W state with the charge detection,” Quant. Info. Proc. 12, 2087–2101 (2013). [CrossRef]
- C. Wang, Y. Zhang, and G. S. Jin, “Entanglement purification and concentration of electron-spin entangled states using quantum-dot spins in optical microcavities,” Phys. Rev. A 84, 032307 (2011). [CrossRef]
- C. Wang, “Efficient entanglement concentration for partially entangled electrons using a quantum-dot and microcavity coupled system,” Phys. Rev. A 86, 012323 (2012). [CrossRef]
- Y. B. Sheng and L. Zhou, “Efficient W-state entanglement concentration using quantum-dot and optical microcavities,” J. Opt. Soc. Am. B 30, 678–686 (2013). [CrossRef]
- C. Simon and J. W. Pan, “Polarization entanglement purification using spatial entanglement,” Phys. Rev. Lett. 89, 257901 (2002). [CrossRef]
- J. W. Pan, C. Simon, Č. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature 410, 1067–1070 (2001). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.