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

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  61. C. Wang, “Efficient entanglement concentration for partially entangled electrons using a quantum-dot and microcavity coupled system,” Phys. Rev. A 86, 012323 (2012).
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  62. 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).
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    [CrossRef]

2013 (5)

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 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]

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]

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]

2012 (10)

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]

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]

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, L. Zhou, and S. M. Zhao, “Efficient two-step entanglement concentration for arbitrary W states,” Phys. Rev. A 85, 042302 (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]

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]

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]

2011 (8)

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. 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]

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]

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]

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]

2010 (5)

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]

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).

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]

2008 (3)

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]

N. Sangouard, C. Simon, T. Coudreau, and N. Gisin, “Purification of single-photon entanglement with linear optics,” Phys. Rev. A 78, 050301 (2008).
[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]

2007 (1)

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]

2005 (3)

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]

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]

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]

2004 (2)

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]

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]

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]

M. G. A. Paris, M. Cola, and R. Bonifacio, “Quantum state engineering assisted by entanglement,” Phys. Rev. A 67, 042104 (2003).
[CrossRef]

2002 (5)

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]

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

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

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

2001 (6)

J. W. Pan, C. Simon, Č. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature 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]

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]

2000 (1)

B. S. Shi, Y. K. Jiang, and G. C. Guo, “Optimal entanglement purification via entanglement swapping,” Phys. Rev. A 62, 054301 (2000).
[CrossRef]

1999 (4)

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

R. Cleve, D. Gottesman, and H. K. Lo, “How to share a quantum secret,” Phys. Rev. Lett. 83, 648–651 (1999).
[CrossRef]

1998 (1)

A. Karlsson and M. Bourennane, “Quantum teleportation using three-particle entanglement,” Phys. Rev. A 58, 4394–4400 (1998).
[CrossRef]

1996 (1)

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]

1995 (1)

A. Peres, “Nonlocal effects in Fock space,” Phys. Rev. Lett. 74, 4571 (1995).
[CrossRef]

1994 (1)

L. Hardy, “Nonlocality of a single photon revisited,” Phys. Rev. Lett. 73, 2279–2283 (1994).
[CrossRef]

1993 (1)

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]

1991 (2)

A. K. Ekert, “Quantum cryptography based on Bells theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
[CrossRef]

S. M. Tan, D. F. Walls, and M. J. Collett, “Nonlocality of a single photon,” Phys. Rev. Lett. 66, 252–255 (1991).
[CrossRef]

Afzelius, M.

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]

Ariano, G. M.

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]

Bennett, C. H.

C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046–2052 (1996).
[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]

Bernstein, H. J.

C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046–2052 (1996).
[CrossRef]

Berthiaume, A.

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

Bonifacio, R.

M. G. A. Paris, M. Cola, and R. Bonifacio, “Quantum state engineering assisted by entanglement,” Phys. Rev. A 67, 042104 (2003).
[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]

Bourennane, M.

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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).

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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).
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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).
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N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
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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).
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L. Zhou, “Efficient entanglement concentration for electron-spin W state with the charge detection,” Quant. Info. Proc. 12, 2087–2101 (2013).
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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.

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Figures (7)

Fig. 1.
Fig. 1.

Schematic drawing of the ELACP for single-photon entangled state. Two different VBSs are used here.

Fig. 2.
Fig. 2.

Transmission coefficient t2 is altered with t1 to satisfy the concentration condition as shown in Eq. (15). Curve A, α2=0.1; curve B, α2=0.2; curve C, α2=0.4; curve D, α2=0.5; curve E, α2=0.8; curve F, α2=0.9.

Fig. 3.
Fig. 3.

Transmission coefficient t2 (curve A) and the amplification factor g (curve B) are altered with t1, with α2=0.4. Here we choose η=0.6.

Fig. 4.
Fig. 4.

Transmission coefficient t2 (curve A) and the amplification factor g (curve B) are altered with t1, with α2=0.8. Here we choose η=0.6.

Fig. 5.
Fig. 5.

Amplification factor g is altered with the transmission coefficient t1 with α2=0.4. Curve A, η=0.2; curve B, η=0.4; curve C, η=0.6; curve D, η=0.8. All four curves pass through the same point K with g=1.

Fig. 6.
Fig. 6.

Amplification factor g is altered with the transmission coefficient t1 with α2=0.8. Curve A, η=0.2; curve B, η=0.4; curve C, η=0.6; curve D, η=0.8. All four curves pass through the same point K with g=1. The numerical simulation of the limitation g shows that it is equal to 1/η, which is consistent with the theoretical derivation.

Fig. 7.
Fig. 7.

Schematic drawing of the possible experimental realization of ELACP for single-photon entangled state.

Equations (17)

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ρAB=η|ΦABΦ|+(1η)|vacvac|.
ρAB=η|Ψa1b1Ψ|+(1η)|vacvac|.
|1At1|1d1|0d2+1t1|0d1|1d2,
|1Bt2|1c1|0c2+1t2|0c1|1c2.
|Ψa1b1|1A|1B=(α|1a1|0b1+β|0a1|1b1)|1A|1B(α|1a1|0b1+β|0a1|1b1)(t1|1d1|0d2+1t1|0d1|1d2)(t2|1c1|0c2+1t2|0c1|1c2)=αt1t2|1a1|0b1|1d1|0d2|1c1|0c2+αt1(1t2)|1a1|0b1|1d1|0d2|0c1|1c2+αt2(1t1)|1a1|0b1|0d1|1d2|1c1|0c2+α(1t1)(1t2)|1a1|0b1|0d1|1d2|0c1|1c2+βt1t2|0a1|1b1|1d1|0d2|1c1|0c2+βt1(1t2)|0a1|1b1|1d1|0d2|0c1|1c2+βt2(1t1)|0a1|1b1|0d1|1d2|1c1|0c2+β(1t1)(1t2)|0a1|1b1|0d1|1d2|0c1|1c2.
|Ψ1=αt2(1t1)|1a1|0b1|0d1|1d2|1c1|0c2+βt1(1t2)|0a1|1b1|1d1|0d2|0c1|1c2.
|vac|1A|1B=|vac(t1|1d1|0d2+1t1|0d1|1d2)(t2|1c1|0c2+1t2|0c1|1c2)=|vac(t1t2|1d1|0d2|1c1|0c2+(1t1)t2|0d1|1d2|1c1|0c2+t1(1t2)|1d1|0d2|0c1|1c2+(1t1)(1t2)|0d1|1d2|0c1|1c2).
|Ψ2=t1t2|1d1|0d2|1c1|0c2,
P=η(α2t2+β2t1)+t1t22ηt1t2.
|1a112(|1f1+|1f2),|1d112(|1f1|1f2),|1b112(|1e1+|1e2),|1c112(|1e1|1e2).
|Ψ2=αt2(1t1)|1a1|0b1+βt1(1t2)|0a1|1b1.
|Ψ2=αt2(1t1)|1a1|0b1βt1(1t2)|0a1|1b1.
ρAB=η|Ψ2Ψ2|+(1η)|vacvac|.
η=η(α2t2+β2t1t1t2)η(α2t2+β2t1)+t1t22ηt1t2.
α2β2=t1(1t2)t2(1t1).
g=α2t2+β2t1t1t2η(α2t2+β2t1)+t1t22ηt1t2.
limt1,t20g=α2t2+β2t1η(α2t2+β2t1)=1η.

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