Abstract

We present an entanglement concentration protocol (ECP) for the less-entangled W-state with quantum-dot and microcavity coupled systems. The present protocol uses quantum nondemolition measurement on the spin parity to construct the hybrid parity check gate. Different from other ECPs, the less-entangled W-state with quantum-dot and microcavity coupled systems can be concentrated with the help of some single photons. The most significant advantage is that during the whole ECP, we do not destroy the W-state and only consume some local single photons. The whole protocol can be repeated to obtain a higher success probability. It may be useful in current quantum information processing.

© 2013 Optical Society of America

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    [CrossRef]

2013 (2)

L. Zhou, Y. B. Sheng, W. W. Cheng, G. L. Yan, and S. M. Zhao, “Efficient entanglement concentration for arbitrary less-entangled NOON states,” Quantum Inf. Process. 12, 1307–1320 (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]

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]

B. C. Ren, H. R. Wei, M. Hua, T. Li, and F. G. Deng, “Complete hyperentangled-Bell-state analysis for photon systems assisted by quantum-dot spins in optical microcavities,” Opt. Express 20, 24664–24667 (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]

T. J. Wang, S. Y. Song, and G. L. Long, “Quantum repeater based on spatial entanglement of photons and quantum-dot spins in optical microcavities,” Phys. Rev. A 85, 062311 (2012).
[CrossRef]

F. G. Deng, “Optimal nonlocal multipartite entanglement concentration based on projection measurements,” Phys. Rev. A 85, 022311 (2012).
[CrossRef]

H. F. Wang, L. L. Sun, S. Zhang, and K. H. Yeon, “Scheme for entanglement concentration of unkonwn partially entangled three-atom W-states in cavity QED,” Quantum Inf. Process. 11, 431–441 (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]

T. J. Wang, Y. Lu, and G. L. Long, “Generation and complete analysis of the hyperentangled Bell state for photons assisted by quantum-dot spins in optical microcavities,” Phys. Rev. A 86, 042337 (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]

2011 (4)

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. Y. Hu and J. G. Rarity, “Loss-resistant state teleportation and entanglement swapping using a quantum-dot spin in an optical microcavity,” Phys. Rev. B 83, 115303 (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]

C. Wang, Y. Zhang, and R. Zhang, “Entanglement purification based on hybrid entangled state using quantum-dot and microcavity coupled system,” Opt. Express 19, 25685–25689 (2011).
[CrossRef]

2010 (6)

H. F. Wang, S. Zhang, and K. H. Yeon, “Linear-optics-based entanglement concentration of unknown partially entangled threephoton W-states,” J. Opt. Soc. Am. B 27, 2159–2164 (2010).
[CrossRef]

C. Bonato, F. Haupt, S. S. R. Oemrawsingh, J. Gudat, D. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett. 104, 160503 (2010).
[CrossRef]

D. Press, L. De Greve, P. L. McMahon, T. D. Ladd, B. Friess, C. Schneider, M. Kamp, S. Höfling, A. Forchel, and Y. Yamamoto, “Ultrafast optical spin echo in a single quantum dot,” Nat. Photonics 4, 367–370 (2010).
[CrossRef]

H. F. Wang, S. Zhang, and K. H. Yeon, “Linear optical scheme for entanglement concentration of two partially entangled threephoton W-states,” Eur. Phys. J. D 56, 271–275 (2010).
[CrossRef]

A. Yildiz, “Optimal distillation of three-qubit W-states,” Phys. Rev. A 82, 012317 (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).

2009 (5)

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Efficient polarization entanglement concentration for electrons with charge detection,” Phys. Lett. A 373, 1823–1825 (2009).
[CrossRef]

M. T. Rakher, N. G. Stoltz, L. A. Coldren, P. M. Petroff, and D. Bouwmeester, “Externally mode-matched cavity quantum electrodynamics with charge-tunable quantum dots,” Phys. Rev. Lett. 102, 097403 (2009).
[CrossRef]

A. Greilich, S. E. Economou, S. Spatzek, D. R. yakovlev, D. Reuter, A. D. Wieck, T. L. Reinecke, and M. Bayer, “Ultrafast optical rotations of electron spins in quantum dots,” Nat. Phys. 5, 262–266 (2009).
[CrossRef]

D. Brunner, B. D. Gerardot, P. A. Dalgarno, G. Wüst, K. Karrai, N. G. Stoltz, P. M. Petroff, and R. J. Warburton, “A coherent single-hole spin in a semiconductor,” Science 325, 70–72(2009).
[CrossRef]

C. Y. Hu, W. J. Munro, J. L. ÓBrien, and J. G. Rarity, “Proposed entanglement beam splitter using a quantum-dot spin in a double-sided optical microcavity,” Phys. Rev. B 80, 205326 (2009).
[CrossRef]

2008 (5)

C. Y. Hu, A. Young, J. L. ÓBrien, W. J. Munro, and J. G. Rarity, “Giant optical Faraday rotation induced by a single-electron spin in a quantum dot: applications to entangling remote spins via a single photon,” Phys. Rev. B 78, 085307 (2008).
[CrossRef]

B. D. Gerardot, D. Brunner, P. A. Dalgarno, P. Öhberg, S. Seidl, M. Kronere, K. Karrai, N. G. Stoltz, P. M. Petroff, and R. J. Warburton, “Optical pumping of a single hole spin in a quantum dot,” Nature (London) 451, 441–444 (2008).
[CrossRef]

C. Y. Hu, W. J. Munro, and J. G. Rarity, “Deterministic photon entangler using a charged quantum dot inside a microcavity,” Phys. Rev. B 78, 125318 (2008).
[CrossRef]

D. Press, T. D. Ladd, B. Zhang, and Y. Yamamoto, “Complete quantum control of a single quantum dot spin using ultrafast optical pulses,” Nature 456, 218–221 (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]

2007 (1)

L. H. Zhang, M. Yang, and Z. L. Cao, “Entanglement concentration for unknown W class states,” Phys. A 374, 611–616 (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]

2005 (4)

M. Yang, Y. Zhao, W. Song, and Z. L. Cao, “Entanglement concentration for unknown atomic entangled states via entanglement swapping,” Phys. Rev. A 71, 044302 (2005).
[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]

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, 042305 (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 (3)

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]

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]

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432, 197–200 (2004).
[CrossRef]

2003 (3)

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]

X.-B. Wang and H. Fan, “Entanglement concentration by ordinary linear optical devices without postselection,” Phys. Rev. A 68, 060302 (2003).
[CrossRef]

Z. L. Cao and M. Yang, “Entanglement distillation for three-particle W class states,” J. Phys. B 36, 4245–4253 (2003).
[CrossRef]

2002 (3)

N. Paunković, Y. Omar, S. Bose, and V. Vedral, “Entanglement concentration using quantum statistics,” Phys. Rev. Lett. 88, 187903 (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]

2001 (3)

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]

L. M. Duan, M. D. Lukin, J. T. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature (London) 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]

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

1998 (2)

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. 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]

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]

1992 (2)

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1991 (1)

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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).
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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).
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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).
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M. Hillery, V. Bužek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999).
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C. Bonato, F. Haupt, S. S. R. Oemrawsingh, J. Gudat, D. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett. 104, 160503 (2010).
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A. Karlsson and M. Bourennane, “Quantum teleportation using three-particle entanglement,” Phys. Rev. A 58, 4394–4400 (1998).
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Bouwmeester, D.

C. Bonato, F. Haupt, S. S. R. Oemrawsingh, J. Gudat, D. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett. 104, 160503 (2010).
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M. T. Rakher, N. G. Stoltz, L. A. Coldren, P. M. Petroff, and D. Bouwmeester, “Externally mode-matched cavity quantum electrodynamics with charge-tunable quantum dots,” Phys. Rev. Lett. 102, 097403 (2009).
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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).
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Brassard, G.

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).
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Brassard, G. B.

C. H. Bennett, G. B. Brassard, and N. D. Mermin, “Quantum cryptography without Bells theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
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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).
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D. Brunner, B. D. Gerardot, P. A. Dalgarno, G. Wüst, K. Karrai, N. G. Stoltz, P. M. Petroff, and R. J. Warburton, “A coherent single-hole spin in a semiconductor,” Science 325, 70–72(2009).
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B. D. Gerardot, D. Brunner, P. A. Dalgarno, P. Öhberg, S. Seidl, M. Kronere, K. Karrai, N. G. Stoltz, P. M. Petroff, and R. J. Warburton, “Optical pumping of a single hole spin in a quantum dot,” Nature (London) 451, 441–444 (2008).
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Bužek, V.

M. Hillery, V. Bužek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999).
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L. H. Zhang, M. Yang, and Z. L. Cao, “Entanglement concentration for unknown W class states,” Phys. A 374, 611–616 (2007).
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M. Yang, Y. Zhao, W. Song, and Z. L. Cao, “Entanglement concentration for unknown atomic entangled states via entanglement swapping,” Phys. Rev. A 71, 044302 (2005).
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Z. L. Cao and M. Yang, “Entanglement distillation for three-particle W class states,” J. Phys. B 36, 4245–4253 (2003).
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L. Zhou, Y. B. Sheng, W. W. Cheng, G. L. Yan, and S. M. Zhao, “Efficient entanglement concentration for arbitrary less-entangled NOON states,” Quantum Inf. Process. 12, 1307–1320 (2013).
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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).
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M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).

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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).
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Cirac, J. T.

L. M. Duan, M. D. Lukin, J. T. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature (London) 414, 413–418 (2001).
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R. Cleve, D. Gottesman, and H. K. Lo, “How to share a quantum secret,” Phys. Rev. Lett. 83, 648–651 (1999).
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M. T. Rakher, N. G. Stoltz, L. A. Coldren, P. M. Petroff, and D. Bouwmeester, “Externally mode-matched cavity quantum electrodynamics with charge-tunable quantum dots,” Phys. Rev. Lett. 102, 097403 (2009).
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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).
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D. Brunner, B. D. Gerardot, P. A. Dalgarno, G. Wüst, K. Karrai, N. G. Stoltz, P. M. Petroff, and R. J. Warburton, “A coherent single-hole spin in a semiconductor,” Science 325, 70–72(2009).
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B. D. Gerardot, D. Brunner, P. A. Dalgarno, P. Öhberg, S. Seidl, M. Kronere, K. Karrai, N. G. Stoltz, P. M. Petroff, and R. J. Warburton, “Optical pumping of a single hole spin in a quantum dot,” Nature (London) 451, 441–444 (2008).
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D. Press, L. De Greve, P. L. McMahon, T. D. Ladd, B. Friess, C. Schneider, M. Kamp, S. Höfling, A. Forchel, and Y. Yamamoto, “Ultrafast optical spin echo in a single quantum dot,” Nat. Photonics 4, 367–370 (2010).
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B. C. Ren, H. R. Wei, M. Hua, T. Li, and F. G. Deng, “Complete hyperentangled-Bell-state analysis for photon systems assisted by quantum-dot spins in optical microcavities,” Opt. Express 20, 24664–24667 (2012).
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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).
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F. G. Deng, “Optimal nonlocal multipartite entanglement concentration based on projection measurements,” Phys. Rev. A 85, 022311 (2012).
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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).

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Efficient polarization entanglement concentration for electrons with charge detection,” Phys. Lett. A 373, 1823–1825 (2009).
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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).
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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).
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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, 042305 (2005).
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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).
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L. Xiao, G.-L. Long, F.-G. Deng, and J.-W. Pan, “Efficient multiparty quantum-secret-sharing schemes,” Phys. Rev. A 69, 052307 (2004).
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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).
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C. Bonato, F. Haupt, S. S. R. Oemrawsingh, J. Gudat, D. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett. 104, 160503 (2010).
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Du, F. F.

Duan, L. M.

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

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).
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Economou, S. E.

A. Greilich, S. E. Economou, S. Spatzek, D. R. yakovlev, D. Reuter, A. D. Wieck, T. L. Reinecke, and M. Bayer, “Ultrafast optical rotations of electron spins in quantum dots,” Nat. Phys. 5, 262–266 (2009).
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Ekert, A. K.

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

X.-B. Wang and H. Fan, “Entanglement concentration by ordinary linear optical devices without postselection,” Phys. Rev. A 68, 060302 (2003).
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Forchel, A.

D. Press, L. De Greve, P. L. McMahon, T. D. Ladd, B. Friess, C. Schneider, M. Kamp, S. Höfling, A. Forchel, and Y. Yamamoto, “Ultrafast optical spin echo in a single quantum dot,” Nat. Photonics 4, 367–370 (2010).
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J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432, 197–200 (2004).
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Friess, B.

D. Press, L. De Greve, P. L. McMahon, T. D. Ladd, B. Friess, C. Schneider, M. Kamp, S. Höfling, A. Forchel, and Y. Yamamoto, “Ultrafast optical spin echo in a single quantum dot,” Nat. Photonics 4, 367–370 (2010).
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Gerardot, B. D.

D. Brunner, B. D. Gerardot, P. A. Dalgarno, G. Wüst, K. Karrai, N. G. Stoltz, P. M. Petroff, and R. J. Warburton, “A coherent single-hole spin in a semiconductor,” Science 325, 70–72(2009).
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B. D. Gerardot, D. Brunner, P. A. Dalgarno, P. Öhberg, S. Seidl, M. Kronere, K. Karrai, N. G. Stoltz, P. M. Petroff, and R. J. Warburton, “Optical pumping of a single hole spin in a quantum dot,” Nature (London) 451, 441–444 (2008).
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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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Gong, L. Y.

Gottesman, D.

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

A. Greilich, S. E. Economou, S. Spatzek, D. R. yakovlev, D. Reuter, A. D. Wieck, T. L. Reinecke, and M. Bayer, “Ultrafast optical rotations of electron spins in quantum dots,” Nat. Phys. 5, 262–266 (2009).
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Gu, B.

Gudat, J.

C. Bonato, F. Haupt, S. S. R. Oemrawsingh, J. Gudat, D. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett. 104, 160503 (2010).
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B. S. Shi, Y. K. Jiang, and G. C. Guo, “Optimal entanglement purification via entanglement swapping,” Phys. Rev. A 62, 054301 (2000).
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C. Bonato, F. Haupt, S. S. R. Oemrawsingh, J. Gudat, D. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett. 104, 160503 (2010).
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Hillery, M.

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

D. Press, L. De Greve, P. L. McMahon, T. D. Ladd, B. Friess, C. Schneider, M. Kamp, S. Höfling, A. Forchel, and Y. Yamamoto, “Ultrafast optical spin echo in a single quantum dot,” Nat. Photonics 4, 367–370 (2010).
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Hofmann, C.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432, 197–200 (2004).
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Hu, C. Y.

C. Y. Hu and J. G. Rarity, “Loss-resistant state teleportation and entanglement swapping using a quantum-dot spin in an optical microcavity,” Phys. Rev. B 83, 115303 (2011).
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C. Y. Hu, W. J. Munro, J. L. ÓBrien, and J. G. Rarity, “Proposed entanglement beam splitter using a quantum-dot spin in a double-sided optical microcavity,” Phys. Rev. B 80, 205326 (2009).
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C. Y. Hu, W. J. Munro, and J. G. Rarity, “Deterministic photon entangler using a charged quantum dot inside a microcavity,” Phys. Rev. B 78, 125318 (2008).
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C. Y. Hu, A. Young, J. L. ÓBrien, W. J. Munro, and J. G. Rarity, “Giant optical Faraday rotation induced by a single-electron spin in a quantum dot: applications to entangling remote spins via a single photon,” Phys. Rev. B 78, 085307 (2008).
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Hua, M.

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).
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A. Karlsson, M. Koashi, and N. Imoto, “Quantum entanglement for secret sharing and secret splitting,” Phys. Rev. A 59, 162–168 (1999).
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Jiang, Y. K.

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

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).
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Jozsa, R.

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).
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Kamp, M.

D. Press, L. De Greve, P. L. McMahon, T. D. Ladd, B. Friess, C. Schneider, M. Kamp, S. Höfling, A. Forchel, and Y. Yamamoto, “Ultrafast optical spin echo in a single quantum dot,” Nat. Photonics 4, 367–370 (2010).
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Karlsson, A.

A. Karlsson, M. Koashi, and N. Imoto, “Quantum entanglement for secret sharing and secret splitting,” Phys. Rev. A 59, 162–168 (1999).
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A. Karlsson and M. Bourennane, “Quantum teleportation using three-particle entanglement,” Phys. Rev. A 58, 4394–4400 (1998).
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Karrai, K.

D. Brunner, B. D. Gerardot, P. A. Dalgarno, G. Wüst, K. Karrai, N. G. Stoltz, P. M. Petroff, and R. J. Warburton, “A coherent single-hole spin in a semiconductor,” Science 325, 70–72(2009).
[CrossRef]

B. D. Gerardot, D. Brunner, P. A. Dalgarno, P. Öhberg, S. Seidl, M. Kronere, K. Karrai, N. G. Stoltz, P. M. Petroff, and R. J. Warburton, “Optical pumping of a single hole spin in a quantum dot,” Nature (London) 451, 441–444 (2008).
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Keldysh, L. V.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432, 197–200 (2004).
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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).
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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).
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A. Karlsson, M. Koashi, and N. Imoto, “Quantum entanglement for secret sharing and secret splitting,” Phys. Rev. A 59, 162–168 (1999).
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Kronere, M.

B. D. Gerardot, D. Brunner, P. A. Dalgarno, P. Öhberg, S. Seidl, M. Kronere, K. Karrai, N. G. Stoltz, P. M. Petroff, and R. J. Warburton, “Optical pumping of a single hole spin in a quantum dot,” Nature (London) 451, 441–444 (2008).
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Kuhn, S.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432, 197–200 (2004).
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Kulakovskii, V. D.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432, 197–200 (2004).
[CrossRef]

Ladd, T. D.

D. Press, L. De Greve, P. L. McMahon, T. D. Ladd, B. Friess, C. Schneider, M. Kamp, S. Höfling, A. Forchel, and Y. Yamamoto, “Ultrafast optical spin echo in a single quantum dot,” Nat. Photonics 4, 367–370 (2010).
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D. Press, T. D. Ladd, B. Zhang, and Y. Yamamoto, “Complete quantum control of a single quantum dot spin using ultrafast optical pulses,” Nature 456, 218–221 (2008).
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Lam, P. K.

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).
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Lance, A. M.

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]

Li, C. Y.

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]

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).
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Li, T.

Li, X. H.

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).
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Li, Y. S.

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).
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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, 042305 (2005).
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Liu, X. S.

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, 042305 (2005).
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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]

Lo, H. K.

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

Löffler, A.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432, 197–200 (2004).
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Long, G. L.

T. J. Wang, Y. Lu, and G. L. Long, “Generation and complete analysis of the hyperentangled Bell state for photons assisted by quantum-dot spins in optical microcavities,” Phys. Rev. A 86, 042337 (2012).
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T. J. Wang, S. Y. Song, and G. L. Long, “Quantum repeater based on spatial entanglement of photons and quantum-dot spins in optical microcavities,” Phys. Rev. A 85, 062311 (2012).
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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, 042305 (2005).
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Long, G.-L.

L. Xiao, G.-L. Long, F.-G. Deng, and J.-W. Pan, “Efficient multiparty quantum-secret-sharing schemes,” Phys. Rev. A 69, 052307 (2004).
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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).
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G.-L. Long and X.-S. Liu, “Theoretically efficient high-capacity quantum-key-distribution scheme,” Phys. Rev. A 65, 032302 (2002).
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Figures (6)

Fig. 1.
Fig. 1.

Schematic drawing of the hybrid parity check gate for our ECP. The quantum-dot spin is coupled in the optical microcavity. The input and output represent the input and output ports of a photon. This setup can split a photon-spin product state into two constituent hybrid photon-spin entangled states. One is in the output 1 mode, and the other is in the output 2 mode.

Fig. 2.
Fig. 2.

Schematic drawing of our ECP. The quantum-dot spin is coupled in an optical microcavity. Input represents the input port of a photon. After the photon passes through the cavity, it will finally be detected in one of the single-photon detectors in each output mode.

Fig. 3.
Fig. 3.

Success probability P for obtaining a maximally entangled W-state after performing this ECP is altered with the initial coefficient α1(0,2/3). We choose α2=1/3. Curve A is the ideal case with no leakage. Curve B is the success probability with κs=0.1κ, g=0.5κ, and γ=0.1κ.

Fig. 4.
Fig. 4.

Success probability P1 for Alice performing this ECP one time as shown in Eq. (34). We choose α2=1/3 and α1(0,2/3). Curve A is the ideal case with no leakage, and Curve B represents the success probability with κs=0.5κ, g=0.5κ, and γ=0.1κ.

Fig. 5.
Fig. 5.

Success probability P2 for Charlie performing this ECP as shown in Eq. (35). We choose α2=1/3 and α1(0,2/3). Curve A is the ideal case with no leakage, and Curve B represents the success probability with κs=0.5κ, g=0.5κ, and γ=0.1κ.

Fig. 6.
Fig. 6.

Success probability P for obtaining a maximally entangled W-state after performing this ECP is altered with the initial coefficient α1(0,2/3). We chose α2=1/3. Curve A is the ideal case with no leakage. Curve B is the success probability with κs=0.5κ, g=0.5κ, and γ=0.1κ.

Equations (38)

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t^=|RR|||+|LL|||,r^=|RR|||+|LL|||.
|R,|L,,|R,|R,,|R,|R,,|R,|L,,|L,|L,,|L,|R,,|L,|R,,|L,|L,.
|Φ123=α1|1|2|3+α2|1|2|3+α3|1|2|3.
|ΦP1=α1α12+α22|R1+α2α12+α22|L1.
|Ψ=|Φ123|ΦP1=(α1|1|2|3+α2|1|2|3+α3|1|2|3)(α1α12+α22|R1+α2α12+α22|L1)=α12α12+α22|R1|1|2|3+α1α2α12+α22|L1|1|2|3+α1α2α12+α22|R1|1|2|3+α22α12+α22|L1|1|2|3+α1α3α12+α22|R1|1|2|3+α2α3α12+α22|L1|1|2|3α12α12+α22|L1|1|2|3α1α2α12+α22|L1|1|2|3α1α2α12+α22|R1|1|2|3+α22α12+α22|R1|1|2|3α1α3α12+α22|R1|1|2|3+α2α3α12+α22|R1|1|2|3.
|Ψ=α1α2α12+α22|L1|1|2|3+α1α2α12+α22|R1|1|2|3+α1α3α12+α22|R1|1|2|3
|R12(|H+|V),|L12(|H|V),
|Φ1123=α1α2α12+α22|1|2|3+α1α2α12+α22|1|2|3+α1α3α12+α22|1|2|3,
|Φ1123=α2α32+2α22|1|2|3+α2α32+2α22|1|2|3+α3α32+2α22|1|2|3.
|Φ2123=α2α32+2α22|1|2|3+α2α32+2α22|1|2|3+α3α32+2α22|1|2|3.
|Ψ=α12α12+α22|L1|1|2|3+α22α12+α22|R,1|1|2|3+α2α3α12+α22|R1|1|2|3.
|Φ3123=α12α14+α24+α22α32|1|2|3+α22α14+α24+α22α32|1|2|3+α2α3α14+α24+α22α32|1|2|3.
|Φ4123=α12α14+α24+α22α32|1|2|3+α22α14+α24+α22α32|1|2|3+α2α3α14+α24+α22α32|1|2|3.
|ΦP1=α1α12+α22|R1+α2α12+α22|L1.
P12=|α1|4(|α2|2|α3|2+2|α2|4)(|α1|4+|α2|4)(|α1|2+|α2|2).
P1K=|α1|2K(|α2|2K2|α3|2+2|α2|2K)(|α1|2+|α2|2)(|α1|4+|α2|4)(|α1|2K+|α2|2K).
P1=P11+P12++P1K=K=1P1K.
|ΦP3=α2α32+α22|R3+α3α32+α22|L3.
|Ψ1=|Φ1123|ΦP2=(α2α32+2α22|1|2|3+α2α32+2α22|1|2|3+α3α32+2α22|1|2|3)(α2α32+α22|R3+α3α32+α22|L3)=α2α3α32+2α22α32+α22|L3|1|2|3+α22α32+2α22α32+α22|R3|1|2|3+α2α3α32+2α22α32+α22|L3|1|2|3+α22α32+2α22α32+α22|R3|1|2|3+α2α3α32+2α22α32+α22|R3|1|2|3+α32α32+2α22α32+α22|L3|1|2|3α2α3α32+2α22α32+α22|R3|1|2|3α22α32+2α22α32+α22|R3|1|2|3+α2α3α32+2α22α32+α22|R3|1|2|3α22α32+2α22α32+α22|R3|1|2|3+α2α3α32+2α22α32+α22|L3|1|2|3α32α32+2α22α32+α22|L3|1|2|3.
|Ψ1=α2α3α32+2α22α32+α22|R3|1|2|3+α2α3α32+2α22α32+α22|R3|1|2|3+α2α3α32+2α22α32+α22|L3|1|2|3,
|Ψ1=13(|R3|1|2|3+|R3|1|2|3+|L3|1|2|3).
|Φ5123=13(|1|2|3+|1|2|3+|1|2|3).
|Φ6123=13(|1|2|3+|1|2|3|1|2|3),
|Φ7123=α22α32+2α22α32+α22|1|2|3+α22α32+2α22α32+α22|1|2|3+α32α32+2α22α32+α22|1|2|3.
|Φ7123=α222α24+α34|1|2|3+α222α24+α34|1|2|3+α322α24+α34|1|2|3.
|Φ8123=α222α24+α34|1|2|3+α222α24+α34|1|2|3α322α24+α34|1|2|3,
P21=3|α2|2|α3|2(|α3|2+|α2|2)(|α3|2+2|α2|2),P22=3|α2|4|α3|4(|α3|2+|α2|2)(|α3|4+|α2|4)(|α3|2+2|α2|2)P2K=3|α2|2K|α3|2K(|α3|2+|α2|2)(|α3|4+|α2|4)(|α3|2K+|α2|2K)×1(|α3|2+2|α2|2).
P2=P21+P22++=K=1P2K.
Pt=K=1P1KK=1P2K.
Pt1=P11P21=3|α1|2|α2|2|α3|2(|α1|2+|α2|2)(|α3|2+|α2|2).
r(w)=1+t(ω),t(ω)=κ[i(ωXω)+γ2][i(ωXω)+γ2][i(ωcω)+κ+κs2]+g2,
r0(ω)=i(ω0ω)+κs2i(ω0ω)+κs2+κ,t0(ω)=κi(ω0ω)+κs2+κ.
t^(ω)=t0(ω)(|RR|||+|LL|||)+t(ω)(|RR|||+|LL|||),r^(ω)=r0(ω)(|RR|||+|LL|||)+r(ω)(|RR|||+|LL|||).
P1=|α1|2(|α3|2+2|α2|2)|α1|2+|α2|2|t0(ω)||t0(ω)|2+|t(ω)|2,
P2=3|α2|2|α3|2(|α3|2+|α2|2)(|α3|2+2|α2|2)|r(ω)||r0(ω)|2+|r(ω)|2,
P=P1P2=3|α1|2|α2|2|α3|2(|α1|2+|α2|2)(|α3|2+|α2|2)|t0(ω)|r0(ω)|(|t0(ω)|2+|t(ω)|2)(|r0(ω)|2+|r(ω)|2).
P2=23|α1|2(1|α1|2)(43|α1|2),
P2=23|α1|2(1|α1|2)(43|α1|2)|r(ω)||r0(ω)|2+|r(ω)|2.

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