Abstract

Atomic ensembles are effective memory nodes for quantum communication network due to the long coherence time and the collective enhancement effect for the nonlinear interaction between an ensemble and a photon. Here we investigate the possibility of achieving the entanglement distillation for nonlocal atomic ensembles by the input-output process of a single photon as a result of cavity quantum electrodynamics. We give an optimal entanglement concentration protocol (ECP) for two-atomic-ensemble systems in a partially entangled pure state with known parameters and an efficient ECP for the systems in an unknown partially entangled pure state with a nondestructive parity-check detector (PCD). For the systems in a mixed entangled state, we introduce an entanglement purification protocol with PCDs. These entanglement distillation protocols have high fidelity and efficiency with current experimental techniques, and they are useful for quantum communication network with atomic-ensemble memories.

© 2014 Optical Society of America

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References

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2014 (4)

Y. B. Sheng and L. Zhou, “Deterministic polarization entanglement purification using time-bin entanglement,” Laser Phys. Lett. 11, 085203 (2014).
[Crossref]

B. C. Ren and G. L. long, “General hyperentanglement concentration for photon systems assisted by quantum-dot spins inside optical microcavities,” Opt. Express 22, 6547–6561 (2014).
[Crossref] [PubMed]

A. Reiserer, N. Kalb, G. Rempe, and S. Ritter, “A quantum gate between a flying optical photon and a single trapped atom,” Nature (London) 508, 237–240 (2014).
[Crossref]

T. G. Tiecke, J. D. Thompson, N. P. de Leon, L. R. Liu, V. Vuletić, and M. D. Lukin, “Nanophotonic quantum phase switch with a single atom,” Nature (London) 508, 241–244 (2014).
[Crossref]

2013 (5)

H. Ritsch, P. Domokos, F. Brennecke, and T. Esslinger, “Cold atoms in cavity-generated dynamical optical potentials,” Rev. Mod. Phys. 85, 553–601 (2013).
[Crossref]

C. Cao, C. Wang, L. Y. He, and R. Zhang, “Atomic entanglement purification and concentration using coherent state input-output process in low-Q cavity QED regime,” Opt. Express 21, 4093–4105 (2013).
[Crossref] [PubMed]

Y. B. Sheng and L. Zhou, “Quantum Entanglement Concentration Based on Nonlinear Optics for Quantum Communications,” Entropy 15, 1776–1820 (2013).
[Crossref]

B. C. Ren, F. F. Du, and F. G. Deng, “Hyperentanglement concentration for two-photon four-qubit systems with linear optics,” Phys. Rev. A 88, 012302 (2013).
[Crossref]

B. C. Ren and F. G. Deng, “Hyperentanglement purification and concentration assisted by diamond NV centers inside photonic crystal cavities,” Laser. Phys. Lett. 10, 115201 (2013).
[Crossref]

2012 (3)

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]

Z. H. Peng, J. Zou, X. J. Liu, Y. J. Xiao, and L. M. Kuang, “Atomic and photonic entanglement concentration via photonic Faraday rotation,” Phys. Rev. A 86, 034305 (2012).
[Crossref]

Y. Li, L. Aolita, D. E. Chang, and L. C. Kwek, “Robust-fidelity atom-photon entangling gates in the weak-coupling regime,” Phys. Rev. Lett. 109, 160504 (2012).
[Crossref] [PubMed]

2011 (4)

M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Single-photon sources and detectors,” Rev. Sci. Instrum. 82, 071101 (2011).
[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]

D. Aghamalyan and Y. Malakyan, “Quantum repeaters based on deterministic storage of a single photon in distant atomic ensembles,” Phys. Rev. A 84, 042305 (2011).
[Crossref]

F. G. Deng, “One-step error correction for multipartite polarization entanglement,” Phys. Rev. A 83, 062316 (2011).
[Crossref]

2010 (6)

Y. B. Sheng and F. G. Deng, “Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement,” Phys. Rev. A 81, 032307 (2010).
[Crossref]

Y. B. Sheng and F. G. Deng, “One-step deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044305 (2010).
[Crossref]

X. H. Li, “Deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044304 (2010).
[Crossref]

B. Zhao, M. Müller, K. Hammerer, and P. Zoller, “Efficient quantum repeater based on deterministic Rydberg gates,” Phys. Rev. A 81, 052329 (2010).
[Crossref]

M. Saffman, T. G. Walker, and K. Mølmer, “Quantum information with Rydberg atoms,” Rev. Mod. Phys. 82, 2313–2363 (2010).
[Crossref]

D. Hunger, T. Steinmetz, Y. Colombe, C. Deutsch, T. W. Häensch, and J. Reichel, “A fiber Fabry-Perot cavity with high finesse,” New. J. Phys. 12, 065038 (2010).
[Crossref]

2009 (2)

A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photon. 3, 706–714 (2009).
[Crossref]

F. Mei, M. Feng, Y. F. Yu, and Z. M. Zhang, “Scalable quantum information processing with atomic ensembles and flying photons,” Phys. Rev. A 80, 042319 (2009).
[Crossref]

2008 (4)

E. Brion, L. H. Pedersen, M. Saffman, and K. Mølmer, “Error correction in ensemble registers for quantum repeaters and quantum computers,” Phys. Rev. Lett. 100, 110506 (2008).
[Crossref] [PubMed]

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity,” Phys. Rev. A 77, 042308 (2008).
[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]

X. H. Li, F. G. Deng, and H. Y. Zhou, “Efficient quantum key distribution over a collective noise channel,” Phys. Rev. A 78, 022321 (2008).
[Crossref]

2007 (3)

X. H. Li, F. G. Deng, and H. Y. Zhou, “Faithful qubit transmission against collective noise without ancillary qubits,” Appl. Phys. Lett. 91, 144101 (2007).
[Crossref]

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom-field coupling for Bose-Einstein condensates in an optical cavity on a chip,” Nature (London) 450, 272–276 (2007).
[Crossref]

Z. B. Chen, B. Zhao, Y. A. Chen, J. Schmiedmayer, and J. W. Pan, “Fault-tolerant quantum repeater with atomic ensembles and linear optics,” Phys. Rev. A 76, 022329 (2007).
[Crossref]

2006 (1)

Z. L. Cao, L. H. Zhang, and M. Yang, “Concentration for unknown atomic entangled states via cavity decay,” Phys. Rev. A 73, 014303 (2006).
[Crossref]

2004 (1)

L. M. Duan and H. J. Kimble, “Scalable photonic quantum computation through cavity-assisted interactions,” Phys. Rev. Lett. 92, 127902 (2004).
[Crossref] [PubMed]

2003 (2)

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]

J. W. Pan, S. Gasparoni, R. Ursin, G. Weihs, and A. Zellinger, “Experimental entanglement purification of arbitrary unknown states,” Nature (London) 423, 417–422 (2003).
[Crossref]

2002 (5)

C. Simon and J. W. Pan, “Polarization entanglement purification using spatial entanglement,” Phys. Rev. Lett. 89, 257901 (2002).
[Crossref] [PubMed]

G. L. Long and X. S. Liu, “Theoretically efficient high-capacity quantum-key-distribution scheme,” Phys. Rev. A 65, 032302 (2002).
[Crossref]

X. S. Liu, G. L. Long, D. M. Tong, and F. Li, “General scheme for superdense coding between multiparties,” Phys. Rev. A 65, 022304 (2002).
[Crossref]

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

M. Saffman and T. G. Walker, “Creating single-atom and single-photon sources from entangled atomic ensembles,” Phys. Rev. A 66, 065403 (2002).
[Crossref]

2001 (4)

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

J. W. Pan, C. Simon, C. Brukner, and A. Zellinger, “Entanglement purification for quantum communication,” Nature (London) 410, 1067–1070 (2001).
[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]

1999 (3)

S. Bose, V. Vedral, and P. L. Knight, “Purification via entanglement swapping and conserved entanglement,” Phys. Rev. A 60, 194–197 (1999).
[Crossref]

W. Dür, H. J. Briegel, J. I. Cirac, and P. Zoller, “Quantum repeaters based on entanglement purification,” Phys. Rev. A 59, 169–181 (1999).
[Crossref]

M. Hillery, V. Buzek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999).
[Crossref]

1998 (1)

H. J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932–5935 (1998).
[Crossref]

1996 (3)

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722–725 (1996).
[Crossref] [PubMed]

D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 77, 2818–2821 (1996).
[Crossref] [PubMed]

C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046 (1996).
[Crossref] [PubMed]

1993 (1)

C. H. Bennett, G. Brassard, C. Crépeau, 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] [PubMed]

1992 (2)

C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69, 2881–2884 (1992).
[Crossref] [PubMed]

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bell’s theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
[Crossref] [PubMed]

1991 (1)

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
[Crossref] [PubMed]

Aghamalyan, D.

D. Aghamalyan and Y. Malakyan, “Quantum repeaters based on deterministic storage of a single photon in distant atomic ensembles,” Phys. Rev. A 84, 042305 (2011).
[Crossref]

Aolita, L.

Y. Li, L. Aolita, D. E. Chang, and L. C. Kwek, “Robust-fidelity atom-photon entangling gates in the weak-coupling regime,” Phys. Rev. Lett. 109, 160504 (2012).
[Crossref] [PubMed]

Bennett, C. H.

C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046 (1996).
[Crossref] [PubMed]

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722–725 (1996).
[Crossref] [PubMed]

C. H. Bennett, G. Brassard, C. Crépeau, 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] [PubMed]

C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69, 2881–2884 (1992).
[Crossref] [PubMed]

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bell’s theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
[Crossref] [PubMed]

Bernstein, H. J.

C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046 (1996).
[Crossref] [PubMed]

Berthiaume, A.

M. Hillery, V. Buzek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999).
[Crossref]

Bose, S.

S. Bose, V. Vedral, and P. L. Knight, “Purification via entanglement swapping and conserved entanglement,” Phys. Rev. A 60, 194–197 (1999).
[Crossref]

Brassard, G.

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722–725 (1996).
[Crossref] [PubMed]

C. H. Bennett, G. Brassard, C. Crépeau, 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] [PubMed]

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bell’s theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
[Crossref] [PubMed]

Brennecke, F.

H. Ritsch, P. Domokos, F. Brennecke, and T. Esslinger, “Cold atoms in cavity-generated dynamical optical potentials,” Rev. Mod. Phys. 85, 553–601 (2013).
[Crossref]

Briegel, H. J.

W. Dür, H. J. Briegel, J. I. Cirac, and P. Zoller, “Quantum repeaters based on entanglement purification,” Phys. Rev. A 59, 169–181 (1999).
[Crossref]

H. J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932–5935 (1998).
[Crossref]

Brion, E.

E. Brion, L. H. Pedersen, M. Saffman, and K. Mølmer, “Error correction in ensemble registers for quantum repeaters and quantum computers,” Phys. Rev. Lett. 100, 110506 (2008).
[Crossref] [PubMed]

Brukner, C.

J. W. Pan, C. Simon, C. Brukner, and A. Zellinger, “Entanglement purification for quantum communication,” Nature (London) 410, 1067–1070 (2001).
[Crossref]

Buzek, V.

M. Hillery, V. Buzek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999).
[Crossref]

Cao, C.

Cao, Z. L.

Z. L. Cao, L. H. Zhang, and M. Yang, “Concentration for unknown atomic entangled states via cavity decay,” Phys. Rev. A 73, 014303 (2006).
[Crossref]

Chang, D. E.

Y. Li, L. Aolita, D. E. Chang, and L. C. Kwek, “Robust-fidelity atom-photon entangling gates in the weak-coupling regime,” Phys. Rev. Lett. 109, 160504 (2012).
[Crossref] [PubMed]

Chen, Y. A.

Z. B. Chen, B. Zhao, Y. A. Chen, J. Schmiedmayer, and J. W. Pan, “Fault-tolerant quantum repeater with atomic ensembles and linear optics,” Phys. Rev. A 76, 022329 (2007).
[Crossref]

Chen, Z. B.

Z. B. Chen, B. Zhao, Y. A. Chen, J. Schmiedmayer, and J. W. Pan, “Fault-tolerant quantum repeater with atomic ensembles and linear optics,” Phys. Rev. A 76, 022329 (2007).
[Crossref]

Cirac, J. I.

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

W. Dür, H. J. Briegel, J. I. Cirac, and P. Zoller, “Quantum repeaters based on entanglement purification,” Phys. Rev. A 59, 169–181 (1999).
[Crossref]

H. J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932–5935 (1998).
[Crossref]

Colombe, Y.

D. Hunger, T. Steinmetz, Y. Colombe, C. Deutsch, T. W. Häensch, and J. Reichel, “A fiber Fabry-Perot cavity with high finesse,” New. J. Phys. 12, 065038 (2010).
[Crossref]

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom-field coupling for Bose-Einstein condensates in an optical cavity on a chip,” Nature (London) 450, 272–276 (2007).
[Crossref]

Crépeau, C.

C. H. Bennett, G. Brassard, C. Crépeau, 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] [PubMed]

de Leon, N. P.

T. G. Tiecke, J. D. Thompson, N. P. de Leon, L. R. Liu, V. Vuletić, and M. D. Lukin, “Nanophotonic quantum phase switch with a single atom,” Nature (London) 508, 241–244 (2014).
[Crossref]

de Riedmatten, H.

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]

Deng, F. G.

B. C. Ren, F. F. Du, and F. G. Deng, “Hyperentanglement concentration for two-photon four-qubit systems with linear optics,” Phys. Rev. A 88, 012302 (2013).
[Crossref]

B. C. Ren and F. G. Deng, “Hyperentanglement purification and concentration assisted by diamond NV centers inside photonic crystal cavities,” Laser. Phys. Lett. 10, 115201 (2013).
[Crossref]

F. G. Deng, “One-step error correction for multipartite polarization entanglement,” Phys. Rev. A 83, 062316 (2011).
[Crossref]

Y. B. Sheng and F. G. Deng, “One-step deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044305 (2010).
[Crossref]

Y. B. Sheng and F. G. Deng, “Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement,” Phys. Rev. A 81, 032307 (2010).
[Crossref]

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity,” Phys. Rev. A 77, 042308 (2008).
[Crossref]

X. H. Li, F. G. Deng, and H. Y. Zhou, “Efficient quantum key distribution over a collective noise channel,” Phys. Rev. A 78, 022321 (2008).
[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]

X. H. Li, F. G. Deng, and H. Y. Zhou, “Faithful qubit transmission against collective noise without ancillary qubits,” Appl. Phys. Lett. 91, 144101 (2007).
[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]

Deutsch, C.

D. Hunger, T. Steinmetz, Y. Colombe, C. Deutsch, T. W. Häensch, and J. Reichel, “A fiber Fabry-Perot cavity with high finesse,” New. J. Phys. 12, 065038 (2010).
[Crossref]

Deutsch, D.

D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 77, 2818–2821 (1996).
[Crossref] [PubMed]

Domokos, P.

H. Ritsch, P. Domokos, F. Brennecke, and T. Esslinger, “Cold atoms in cavity-generated dynamical optical potentials,” Rev. Mod. Phys. 85, 553–601 (2013).
[Crossref]

Du, F. F.

B. C. Ren, F. F. Du, and F. G. Deng, “Hyperentanglement concentration for two-photon four-qubit systems with linear optics,” Phys. Rev. A 88, 012302 (2013).
[Crossref]

Duan, L. M.

L. M. Duan and H. J. Kimble, “Scalable photonic quantum computation through cavity-assisted interactions,” Phys. Rev. Lett. 92, 127902 (2004).
[Crossref] [PubMed]

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

Dubois, G.

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom-field coupling for Bose-Einstein condensates in an optical cavity on a chip,” Nature (London) 450, 272–276 (2007).
[Crossref]

Dür, W.

W. Dür, H. J. Briegel, J. I. Cirac, and P. Zoller, “Quantum repeaters based on entanglement purification,” Phys. Rev. A 59, 169–181 (1999).
[Crossref]

H. J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932–5935 (1998).
[Crossref]

Eisaman, M. D.

M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Single-photon sources and detectors,” Rev. Sci. Instrum. 82, 071101 (2011).
[Crossref]

Ekert, A.

D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 77, 2818–2821 (1996).
[Crossref] [PubMed]

Ekert, A. K.

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
[Crossref] [PubMed]

Esslinger, T.

H. Ritsch, P. Domokos, F. Brennecke, and T. Esslinger, “Cold atoms in cavity-generated dynamical optical potentials,” Rev. Mod. Phys. 85, 553–601 (2013).
[Crossref]

Fan, J.

M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Single-photon sources and detectors,” Rev. Sci. Instrum. 82, 071101 (2011).
[Crossref]

Feng, M.

F. Mei, M. Feng, Y. F. Yu, and Z. M. Zhang, “Scalable quantum information processing with atomic ensembles and flying photons,” Phys. Rev. A 80, 042319 (2009).
[Crossref]

Gasparoni, S.

J. W. Pan, S. Gasparoni, R. Ursin, G. Weihs, and A. Zellinger, “Experimental entanglement purification of arbitrary unknown states,” Nature (London) 423, 417–422 (2003).
[Crossref]

Gisin, N.

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. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

Häensch, T. W.

D. Hunger, T. Steinmetz, Y. Colombe, C. Deutsch, T. W. Häensch, and J. Reichel, “A fiber Fabry-Perot cavity with high finesse,” New. J. Phys. 12, 065038 (2010).
[Crossref]

Hammerer, K.

B. Zhao, M. Müller, K. Hammerer, and P. Zoller, “Efficient quantum repeater based on deterministic Rydberg gates,” Phys. Rev. A 81, 052329 (2010).
[Crossref]

He, L. Y.

Hillery, M.

M. Hillery, V. Buzek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999).
[Crossref]

Hunger, D.

D. Hunger, T. Steinmetz, Y. Colombe, C. Deutsch, T. W. Häensch, and J. Reichel, “A fiber Fabry-Perot cavity with high finesse,” New. J. Phys. 12, 065038 (2010).
[Crossref]

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom-field coupling for Bose-Einstein condensates in an optical cavity on a chip,” Nature (London) 450, 272–276 (2007).
[Crossref]

Imoto, N.

T. Yamamoto, M. Koashi, and N. Imoto, “Concentration and purification scheme for two partially entangled photon pairs,” Phys. Rev. A 64, 012304 (2001).
[Crossref]

Jozsa, R.

D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 77, 2818–2821 (1996).
[Crossref] [PubMed]

C. H. Bennett, G. Brassard, C. Crépeau, 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] [PubMed]

Kalb, N.

A. Reiserer, N. Kalb, G. Rempe, and S. Ritter, “A quantum gate between a flying optical photon and a single trapped atom,” Nature (London) 508, 237–240 (2014).
[Crossref]

Kimble, H. J.

L. M. Duan and H. J. Kimble, “Scalable photonic quantum computation through cavity-assisted interactions,” Phys. Rev. Lett. 92, 127902 (2004).
[Crossref] [PubMed]

Knight, P. L.

S. Bose, V. Vedral, and P. L. Knight, “Purification via entanglement swapping and conserved entanglement,” Phys. Rev. A 60, 194–197 (1999).
[Crossref]

Koashi, M.

T. Yamamoto, M. Koashi, and N. Imoto, “Concentration and purification scheme for two partially entangled photon pairs,” Phys. Rev. A 64, 012304 (2001).
[Crossref]

Kuang, L. M.

Z. H. Peng, J. Zou, X. J. Liu, Y. J. Xiao, and L. M. Kuang, “Atomic and photonic entanglement concentration via photonic Faraday rotation,” Phys. Rev. A 86, 034305 (2012).
[Crossref]

Kwek, L. C.

Y. Li, L. Aolita, D. E. Chang, and L. C. Kwek, “Robust-fidelity atom-photon entangling gates in the weak-coupling regime,” Phys. Rev. Lett. 109, 160504 (2012).
[Crossref] [PubMed]

Li, F.

X. S. Liu, G. L. Long, D. M. Tong, and F. Li, “General scheme for superdense coding between multiparties,” Phys. Rev. A 65, 022304 (2002).
[Crossref]

Li, X. H.

X. H. Li, “Deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044304 (2010).
[Crossref]

X. H. Li, F. G. Deng, and H. Y. Zhou, “Efficient quantum key distribution over a collective noise channel,” Phys. Rev. A 78, 022321 (2008).
[Crossref]

X. H. Li, F. G. Deng, and H. Y. Zhou, “Faithful qubit transmission against collective noise without ancillary qubits,” Appl. Phys. Lett. 91, 144101 (2007).
[Crossref]

Li, Y.

Y. Li, L. Aolita, D. E. Chang, and L. C. Kwek, “Robust-fidelity atom-photon entangling gates in the weak-coupling regime,” Phys. Rev. Lett. 109, 160504 (2012).
[Crossref] [PubMed]

Linke, F.

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom-field coupling for Bose-Einstein condensates in an optical cavity on a chip,” Nature (London) 450, 272–276 (2007).
[Crossref]

Liu, L. R.

T. G. Tiecke, J. D. Thompson, N. P. de Leon, L. R. Liu, V. Vuletić, and M. D. Lukin, “Nanophotonic quantum phase switch with a single atom,” Nature (London) 508, 241–244 (2014).
[Crossref]

Liu, X. J.

Z. H. Peng, J. Zou, X. J. Liu, Y. J. Xiao, and L. M. Kuang, “Atomic and photonic entanglement concentration via photonic Faraday rotation,” Phys. Rev. A 86, 034305 (2012).
[Crossref]

Liu, X. S.

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]

G. L. Long and X. S. Liu, “Theoretically efficient high-capacity quantum-key-distribution scheme,” Phys. Rev. A 65, 032302 (2002).
[Crossref]

X. S. Liu, G. L. Long, D. M. Tong, and F. Li, “General scheme for superdense coding between multiparties,” Phys. Rev. A 65, 022304 (2002).
[Crossref]

long, G. L.

B. C. Ren and G. L. long, “General hyperentanglement concentration for photon systems assisted by quantum-dot spins inside optical microcavities,” Opt. Express 22, 6547–6561 (2014).
[Crossref] [PubMed]

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]

G. L. Long and X. S. Liu, “Theoretically efficient high-capacity quantum-key-distribution scheme,” Phys. Rev. A 65, 032302 (2002).
[Crossref]

X. S. Liu, G. L. Long, D. M. Tong, and F. Li, “General scheme for superdense coding between multiparties,” Phys. Rev. A 65, 022304 (2002).
[Crossref]

Lukin, M. D.

T. G. Tiecke, J. D. Thompson, N. P. de Leon, L. R. Liu, V. Vuletić, and M. D. Lukin, “Nanophotonic quantum phase switch with a single atom,” Nature (London) 508, 241–244 (2014).
[Crossref]

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

Lvovsky, A. I.

A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photon. 3, 706–714 (2009).
[Crossref]

Macchiavello, C.

D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 77, 2818–2821 (1996).
[Crossref] [PubMed]

Malakyan, Y.

D. Aghamalyan and Y. Malakyan, “Quantum repeaters based on deterministic storage of a single photon in distant atomic ensembles,” Phys. Rev. A 84, 042305 (2011).
[Crossref]

Mei, F.

F. Mei, M. Feng, Y. F. Yu, and Z. M. Zhang, “Scalable quantum information processing with atomic ensembles and flying photons,” Phys. Rev. A 80, 042319 (2009).
[Crossref]

Mermin, N. D.

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bell’s theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
[Crossref] [PubMed]

Migdall, A.

M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Single-photon sources and detectors,” Rev. Sci. Instrum. 82, 071101 (2011).
[Crossref]

Milburn, G. J.

D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, 1994).
[Crossref]

Mølmer, K.

M. Saffman, T. G. Walker, and K. Mølmer, “Quantum information with Rydberg atoms,” Rev. Mod. Phys. 82, 2313–2363 (2010).
[Crossref]

E. Brion, L. H. Pedersen, M. Saffman, and K. Mølmer, “Error correction in ensemble registers for quantum repeaters and quantum computers,” Phys. Rev. Lett. 100, 110506 (2008).
[Crossref] [PubMed]

Müller, M.

B. Zhao, M. Müller, K. Hammerer, and P. Zoller, “Efficient quantum repeater based on deterministic Rydberg gates,” Phys. Rev. A 81, 052329 (2010).
[Crossref]

Pan, J. W.

Z. B. Chen, B. Zhao, Y. A. Chen, J. Schmiedmayer, and J. W. Pan, “Fault-tolerant quantum repeater with atomic ensembles and linear optics,” Phys. Rev. A 76, 022329 (2007).
[Crossref]

J. W. Pan, S. Gasparoni, R. Ursin, G. Weihs, and A. Zellinger, “Experimental entanglement purification of arbitrary unknown states,” Nature (London) 423, 417–422 (2003).
[Crossref]

C. Simon and J. W. Pan, “Polarization entanglement purification using spatial entanglement,” Phys. Rev. Lett. 89, 257901 (2002).
[Crossref] [PubMed]

J. W. Pan, C. Simon, C. Brukner, and A. Zellinger, “Entanglement purification for quantum communication,” Nature (London) 410, 1067–1070 (2001).
[Crossref]

Pan, J.W.

Z. Zhao, J.W. Pan, and M. S. Zhan, “Practical scheme for entanglement concentration,” Phys. Rev. A 64, 014301 (2001).
[Crossref]

Pedersen, L. H.

E. Brion, L. H. Pedersen, M. Saffman, and K. Mølmer, “Error correction in ensemble registers for quantum repeaters and quantum computers,” Phys. Rev. Lett. 100, 110506 (2008).
[Crossref] [PubMed]

Peng, Z. H.

Z. H. Peng, J. Zou, X. J. Liu, Y. J. Xiao, and L. M. Kuang, “Atomic and photonic entanglement concentration via photonic Faraday rotation,” Phys. Rev. A 86, 034305 (2012).
[Crossref]

Peres, A.

C. H. Bennett, G. Brassard, C. Crépeau, 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] [PubMed]

Polyakov, S. V.

M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Single-photon sources and detectors,” Rev. Sci. Instrum. 82, 071101 (2011).
[Crossref]

Popescu, S.

D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 77, 2818–2821 (1996).
[Crossref] [PubMed]

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722–725 (1996).
[Crossref] [PubMed]

C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046 (1996).
[Crossref] [PubMed]

Reichel, J.

D. Hunger, T. Steinmetz, Y. Colombe, C. Deutsch, T. W. Häensch, and J. Reichel, “A fiber Fabry-Perot cavity with high finesse,” New. J. Phys. 12, 065038 (2010).
[Crossref]

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom-field coupling for Bose-Einstein condensates in an optical cavity on a chip,” Nature (London) 450, 272–276 (2007).
[Crossref]

Reiserer, A.

A. Reiserer, N. Kalb, G. Rempe, and S. Ritter, “A quantum gate between a flying optical photon and a single trapped atom,” Nature (London) 508, 237–240 (2014).
[Crossref]

Rempe, G.

A. Reiserer, N. Kalb, G. Rempe, and S. Ritter, “A quantum gate between a flying optical photon and a single trapped atom,” Nature (London) 508, 237–240 (2014).
[Crossref]

Ren, B. C.

B. C. Ren and G. L. long, “General hyperentanglement concentration for photon systems assisted by quantum-dot spins inside optical microcavities,” Opt. Express 22, 6547–6561 (2014).
[Crossref] [PubMed]

B. C. Ren, F. F. Du, and F. G. Deng, “Hyperentanglement concentration for two-photon four-qubit systems with linear optics,” Phys. Rev. A 88, 012302 (2013).
[Crossref]

B. C. Ren and F. G. Deng, “Hyperentanglement purification and concentration assisted by diamond NV centers inside photonic crystal cavities,” Laser. Phys. Lett. 10, 115201 (2013).
[Crossref]

Ribordy, G.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

Ritsch, H.

H. Ritsch, P. Domokos, F. Brennecke, and T. Esslinger, “Cold atoms in cavity-generated dynamical optical potentials,” Rev. Mod. Phys. 85, 553–601 (2013).
[Crossref]

Ritter, S.

A. Reiserer, N. Kalb, G. Rempe, and S. Ritter, “A quantum gate between a flying optical photon and a single trapped atom,” Nature (London) 508, 237–240 (2014).
[Crossref]

Saffman, M.

M. Saffman, T. G. Walker, and K. Mølmer, “Quantum information with Rydberg atoms,” Rev. Mod. Phys. 82, 2313–2363 (2010).
[Crossref]

E. Brion, L. H. Pedersen, M. Saffman, and K. Mølmer, “Error correction in ensemble registers for quantum repeaters and quantum computers,” Phys. Rev. Lett. 100, 110506 (2008).
[Crossref] [PubMed]

M. Saffman and T. G. Walker, “Creating single-atom and single-photon sources from entangled atomic ensembles,” Phys. Rev. A 66, 065403 (2002).
[Crossref]

Sanders, B. C.

A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photon. 3, 706–714 (2009).
[Crossref]

Sangouard, N.

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]

Sanpera, A.

D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 77, 2818–2821 (1996).
[Crossref] [PubMed]

Schmiedmayer, J.

Z. B. Chen, B. Zhao, Y. A. Chen, J. Schmiedmayer, and J. W. Pan, “Fault-tolerant quantum repeater with atomic ensembles and linear optics,” Phys. Rev. A 76, 022329 (2007).
[Crossref]

Schumacher, B.

C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046 (1996).
[Crossref] [PubMed]

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722–725 (1996).
[Crossref] [PubMed]

Sheng, Y. B.

Y. B. Sheng and L. Zhou, “Deterministic polarization entanglement purification using time-bin entanglement,” Laser Phys. Lett. 11, 085203 (2014).
[Crossref]

Y. B. Sheng and L. Zhou, “Quantum Entanglement Concentration Based on Nonlinear Optics for Quantum Communications,” Entropy 15, 1776–1820 (2013).
[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]

Y. B. Sheng and F. G. Deng, “One-step deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044305 (2010).
[Crossref]

Y. B. Sheng and F. G. Deng, “Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement,” Phys. Rev. A 81, 032307 (2010).
[Crossref]

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity,” Phys. Rev. A 77, 042308 (2008).
[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]

Simon, C.

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]

C. Simon and J. W. Pan, “Polarization entanglement purification using spatial entanglement,” Phys. Rev. Lett. 89, 257901 (2002).
[Crossref] [PubMed]

J. W. Pan, C. Simon, C. Brukner, and A. Zellinger, “Entanglement purification for quantum communication,” Nature (London) 410, 1067–1070 (2001).
[Crossref]

Smolin, J. A.

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722–725 (1996).
[Crossref] [PubMed]

Steinmetz, T.

D. Hunger, T. Steinmetz, Y. Colombe, C. Deutsch, T. W. Häensch, and J. Reichel, “A fiber Fabry-Perot cavity with high finesse,” New. J. Phys. 12, 065038 (2010).
[Crossref]

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom-field coupling for Bose-Einstein condensates in an optical cavity on a chip,” Nature (London) 450, 272–276 (2007).
[Crossref]

Thompson, J. D.

T. G. Tiecke, J. D. Thompson, N. P. de Leon, L. R. Liu, V. Vuletić, and M. D. Lukin, “Nanophotonic quantum phase switch with a single atom,” Nature (London) 508, 241–244 (2014).
[Crossref]

Tiecke, T. G.

T. G. Tiecke, J. D. Thompson, N. P. de Leon, L. R. Liu, V. Vuletić, and M. D. Lukin, “Nanophotonic quantum phase switch with a single atom,” Nature (London) 508, 241–244 (2014).
[Crossref]

Tittel, W.

A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photon. 3, 706–714 (2009).
[Crossref]

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

Tong, D. M.

X. S. Liu, G. L. Long, D. M. Tong, and F. Li, “General scheme for superdense coding between multiparties,” Phys. Rev. A 65, 022304 (2002).
[Crossref]

Ursin, R.

J. W. Pan, S. Gasparoni, R. Ursin, G. Weihs, and A. Zellinger, “Experimental entanglement purification of arbitrary unknown states,” Nature (London) 423, 417–422 (2003).
[Crossref]

Vedral, V.

S. Bose, V. Vedral, and P. L. Knight, “Purification via entanglement swapping and conserved entanglement,” Phys. Rev. A 60, 194–197 (1999).
[Crossref]

Vuletic, V.

T. G. Tiecke, J. D. Thompson, N. P. de Leon, L. R. Liu, V. Vuletić, and M. D. Lukin, “Nanophotonic quantum phase switch with a single atom,” Nature (London) 508, 241–244 (2014).
[Crossref]

Walker, T. G.

M. Saffman, T. G. Walker, and K. Mølmer, “Quantum information with Rydberg atoms,” Rev. Mod. Phys. 82, 2313–2363 (2010).
[Crossref]

M. Saffman and T. G. Walker, “Creating single-atom and single-photon sources from entangled atomic ensembles,” Phys. Rev. A 66, 065403 (2002).
[Crossref]

Walls, D. F.

D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, 1994).
[Crossref]

Wang, C.

Weihs, G.

J. W. Pan, S. Gasparoni, R. Ursin, G. Weihs, and A. Zellinger, “Experimental entanglement purification of arbitrary unknown states,” Nature (London) 423, 417–422 (2003).
[Crossref]

Wiesner, S. J.

C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69, 2881–2884 (1992).
[Crossref] [PubMed]

Wootters, W. K.

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722–725 (1996).
[Crossref] [PubMed]

C. H. Bennett, G. Brassard, C. Crépeau, 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] [PubMed]

Xiao, Y. J.

Z. H. Peng, J. Zou, X. J. Liu, Y. J. Xiao, and L. M. Kuang, “Atomic and photonic entanglement concentration via photonic Faraday rotation,” Phys. Rev. A 86, 034305 (2012).
[Crossref]

Yamamoto, T.

T. Yamamoto, M. Koashi, and N. Imoto, “Concentration and purification scheme for two partially entangled photon pairs,” Phys. Rev. A 64, 012304 (2001).
[Crossref]

Yang, M.

Z. L. Cao, L. H. Zhang, and M. Yang, “Concentration for unknown atomic entangled states via cavity decay,” Phys. Rev. A 73, 014303 (2006).
[Crossref]

Yu, Y. F.

F. Mei, M. Feng, Y. F. Yu, and Z. M. Zhang, “Scalable quantum information processing with atomic ensembles and flying photons,” Phys. Rev. A 80, 042319 (2009).
[Crossref]

Zbinden, H.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

Zellinger, A.

J. W. Pan, S. Gasparoni, R. Ursin, G. Weihs, and A. Zellinger, “Experimental entanglement purification of arbitrary unknown states,” Nature (London) 423, 417–422 (2003).
[Crossref]

J. W. Pan, C. Simon, C. Brukner, and A. Zellinger, “Entanglement purification for quantum communication,” Nature (London) 410, 1067–1070 (2001).
[Crossref]

Zhan, M. S.

Z. Zhao, J.W. Pan, and M. S. Zhan, “Practical scheme for entanglement concentration,” Phys. Rev. A 64, 014301 (2001).
[Crossref]

Zhang, L. H.

Z. L. Cao, L. H. Zhang, and M. Yang, “Concentration for unknown atomic entangled states via cavity decay,” Phys. Rev. A 73, 014303 (2006).
[Crossref]

Zhang, R.

Zhang, Z. M.

F. Mei, M. Feng, Y. F. Yu, and Z. M. Zhang, “Scalable quantum information processing with atomic ensembles and flying photons,” Phys. Rev. A 80, 042319 (2009).
[Crossref]

Zhao, B.

B. Zhao, M. Müller, K. Hammerer, and P. Zoller, “Efficient quantum repeater based on deterministic Rydberg gates,” Phys. Rev. A 81, 052329 (2010).
[Crossref]

Z. B. Chen, B. Zhao, Y. A. Chen, J. Schmiedmayer, and J. W. Pan, “Fault-tolerant quantum repeater with atomic ensembles and linear optics,” Phys. Rev. A 76, 022329 (2007).
[Crossref]

Zhao, S. M.

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]

Zhao, Z.

Z. Zhao, J.W. Pan, and M. S. Zhan, “Practical scheme for entanglement concentration,” Phys. Rev. A 64, 014301 (2001).
[Crossref]

Zheng, B. Y.

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]

Zhou, H. Y.

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, F. G. Deng, and H. Y. Zhou, “Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity,” Phys. Rev. A 77, 042308 (2008).
[Crossref]

X. H. Li, F. G. Deng, and H. Y. Zhou, “Efficient quantum key distribution over a collective noise channel,” Phys. Rev. A 78, 022321 (2008).
[Crossref]

X. H. Li, F. G. Deng, and H. Y. Zhou, “Faithful qubit transmission against collective noise without ancillary qubits,” Appl. Phys. Lett. 91, 144101 (2007).
[Crossref]

Zhou, L.

Y. B. Sheng and L. Zhou, “Deterministic polarization entanglement purification using time-bin entanglement,” Laser Phys. Lett. 11, 085203 (2014).
[Crossref]

Y. B. Sheng and L. Zhou, “Quantum Entanglement Concentration Based on Nonlinear Optics for Quantum Communications,” Entropy 15, 1776–1820 (2013).
[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]

Zoller, P.

B. Zhao, M. Müller, K. Hammerer, and P. Zoller, “Efficient quantum repeater based on deterministic Rydberg gates,” Phys. Rev. A 81, 052329 (2010).
[Crossref]

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

W. Dür, H. J. Briegel, J. I. Cirac, and P. Zoller, “Quantum repeaters based on entanglement purification,” Phys. Rev. A 59, 169–181 (1999).
[Crossref]

H. J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932–5935 (1998).
[Crossref]

Zou, J.

Z. H. Peng, J. Zou, X. J. Liu, Y. J. Xiao, and L. M. Kuang, “Atomic and photonic entanglement concentration via photonic Faraday rotation,” Phys. Rev. A 86, 034305 (2012).
[Crossref]

Appl. Phys. Lett. (1)

X. H. Li, F. G. Deng, and H. Y. Zhou, “Faithful qubit transmission against collective noise without ancillary qubits,” Appl. Phys. Lett. 91, 144101 (2007).
[Crossref]

Entropy (1)

Y. B. Sheng and L. Zhou, “Quantum Entanglement Concentration Based on Nonlinear Optics for Quantum Communications,” Entropy 15, 1776–1820 (2013).
[Crossref]

Laser Phys. Lett. (1)

Y. B. Sheng and L. Zhou, “Deterministic polarization entanglement purification using time-bin entanglement,” Laser Phys. Lett. 11, 085203 (2014).
[Crossref]

Laser. Phys. Lett. (1)

B. C. Ren and F. G. Deng, “Hyperentanglement purification and concentration assisted by diamond NV centers inside photonic crystal cavities,” Laser. Phys. Lett. 10, 115201 (2013).
[Crossref]

Nat. Photon. (1)

A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photon. 3, 706–714 (2009).
[Crossref]

Nature (London) (6)

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

J. W. Pan, C. Simon, C. Brukner, and A. Zellinger, “Entanglement purification for quantum communication,” Nature (London) 410, 1067–1070 (2001).
[Crossref]

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom-field coupling for Bose-Einstein condensates in an optical cavity on a chip,” Nature (London) 450, 272–276 (2007).
[Crossref]

J. W. Pan, S. Gasparoni, R. Ursin, G. Weihs, and A. Zellinger, “Experimental entanglement purification of arbitrary unknown states,” Nature (London) 423, 417–422 (2003).
[Crossref]

A. Reiserer, N. Kalb, G. Rempe, and S. Ritter, “A quantum gate between a flying optical photon and a single trapped atom,” Nature (London) 508, 237–240 (2014).
[Crossref]

T. G. Tiecke, J. D. Thompson, N. P. de Leon, L. R. Liu, V. Vuletić, and M. D. Lukin, “Nanophotonic quantum phase switch with a single atom,” Nature (London) 508, 241–244 (2014).
[Crossref]

New. J. Phys. (1)

D. Hunger, T. Steinmetz, Y. Colombe, C. Deutsch, T. W. Häensch, and J. Reichel, “A fiber Fabry-Perot cavity with high finesse,” New. J. Phys. 12, 065038 (2010).
[Crossref]

Opt. Express (2)

Phys. Rev. A (25)

Z. L. Cao, L. H. Zhang, and M. Yang, “Concentration for unknown atomic entangled states via cavity decay,” Phys. Rev. A 73, 014303 (2006).
[Crossref]

Z. H. Peng, J. Zou, X. J. Liu, Y. J. Xiao, and L. M. Kuang, “Atomic and photonic entanglement concentration via photonic Faraday rotation,” Phys. Rev. A 86, 034305 (2012).
[Crossref]

M. Saffman and T. G. Walker, “Creating single-atom and single-photon sources from entangled atomic ensembles,” Phys. Rev. A 66, 065403 (2002).
[Crossref]

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity,” Phys. Rev. A 77, 042308 (2008).
[Crossref]

D. Aghamalyan and Y. Malakyan, “Quantum repeaters based on deterministic storage of a single photon in distant atomic ensembles,” Phys. Rev. A 84, 042305 (2011).
[Crossref]

F. Mei, M. Feng, Y. F. Yu, and Z. M. Zhang, “Scalable quantum information processing with atomic ensembles and flying photons,” Phys. Rev. A 80, 042319 (2009).
[Crossref]

W. Dür, H. J. Briegel, J. I. Cirac, and P. Zoller, “Quantum repeaters based on entanglement purification,” Phys. Rev. A 59, 169–181 (1999).
[Crossref]

X. S. Liu, G. L. Long, D. M. Tong, and F. Li, “General scheme for superdense coding between multiparties,” Phys. Rev. A 65, 022304 (2002).
[Crossref]

X. H. Li, F. G. Deng, and H. Y. Zhou, “Efficient quantum key distribution over a collective noise channel,” Phys. Rev. A 78, 022321 (2008).
[Crossref]

M. Hillery, V. Buzek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999).
[Crossref]

G. L. Long and X. S. Liu, “Theoretically efficient high-capacity quantum-key-distribution scheme,” Phys. Rev. A 65, 032302 (2002).
[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]

Z. B. Chen, B. Zhao, Y. A. Chen, J. Schmiedmayer, and J. W. Pan, “Fault-tolerant quantum repeater with atomic ensembles and linear optics,” Phys. Rev. A 76, 022329 (2007).
[Crossref]

B. Zhao, M. Müller, K. Hammerer, and P. Zoller, “Efficient quantum repeater based on deterministic Rydberg gates,” Phys. Rev. A 81, 052329 (2010).
[Crossref]

Y. B. Sheng and F. G. Deng, “Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement,” Phys. Rev. A 81, 032307 (2010).
[Crossref]

Y. B. Sheng and F. G. Deng, “One-step deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044305 (2010).
[Crossref]

X. H. Li, “Deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044304 (2010).
[Crossref]

F. G. Deng, “One-step error correction for multipartite polarization entanglement,” Phys. Rev. A 83, 062316 (2011).
[Crossref]

C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046 (1996).
[Crossref] [PubMed]

S. Bose, V. Vedral, and P. L. Knight, “Purification via entanglement swapping and conserved entanglement,” Phys. Rev. A 60, 194–197 (1999).
[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]

B. C. Ren, F. F. Du, and F. G. Deng, “Hyperentanglement concentration for two-photon four-qubit systems with linear optics,” Phys. Rev. A 88, 012302 (2013).
[Crossref]

Phys. Rev. Lett. (11)

C. H. Bennett, G. Brassard, C. Crépeau, 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] [PubMed]

C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69, 2881–2884 (1992).
[Crossref] [PubMed]

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722–725 (1996).
[Crossref] [PubMed]

D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 77, 2818–2821 (1996).
[Crossref] [PubMed]

C. Simon and J. W. Pan, “Polarization entanglement purification using spatial entanglement,” Phys. Rev. Lett. 89, 257901 (2002).
[Crossref] [PubMed]

H. J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932–5935 (1998).
[Crossref]

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
[Crossref] [PubMed]

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bell’s theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
[Crossref] [PubMed]

L. M. Duan and H. J. Kimble, “Scalable photonic quantum computation through cavity-assisted interactions,” Phys. Rev. Lett. 92, 127902 (2004).
[Crossref] [PubMed]

E. Brion, L. H. Pedersen, M. Saffman, and K. Mølmer, “Error correction in ensemble registers for quantum repeaters and quantum computers,” Phys. Rev. Lett. 100, 110506 (2008).
[Crossref] [PubMed]

Y. Li, L. Aolita, D. E. Chang, and L. C. Kwek, “Robust-fidelity atom-photon entangling gates in the weak-coupling regime,” Phys. Rev. Lett. 109, 160504 (2012).
[Crossref] [PubMed]

Rev. Mod. Phys. (4)

H. Ritsch, P. Domokos, F. Brennecke, and T. Esslinger, “Cold atoms in cavity-generated dynamical optical potentials,” Rev. Mod. Phys. 85, 553–601 (2013).
[Crossref]

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[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]

M. Saffman, T. G. Walker, and K. Mølmer, “Quantum information with Rydberg atoms,” Rev. Mod. Phys. 82, 2313–2363 (2010).
[Crossref]

Rev. Sci. Instrum. (1)

M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Single-photon sources and detectors,” Rev. Sci. Instrum. 82, 071101 (2011).
[Crossref]

Other (1)

D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, 1994).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 (a) Schematic diagram for a single-sided cavity coupled to an atomic ensemble system composed of N cold atoms. (b) Schematic diagram for the level structure of a cold atom.
Fig. 2
Fig. 2 Schematic diagram for a PCD on two ensembles EA1 and EA2. ain is the input port of the photon. HWPi (i = 1, 2) represents a half-wave plate whose optical axis is set to π/4 to perform the bit-flip operation σx = |h〉 〈v| + |v〉 〈h| on the photon. H represents a half-wave plate whose optical axis is set to π/8 and completes the Hadamard transformation. PBS is a polarizing beam splitter, which transmits the |h〉 polarization photon and reflects the |v〉 polarization photon, respectively.
Fig. 3
Fig. 3 Schematic diagram of our optimal ECP for a nonlocal two-atomic-ensemble system in a partially entangled state with known parameters. Alice and Bob are two parties in two nonlocal memory nodes in a quantum communication network. EA and EB are the two nonlocal atomic ensembles which belong to Alice and Bob, respectively. The UBS is an unbalanced beam splitter with the reflection coefficient R = α/β.
Fig. 4
Fig. 4 Schematic diagram of our ECP for a nonlocal two-atomic-ensemble system in a partially entangled state with unknown parameters, achieved by the input-output process of a single photon. Bob completes the parity-check measurement on the ensembles EB1 and EB2 with a PCD, assisted by a single photon.
Fig. 5
Fig. 5 Schematic diagram of our EPP for atomic ensembles with PCDs.
Fig. 6
Fig. 6 The efficiencies ηc, ηc′, and ηp of our optimal ECP, efficient ECP, and EPP for two-atomic-ensemble systems, respectively. Here |α|2 + |β|2 = 1.
Fig. 7
Fig. 7 The fidelities of our EDPs for two-atomic-ensemble systems as the functions of the scaled coupling strength g/κ and the coefficient of the initial state α for our optimal ECP or the initial fidelity f0 for our EPP. Here the scaled detuning δ′/κ = 0.0566. (a) The fidelity of our optimal ECP Fc. (b) The fidelity of our EPP Fp. Here |α|2 + |β|2 = 1.

Equations (30)

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H = j = 1 N [ ( Δ i γ e j 2 ) σ e j e j + i g j ( a σ e j s j a + σ s j e j ) ] + i κ 2 π d δ [ b + ( δ ) a b ( δ ) a + ] + d δ b + ( δ ) b ( δ ) .
| Ψ ( t ) = α ( t ) | S | 1 , 0 + d δ β ( δ , t ) | S | 0 , 1 + ζ | E | 0 , 0 ,
i α ˙ ( t ) = i g ζ ( t ) i κ 2 π d δ β ( δ , t ) ,
i β ˙ ( δ , t ) = i κ 2 π α ( t ) + δ β ( δ , t ) ,
i ζ ˙ j ( t ) = ( Δ i γ 2 ) ζ j ( t ) + i g α ( t ) .
β out ( t ) = β in ( t ) + κ α ( t ) ,
β in ( t ) = 1 2 π e i δ ( t t 0 ) β ( δ , t 0 ) d δ , β out ( t ) = 1 2 π e i δ ( t t 1 ) β ( δ , t 1 ) d δ .
r ( δ ) = ( δ i κ / 2 ) ( Δ + i γ / 2 ) g 2 ( δ + i κ / 2 ) ( Δ + i γ / 2 ) g 2 .
r 0 ( δ ) = δ i κ / 2 δ + i κ / 2 .
R ^ = | h h | ( | G G | + | S S | ) .
| φ p E A 1 E A 2 = | ϕ | φ E A 1 E A 2 HPW 1 PBS 1 σ x A 1 | φ p E A 1 E A 2 R ^ R ^ A 2 R ^ A 1 σ x 1 A 1 | φ p E A 1 E A 2 PBS 1 HPW 2 σ x A 2 R ^ A 2 R ^ A 1 σ x A 1 | φ p E A 1 E A 2 .
| φ p E A 1 E A 2 = | h p ( α 1 | G G α 4 | S S ) A 1 A 2 + | v p ( α 2 | G S α 3 | S G ) A 1 A 2 .
| ϕ E A E B = α | G S A B + β | S G A B ,
| ϕ A B b = α | G S A B | h b β | S G A B | v b .
| ϕ A B b = α ( | G S A B | h b | S G A B | v b ) β 2 α 2 | S G A B | v e b .
| ϕ A B b | ϕ A B b = 1 2 ( | h b | ψ E A E B + | v b | ψ + E A E B ) ,
| ϕ E A E B E C = α | G G G A B C + β | S S S A B C ,
| φ E A 1 E B 1 = α | G S A 1 B 1 + β | S G A 1 B 1 , | φ E A 2 E B 2 = α | G S A 2 B 2 + β | S G A 2 B 2 ,
| Φ E A 1 E B 1 E A 2 E B 2 = 1 2 2 [ ( | G S | S G ) A 1 B 1 ( | G G | S S ) A 2 B 2 + ( | G S + | S G ) A 1 B 1 ( | G S | S G ) A 2 B 2 ] .
ρ E A E B = f 0 | ψ + ψ + | + ( 1 f 0 ) | ϕ + φ + | .
ρ = 1 f 0 2 + ( 1 f 0 ) 2 [ f 0 2 | ψ + ψ + | + ( 1 f 0 ) 2 | ϕ + ϕ + | ] .
R ^ ( δ ) = | h h | ( r 0 | G G | + r | S S | ) .
η c = 1 4 × ( α 2 | r + 1 | 2 + α 4 β 2 | r 1 | 2 + β 2 | r 0 + 1 | 2 + α 2 | r 0 1 | 2 ) .
F c = | α [ r ( 1 + α β ) + 1 α β ] β [ r 0 ( 1 + α β ) + 1 α β ] | 2 | α [ r ( 1 + α β ) + 1 α β ] | 2 + | β [ r 0 ( 1 + α β ) + 1 α β ] | 2 .
η c i = 2 | α | 2 , F c i = 1 .
η c = ( | α | 2 | α | 4 ) ( | r 0 r | 2 ) 2 .
η c i = 2 | α β | 2 = 2 ( | α | 2 | α | 4 ) .
η p = f 0 2 c 00 + f 0 ( 1 f 0 ) c 01 + f 0 ( 1 f 0 ) c 10 + ( 1 f 0 ) 2 c 11 ,
F p = f 0 2 c 00 + f 0 ( 1 f 0 ) c 01 f 0 2 c 00 + f 0 ( 1 f 0 ) c 01 + f 0 ( 1 f 0 ) c 10 + ( 1 f 0 ) 2 c 11 .
η p i = f 0 2 + ( 1 f 0 ) 2 , F p i = f 0 2 f 0 2 + ( 1 f 0 ) 2 .

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