Abstract

Entangled state analysis is one of the basic techniques in quantum information processing. However, it is impossible to fully distinguish the three-photon Greenberger–Horne–Zeilinger (GHZ) states with only linear optical elements. Here, we propose a deterministic scheme to complete three-photon spatial-polarization hyperentangled GHZ-state analysis (HGSA) by using the giant optical Faraday rotation induced by an excess electron spin in a quantum dot inside a one-sided optical microcavity as a result of cavity quantum electrodynamics. It is divided into two steps. The first step is used to distinguish the eight three-photon GHZ states in the spatial-mode degree of freedom (DOF) without destroying the polarization states. The second step is used to distinguish the eight GHZ states in the polarization DOF. This scheme can be generalized to N-photon spatial-polarization HGSA and has useful applications in quantum communication protocols.

© 2013 Optical Society of America

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2013 (5)

S. Y. Song, Y. Cao, Y. B. Sheng, and G. L. Long, “Complete Greenberger–Horne–Zeilinger state analyzer using hyperentanglement,” Quant. Info. Proc. 12, 381–393 (2013).
[CrossRef]

Y. B. Sheng and L. Zhou, “Quantum entanglement concentration based on nonlinear optics for quantum communications,” Entropy 15, 1776–1820 (2013).
[CrossRef]

H. R. Wei and F. G. Deng, “Universal quantum gates for hybrid systems assisted by quantum dots inside double-sided optical microcavities,” Phys. Rev. A 87, 022305 (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]

Y. B. Sheng, L. Zhou, L. Wang, and S. M. Zhao, “Efficient entanglement concentration for quantum dot and optical microcavities systems,” Quant. Info. Proc. 12, 1885–1895 (2013).
[CrossRef]

2012 (7)

Y. Xia, Q. Q. Chen, J. Song, and H. S. Song, “Efficient hyperentangled Greenberger–Horne–Zeilinger states analysis with cross-Kerr nonlinearity,” J. Opt. Soc. Am. B 29, 1029–1037 (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]

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. 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, 24664–24677 (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]

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]

2011 (5)

C. Wang, Y. Zhang, and R. Zhang, “Entanglement purification based on hybrid entangled state using quantum-dot spins in optical microcavities,” Opt. Express 19, 25685 (2011).
[CrossRef]

C. Wang, Y. Zhang, and G. S. Jin, “Entanglement purification and concentration of the electron-spin entangled states using quantum-dot spins in optical microcavities,” Phys. Rev. A 84, 032307 (2011).
[CrossRef]

F. G. Deng, “Efficient multipartite entanglement purification with the entanglement link from a subspace,” Phys. Rev. A 84, 052312 (2011).
[CrossRef]

N. Pisenti, C. P. E. Gaebler, and T. W. Lynn, “Distinguishability of hyperentangled Bell states by linear evolution and local projective measurement,” Phys. Rev. A 84, 022340 (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]

Y. B. Sheng, F. G. Deng, and G. L. Long, “Complete hyperentangled-Bell-state analysis for quantum communication,” Phys. Rev. A 82, 032318 (2010).
[CrossRef]

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

J. Gea-Banacloche, “Impossibility of large phase shifts via the giant Kerr effect with single-photon wave packets,” Phys. Rev. A 81, 043823 (2010).
[CrossRef]

2009 (4)

X. M. Lin, Z. H. Chen, G. W. Lin, X. D. Chen, and B. B. Ni, “Optical Bell state and Greenberger–Horne–Zeilinger-state analyzers through the cavity input-output process,” Opt. Commun. 282, 3371–3374 (2009).
[CrossRef]

C. Y. Hu, W. J. Munro, J. L. O’Brien, 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]

D. Hanneke, J. P. Home, J. D. Jost, J. M. Amini, D. Leibfried, and J. D. Wineland, “Realization of a programmable two-qubit quantum processor,” Nat. Phys. 6, 13–16 (2009).
[CrossRef]

C. Wang, L. Xiao, W. Y. Wang, G. Y. Zhang, and G. L. Long, “Quantum key distribution using polarization and frequency hyperentangled photons,” J. Opt. Soc. Am. B 26, 2072–2076 (2009).
[CrossRef]

2008 (7)

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (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]

J. J. L. Morton, A. M. Tyryshkin, R. M. Brown, S. Shankar, B. W. Lovett, A. Ardavan, T. Schenkel, E. E. Haller, J. W. Ager, and A. S. Lyon, “Solid-state quantum memory using the P31 nuclear spin,” Nature 455, 1085–1088 (2008).
[CrossRef]

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

C. Y. Hu, A. Young, J. L. OBrien, 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]

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]

2007 (6)

K. C. Nowack, F. H. L. Koppens, Y. V. Nazarov, and L. M. K. Vandersypen, “Coherent control of a single electron spin with electric fields,” Science 318, 1430–1433 (2007).
[CrossRef]

M. H. Mikkelsen, J. Berezovsky, L. A. Coldren, N. G. Stoltz, and D. D. Awschalom, “Optically detected coherent spin dynamics of a single electron in a quantum dot,” Nat. Phys. 3, 770–773 (2007).
[CrossRef]

X. Xu, B. Sun, P. R. Berman, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, “Coherent optical spectroscopy of a strongly driven quantum dot,” Science 317, 929–932 (2007).
[CrossRef]

S. Reitzenstein, C. Hofmann, A. Gorbunov, M. Strauß, S. H. Kwon, C. Schneider, A. Löffler, S. Höfling, M. Kamp, and A. Forchel, “AlAs/GaAs micropillar cavities with quality factors exceeding 150.000,” Appl. Phys. Lett. 90, 251109 (2007).
[CrossRef]

M. Barbieri, G. Vallone, P. Mataloni, and F. De Martini, “Complete and deterministic discrimination of polarization Bell states assisted by momentum entanglement,” Phys. Rev. A 75, 042317 (2007).
[CrossRef]

T. C. Wei, J. T. Barreiro, and P. G. Kwiat, “Hyperentangled Bell-state analysis,” Phys. Rev. A 75, 060305 (2007).
[CrossRef]

2006 (3)

C. Schuck, G. Huber, C. Kurtsiefer, and H. Weinfurter, “Complete deterministic linear optics Bell state analysis,” Phys. Rev. Lett. 96, 190501 (2006).
[CrossRef]

J. A. W. van Houwelingen, N. Brunner, A. Beveratos, H. Zbinden, and N. Gisin, “Quantum teleportation with a three-Bell-state analyzer,” Phys. Rev. Lett. 96, 130502 (2006).
[CrossRef]

J. H. Shapiro, “Single-photon Kerr nonlinearities do not help quantum computation,” Phys. Rev. A 73, 062305 (2006).
[CrossRef]

2005 (3)

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]

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, 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]

2004 (5)

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]

A. Yabushita and T. Kobayashi, “Spectroscopy by frequency-entangled photon pairs,” Phys. Rev. A 69, 013806 (2004).
[CrossRef]

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (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)

S. P. Walborn, S. Pádua, and C. H. Monken, “Hyperentanglement-assisted Bell-state analysis,” Phys. Rev. A 68, 042313 (2003).
[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]

F. G. Deng and G. L. Long, “Controlled order rearrangement encryption for quantum key distribution,” Phys. Rev. A 68, 042315 (2003).
[CrossRef]

2002 (3)

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

J. Calsamiglia, “Generalized measurements by linear elements,” Phys. Rev. A 65, 030301 (2002).
[CrossRef]

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

1999 (3)

L. Vaidman and N. Yoran, “Methods for reliable teleportation,” Phys. Rev. A 59, 116–125 (1999).
[CrossRef]

N. Lütkenhaus, J. Calsamiglia, and K. A. Suominen, “Bell measurements for teleportation,” Phys. Rev. A 59, 3295–3300 (1999).
[CrossRef]

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

1998 (1)

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

1993 (2)

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]

M. Żukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert, “Event-ready-detectors Bell experiment via entanglement swapping,” Phys. Rev. Lett. 71, 4287–4290 (1993).
[CrossRef]

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]

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

1991 (1)

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

Ager, J. W.

J. J. L. Morton, A. M. Tyryshkin, R. M. Brown, S. Shankar, B. W. Lovett, A. Ardavan, T. Schenkel, E. E. Haller, J. W. Ager, and A. S. Lyon, “Solid-state quantum memory using the P31 nuclear spin,” Nature 455, 1085–1088 (2008).
[CrossRef]

Amini, J. M.

D. Hanneke, J. P. Home, J. D. Jost, J. M. Amini, D. Leibfried, and J. D. Wineland, “Realization of a programmable two-qubit quantum processor,” Nat. Phys. 6, 13–16 (2009).
[CrossRef]

Ardavan, A.

J. J. L. Morton, A. M. Tyryshkin, R. M. Brown, S. Shankar, B. W. Lovett, A. Ardavan, T. Schenkel, E. E. Haller, J. W. Ager, and A. S. Lyon, “Solid-state quantum memory using the P31 nuclear spin,” Nature 455, 1085–1088 (2008).
[CrossRef]

Awschalom, D. D.

M. H. Mikkelsen, J. Berezovsky, L. A. Coldren, N. G. Stoltz, and D. D. Awschalom, “Optically detected coherent spin dynamics of a single electron in a quantum dot,” Nat. Phys. 3, 770–773 (2007).
[CrossRef]

Barbieri, M.

M. Barbieri, G. Vallone, P. Mataloni, and F. De Martini, “Complete and deterministic discrimination of polarization Bell states assisted by momentum entanglement,” Phys. Rev. A 75, 042317 (2007).
[CrossRef]

Barreiro, J. T.

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
[CrossRef]

T. C. Wei, J. T. Barreiro, and P. G. Kwiat, “Hyperentangled Bell-state analysis,” Phys. Rev. A 75, 060305 (2007).
[CrossRef]

Bennett, C. H.

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]

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]

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

Berezovsky, J.

M. H. Mikkelsen, J. Berezovsky, L. A. Coldren, N. G. Stoltz, and D. D. Awschalom, “Optically detected coherent spin dynamics of a single electron in a quantum dot,” Nat. Phys. 3, 770–773 (2007).
[CrossRef]

Berman, P. R.

X. Xu, B. Sun, P. R. Berman, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, “Coherent optical spectroscopy of a strongly driven quantum dot,” Science 317, 929–932 (2007).
[CrossRef]

Berthiaume, A.

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

Beveratos, A.

J. A. W. van Houwelingen, N. Brunner, A. Beveratos, H. Zbinden, and N. Gisin, “Quantum teleportation with a three-Bell-state analyzer,” Phys. Rev. Lett. 96, 130502 (2006).
[CrossRef]

Bonato, C.

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

Bourennane, M.

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

Bouwmeester, D.

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

Bowen, W. P.

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]

Bracker, A. S.

X. Xu, B. Sun, P. R. Berman, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, “Coherent optical spectroscopy of a strongly driven quantum dot,” Science 317, 929–932 (2007).
[CrossRef]

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).
[CrossRef]

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

Brown, R. M.

J. J. L. Morton, A. M. Tyryshkin, R. M. Brown, S. Shankar, B. W. Lovett, A. Ardavan, T. Schenkel, E. E. Haller, J. W. Ager, and A. S. Lyon, “Solid-state quantum memory using the P31 nuclear spin,” Nature 455, 1085–1088 (2008).
[CrossRef]

Brunner, D.

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

Brunner, N.

J. A. W. van Houwelingen, N. Brunner, A. Beveratos, H. Zbinden, and N. Gisin, “Quantum teleportation with a three-Bell-state analyzer,” Phys. Rev. Lett. 96, 130502 (2006).
[CrossRef]

Bužek, V.

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

Calsamiglia, J.

J. Calsamiglia, “Generalized measurements by linear elements,” Phys. Rev. A 65, 030301 (2002).
[CrossRef]

N. Lütkenhaus, J. Calsamiglia, and K. A. Suominen, “Bell measurements for teleportation,” Phys. Rev. A 59, 3295–3300 (1999).
[CrossRef]

Cao, Y.

S. Y. Song, Y. Cao, Y. B. Sheng, and G. L. Long, “Complete Greenberger–Horne–Zeilinger state analyzer using hyperentanglement,” Quant. Info. Proc. 12, 381–393 (2013).
[CrossRef]

Chen, Q. Q.

Chen, X. D.

X. M. Lin, Z. H. Chen, G. W. Lin, X. D. Chen, and B. B. Ni, “Optical Bell state and Greenberger–Horne–Zeilinger-state analyzers through the cavity input-output process,” Opt. Commun. 282, 3371–3374 (2009).
[CrossRef]

Chen, Z. H.

X. M. Lin, Z. H. Chen, G. W. Lin, X. D. Chen, and B. B. Ni, “Optical Bell state and Greenberger–Horne–Zeilinger-state analyzers through the cavity input-output process,” Opt. Commun. 282, 3371–3374 (2009).
[CrossRef]

Coldren, L. A.

M. H. Mikkelsen, J. Berezovsky, L. A. Coldren, N. G. Stoltz, and D. D. Awschalom, “Optically detected coherent spin dynamics of a single electron in a quantum dot,” Nat. Phys. 3, 770–773 (2007).
[CrossRef]

Crepeau, C.

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]

Dalgarno, P. A.

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

De Martini, F.

M. Barbieri, G. Vallone, P. Mataloni, and F. De Martini, “Complete and deterministic discrimination of polarization Bell states assisted by momentum entanglement,” Phys. Rev. A 75, 042317 (2007).
[CrossRef]

Deng, F. G.

H. R. Wei and F. G. Deng, “Universal quantum gates for hybrid systems assisted by quantum dots inside double-sided optical microcavities,” Phys. Rev. A 87, 022305 (2013).
[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, 24664–24677 (2012).
[CrossRef]

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

F. G. Deng, “Efficient multipartite entanglement purification with the entanglement link from a subspace,” Phys. Rev. A 84, 052312 (2011).
[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 G. L. Long, “Complete hyperentangled-Bell-state analysis for quantum communication,” Phys. Rev. A 82, 032318 (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]

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]

L. Xiao, G. L. Long, F. G. Deng, and J. W. Pan, “Efficient multiparty quantum-secret-sharing schemes,” Phys. Rev. A 69, 052307 (2004).
[CrossRef]

F. G. Deng, G. L. Long, and X. S. Liu, “Two-step quantum direct communication protocol using the Einstein–Podolsky–Rosen pair block,” Phys. Rev. A 68, 042317 (2003).
[CrossRef]

F. G. Deng and G. L. Long, “Controlled order rearrangement encryption for quantum key distribution,” Phys. Rev. A 68, 042315 (2003).
[CrossRef]

B. C. Ren, H. R. Wei, and F. G. Deng, “Deterministic photonic spatial-polarization hyper-controlled-not gate assisted by quantum dot inside one-side optical microcavity,” arXiv.org, arXiv:1303.0056.

Deppe, D. G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[CrossRef]

Ding, D.

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

Ekert, A. K.

M. Żukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert, “Event-ready-detectors Bell experiment via entanglement swapping,” Phys. Rev. Lett. 71, 4287–4290 (1993).
[CrossRef]

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

Ell, C.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[CrossRef]

Exter, M. P.

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

Feng, L.

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

Forchel, A.

S. Reitzenstein, C. Hofmann, A. Gorbunov, M. Strauß, S. H. Kwon, C. Schneider, A. Löffler, S. Höfling, M. Kamp, and A. Forchel, “AlAs/GaAs micropillar cavities with quality factors exceeding 150.000,” Appl. Phys. Lett. 90, 251109 (2007).
[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]

Gaebler, C. P. E.

N. Pisenti, C. P. E. Gaebler, and T. W. Lynn, “Distinguishability of hyperentangled Bell states by linear evolution and local projective measurement,” Phys. Rev. A 84, 022340 (2011).
[CrossRef]

Gammon, D.

X. Xu, B. Sun, P. R. Berman, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, “Coherent optical spectroscopy of a strongly driven quantum dot,” Science 317, 929–932 (2007).
[CrossRef]

Gea-Banacloche, J.

J. Gea-Banacloche, “Impossibility of large phase shifts via the giant Kerr effect with single-photon wave packets,” Phys. Rev. A 81, 043823 (2010).
[CrossRef]

Gerardot, B. D.

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

Gibbs, H. M.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[CrossRef]

Gisin, N.

J. A. W. van Houwelingen, N. Brunner, A. Beveratos, H. Zbinden, and N. Gisin, “Quantum teleportation with a three-Bell-state analyzer,” Phys. Rev. Lett. 96, 130502 (2006).
[CrossRef]

Gorbunov, A.

S. Reitzenstein, C. Hofmann, A. Gorbunov, M. Strauß, S. H. Kwon, C. Schneider, A. Löffler, S. Höfling, M. Kamp, and A. Forchel, “AlAs/GaAs micropillar cavities with quality factors exceeding 150.000,” Appl. Phys. Lett. 90, 251109 (2007).
[CrossRef]

Gudat, J.

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

Haller, E. E.

J. J. L. Morton, A. M. Tyryshkin, R. M. Brown, S. Shankar, B. W. Lovett, A. Ardavan, T. Schenkel, E. E. Haller, J. W. Ager, and A. S. Lyon, “Solid-state quantum memory using the P31 nuclear spin,” Nature 455, 1085–1088 (2008).
[CrossRef]

Hanneke, D.

D. Hanneke, J. P. Home, J. D. Jost, J. M. Amini, D. Leibfried, and J. D. Wineland, “Realization of a programmable two-qubit quantum processor,” Nat. Phys. 6, 13–16 (2009).
[CrossRef]

Haupt, F.

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

Hendrickson, J.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[CrossRef]

Hillery, M.

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

Höfling, S.

S. Reitzenstein, C. Hofmann, A. Gorbunov, M. Strauß, S. H. Kwon, C. Schneider, A. Löffler, S. Höfling, M. Kamp, and A. Forchel, “AlAs/GaAs micropillar cavities with quality factors exceeding 150.000,” Appl. Phys. Lett. 90, 251109 (2007).
[CrossRef]

Hofmann, C.

S. Reitzenstein, C. Hofmann, A. Gorbunov, M. Strauß, S. H. Kwon, C. Schneider, A. Löffler, S. Höfling, M. Kamp, and A. Forchel, “AlAs/GaAs micropillar cavities with quality factors exceeding 150.000,” Appl. Phys. Lett. 90, 251109 (2007).
[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]

Home, J. P.

D. Hanneke, J. P. Home, J. D. Jost, J. M. Amini, D. Leibfried, and J. D. Wineland, “Realization of a programmable two-qubit quantum processor,” Nat. Phys. 6, 13–16 (2009).
[CrossRef]

Horne, M. A.

M. Żukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert, “Event-ready-detectors Bell experiment via entanglement swapping,” Phys. Rev. Lett. 71, 4287–4290 (1993).
[CrossRef]

Hu, C. Y.

C. Y. Hu, W. J. Munro, J. L. O’Brien, 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]

C. Y. Hu, A. Young, J. L. OBrien, 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]

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]

Hua, M.

Huber, G.

C. Schuck, G. Huber, C. Kurtsiefer, and H. Weinfurter, “Complete deterministic linear optics Bell state analysis,” Phys. Rev. Lett. 96, 190501 (2006).
[CrossRef]

Jin, G. S.

C. Wang, Y. Zhang, and G. S. Jin, “Entanglement purification and concentration of the electron-spin entangled states using quantum-dot spins in optical microcavities,” Phys. Rev. A 84, 032307 (2011).
[CrossRef]

Jost, J. D.

D. Hanneke, J. P. Home, J. D. Jost, J. M. Amini, D. Leibfried, and J. D. Wineland, “Realization of a programmable two-qubit quantum processor,” Nat. Phys. 6, 13–16 (2009).
[CrossRef]

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).
[CrossRef]

Kamp, M.

S. Reitzenstein, C. Hofmann, A. Gorbunov, M. Strauß, S. H. Kwon, C. Schneider, A. Löffler, S. Höfling, M. Kamp, and A. Forchel, “AlAs/GaAs micropillar cavities with quality factors exceeding 150.000,” Appl. Phys. Lett. 90, 251109 (2007).
[CrossRef]

Karlsson, A.

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

Karrai, K.

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

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).
[CrossRef]

Khitrova, G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[CrossRef]

Kobayashi, T.

A. Yabushita and T. Kobayashi, “Spectroscopy by frequency-entangled photon pairs,” Phys. Rev. A 69, 013806 (2004).
[CrossRef]

Koppens, F. H. L.

K. C. Nowack, F. H. L. Koppens, Y. V. Nazarov, and L. M. K. Vandersypen, “Coherent control of a single electron spin with electric fields,” Science 318, 1430–1433 (2007).
[CrossRef]

Kroner, M.

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

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).
[CrossRef]

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).
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C. Schuck, G. Huber, C. Kurtsiefer, and H. Weinfurter, “Complete deterministic linear optics Bell state analysis,” Phys. Rev. Lett. 96, 190501 (2006).
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S. Reitzenstein, C. Hofmann, A. Gorbunov, M. Strauß, S. H. Kwon, C. Schneider, A. Löffler, S. Höfling, M. Kamp, and A. Forchel, “AlAs/GaAs micropillar cavities with quality factors exceeding 150.000,” Appl. Phys. Lett. 90, 251109 (2007).
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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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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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X. H. Li, “Deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044304 (2010).
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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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X. M. Lin, Z. H. Chen, G. W. Lin, X. D. Chen, and B. B. Ni, “Optical Bell state and Greenberger–Horne–Zeilinger-state analyzers through the cavity input-output process,” Opt. Commun. 282, 3371–3374 (2009).
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C. Y. Hu, W. J. Munro, J. L. O’Brien, 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, A. Young, J. L. OBrien, 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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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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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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J. J. L. Morton, A. M. Tyryshkin, R. M. Brown, S. Shankar, B. W. Lovett, A. Ardavan, T. Schenkel, E. E. Haller, J. W. Ager, and A. S. Lyon, “Solid-state quantum memory using the P31 nuclear spin,” Nature 455, 1085–1088 (2008).
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T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
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S. Reitzenstein, C. Hofmann, A. Gorbunov, M. Strauß, S. H. Kwon, C. Schneider, A. Löffler, S. Höfling, M. Kamp, and A. Forchel, “AlAs/GaAs micropillar cavities with quality factors exceeding 150.000,” Appl. Phys. Lett. 90, 251109 (2007).
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C. Schuck, G. Huber, C. Kurtsiefer, and H. Weinfurter, “Complete deterministic linear optics Bell state analysis,” Phys. Rev. Lett. 96, 190501 (2006).
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B. D. Gerardot, D. Brunner, P. A. Dalgarno, P. Ohberg, S. Seidl, M. Kroner, K. Karrai, N. G. Stoltz, P. M. Petroff, and R. J. Warburton, “Optical pumping of a single hole spin in a quantum dot,” Nature 451, 441–444 (2008).
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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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J. J. L. Morton, A. M. Tyryshkin, R. M. Brown, S. Shankar, B. W. Lovett, A. Ardavan, T. Schenkel, E. E. Haller, J. W. Ager, and A. S. Lyon, “Solid-state quantum memory using the P31 nuclear spin,” Nature 455, 1085–1088 (2008).
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S. Y. Song, Y. Cao, Y. B. Sheng, and G. L. Long, “Complete Greenberger–Horne–Zeilinger state analyzer using hyperentanglement,” Quant. Info. Proc. 12, 381–393 (2013).
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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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J. J. L. Morton, A. M. Tyryshkin, R. M. Brown, S. Shankar, B. W. Lovett, A. Ardavan, T. Schenkel, E. E. Haller, J. W. Ager, and A. S. Lyon, “Solid-state quantum memory using the P31 nuclear spin,” Nature 455, 1085–1088 (2008).
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J. A. W. van Houwelingen, N. Brunner, A. Beveratos, H. Zbinden, and N. Gisin, “Quantum teleportation with a three-Bell-state analyzer,” Phys. Rev. Lett. 96, 130502 (2006).
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Wang, Y.

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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J. A. W. van Houwelingen, N. Brunner, A. Beveratos, H. Zbinden, and N. Gisin, “Quantum teleportation with a three-Bell-state analyzer,” Phys. Rev. Lett. 96, 130502 (2006).
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Y. B. Sheng and L. Zhou, “Quantum entanglement concentration based on nonlinear optics for quantum communications,” Entropy 15, 1776–1820 (2013).
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Entropy (1)

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J. Opt. Soc. Am. B (3)

Nat. Phys. (3)

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Opt. Express (2)

Phys. Rev. A (34)

C. Wang, Y. Zhang, and G. S. Jin, “Entanglement purification and concentration of the electron-spin entangled states using quantum-dot spins in optical microcavities,” Phys. Rev. A 84, 032307 (2011).
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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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H. R. Wei and F. G. Deng, “Universal quantum gates for hybrid systems assisted by quantum dots inside double-sided optical microcavities,” Phys. Rev. A 87, 022305 (2013).
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Y. B. Sheng, L. Zhou, and S. M. Zhao, “Efficient two-step entanglement concentration for arbitrary W states,” Phys. Rev. A 85, 042302 (2012).
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A. Yabushita and T. Kobayashi, “Spectroscopy by frequency-entangled photon pairs,” Phys. Rev. A 69, 013806 (2004).
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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).
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Y. B. Sheng and F. G. Deng, “Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement,” Phys. Rev. A 81, 032307 (2010).
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Y. B. Sheng and F. G. Deng, “One-step deterministic polarization entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044305 (2010).
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Phys. Rev. B (3)

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C. Y. Hu, A. Young, J. L. OBrien, 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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Phys. Rev. Lett. (10)

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[CrossRef]

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]

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]

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Quant. Info. Proc. (2)

S. Y. Song, Y. Cao, Y. B. Sheng, and G. L. Long, “Complete Greenberger–Horne–Zeilinger state analyzer using hyperentanglement,” Quant. Info. Proc. 12, 381–393 (2013).
[CrossRef]

Y. B. Sheng, L. Zhou, L. Wang, and S. M. Zhao, “Efficient entanglement concentration for quantum dot and optical microcavities systems,” Quant. Info. Proc. 12, 1885–1895 (2013).
[CrossRef]

Science (2)

X. Xu, B. Sun, P. R. Berman, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, “Coherent optical spectroscopy of a strongly driven quantum dot,” Science 317, 929–932 (2007).
[CrossRef]

K. C. Nowack, F. H. L. Koppens, Y. V. Nazarov, and L. M. K. Vandersypen, “Coherent control of a single electron spin with electric fields,” Science 318, 1430–1433 (2007).
[CrossRef]

Other (3)

B. C. Ren, H. R. Wei, and F. G. Deng, “Deterministic photonic spatial-polarization hyper-controlled-not gate assisted by quantum dot inside one-side optical microcavity,” arXiv.org, arXiv:1303.0056.

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G. L. Long and X. S. Liu, “Theoretically efficient high-capacity quantum-key-distribution scheme,” Phys. Rev. A65, 032302 (2002); the first version, submitted on Dec. 13, 2000, to arXiv.org (arXiv:quant-ph/0012056), claims clearly that this protocol can be used to transmit secret message directly.

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Figures (6)

Fig. 1.
Fig. 1.

(a) Schematic diagram for a singly charged QD inside a one-sided optical microcavity. (b) Schematic description of the relevant exciton energy levels and the spin selection rules for the optical transition of a negatively charged exciton. The symbols | (|) and | (|) represent a hole and an excess electron with the spin projections |+3/2 (|3/2) and |+1/2 (|1/2), respectively. |R and |L denote a right-circularly polarized photon and a left-circularly polarized photon, respectively.

Fig. 2.
Fig. 2.

Schematic diagram of the present HGSA scheme for the spatial-mode entangled three-photon GHZ states. This setup is used to distinguish the four groups of GHZ states |Ψ1±S, |Ψ2±S, |Ψ3±S, and |Ψ4±S. The excess electron spin in the QD is initially prepared in the state 1/2(|+|). The small mirror is used to reflect the photon for interacting with the cavity twice. HWP is a half-wave plate that functions as a phase-flip operation Z=|RR||LL|. M is a small mirror that is used to reflect the photon for interacting with the cavity twice.

Fig. 3.
Fig. 3.

Setup for distinguishing the relative phases of the GHZ states in the spatial mode DOF in each group. The spin of each QD is initially prepared in the state 1/2(|+|). HWP1 denotes another half-wave plate which is used to perform a bit-flip operation X=|RL|+|LR| in the polarization DOF. BS represents a 5050 BS, which acts as the Hadamard operation on the spatial-mode DOF.

Fig. 4.
Fig. 4.

Setup for distinguishing the GHZ states in the polarization DOF. PBS denotes a polarization BS that transmits the horizontal polarization photon |H and reflects the vertical polarization photon |V, respectively.

Fig. 5.
Fig. 5.

Fidelity of the present HGSA scheme for the hyperentangled state |Ψ+P|Ψ+S versus the coupling strength g/(κ+κs) for different leakage rates κs/κ. Here the three curves correspond to the cases of κs/κ=0 (solid blue), 0.03 (long-dashed red), and 0.06 (dashed–dotted black), respectively. The decay rate of X is chosen as γ=0.1κ.

Fig. 6.
Fig. 6.

Efficiency of the present HGSA scheme for the hyperentangled state |Ψ+P|Ψ+S versus the coupling strength g/(κ+κs) for different leakage rates κs/κ. Here the three curves correspond to the cases of κs/κ=0 (solid blue), 0.03 (long-dashed red), and 0.06 (dashed–dotted black), respectively. The decay rate of X is chosen as γ=0.1κ.

Tables (3)

Tables Icon

Table 1. Relation between Eight GHZ States in the Spatial-Mode DOF and Outcomes of QD1 and QD2

Tables Icon

Table 2. Corresponding Relations between GHZ States in the Spatial-Mode DOF and States of QDs

Tables Icon

Table 3. Relation between Eight GHZ States in Polarization DOF and Outcomes of QD6 and QD7

Equations (14)

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dadt=[i(ωcω)+κ2+κs2]agσκain,dσdt=[i(ωXω)+γ2]σgσza,aout=ain+κa,
r(ω)=1κ[i(ωXω)+γ2][i(ωXω)+γ2][i(ωcω)+κ2+κs2]+g2.
r0(ω)=i(ωcω)κ2+κs2i(ωcω)+κ2+κs2.
r(ω)=|r0(ω)|eiφ0(|RR|||+|LL|||)+|rh(ω)|eiφh(|LL|||+|RR|||),
|ζ1+PS=12(|RRR+|LLL)abc(|a1b1c1+|a2b2c2)abc.
|Ψ1±P=12(|RRR±|LLL),|Ψ2±P=12(|LRR±|RLL),|Ψ3±P=12(|RLR±|LRL),|Ψ4±P=12(|RRL±|LLR),
|Ψ1±S=12(|a1b1c1±|a2b2c2),|Ψ2±S=12(|a2b1c1±|a1b2c2),|Ψ3±S=12(|a1b2c1±|a2b1c2),|Ψ4±S=12(|a1b1c2±|a2b2c1).
12(|R+|L)12(|+|)e2iφ012(|R|L)12(||).
Ka1(b1c1)12(Kd1(3,5)+Kd2(4,6)),Ka2(b2c2)12(Kd1(3,5)Kd2(4,6)).
|Ψ1+S=12(|d1d3d5+|d1d4d6+|d2d3d6+|d2d4d5),|Ψ1S=12(|d1d3d6+|d1d4d5+|d2d3d5+|d2d4d6),|Ψ2+S=12(|d1d3d5+|d1d4d6|d2d3d6|d2d4d5),|Ψ2S=12(|d1d3d6+|d1d4d5|d2d3d5|d2d4d6),|Ψ3+S=12(|d1d3d5|d1d4d6+|d2d3d6|d2d4d5),|Ψ3S=12(|d1d3d6|d1d4d5+|d2d3d5|d2d4d6),|Ψ4+S=12(|d1d3d5|d1d4d6|d2d3d6+|d2d4d5),|Ψ4S=12(|d1d3d6+|d1d4d5+|d2d3d5|d2d4d6).
1 2 ( | R R R ± | L L L ) ( | + | ) QD 6 1 2 ( | R R R | L L L ) ( | | ) QD 6 , 1 2 ( | R R R | L L L ) ( | + | ) QD 7 1 2 ( | R R R ± | L L L ) ( | | ) QD 7 , 1 2 ( | L R R ± | R L L ) ( | + | ) QD 6 1 2 ( | L R R ± | R L L ) ( | + | ) QD 6 , 1 2 ( | L R R ± | R L L ) ( | + | ) QD 7 1 2 ( | L R R ± | R L L ) ( | + | ) QD 7 .
| Ψ 1 + P = 1 2 ( | D 1 D 3 D 5 + | D 1 D 4 D 6 + | D 2 D 3 D 6 + | D 2 D 4 D 5 ) , | Ψ 1 P = 1 2 ( | D 1 D 3 D 6 + | D 1 D 4 D 5 + | D 2 D 3 D 5 + | D 2 D 4 D 6 ) , | Ψ 2 + P = 1 2 ( | D 1 D 3 D 5 + | D 1 D 4 D 6 | D 2 D 3 D 6 | D 2 D 4 D 5 ) , | Ψ 2 P = 1 2 ( | D 1 D 3 D 6 + | D 1 D 4 D 5 | D 2 D 3 D 5 | D 2 D 4 D 6 ) , | Ψ 3 + P = 1 2 ( | D 1 D 3 D 5 | D 1 D 4 D 6 + | D 2 D 3 D 6 | D 2 D 4 D 5 ) , | Ψ 3 P = 1 2 ( | D 1 D 3 D 6 | D 1 D 4 D 5 + | D 2 D 3 D 5 | D 2 D 4 D 6 ) , | Ψ 4 + P = 1 2 ( | D 1 D 3 D 5 | D 1 D 4 D 6 | D 2 D 3 D 6 + | D 2 D 4 D 5 ) , | Ψ 4 P = 1 2 ( | D 1 D 3 D 6 + | D 1 D 4 D 5 + | D 2 D 3 D 5 | D 2 D 4 D 6 ) .
F=(1+ε2)3(1+ε)14212(1+ε4)5
η=(|r0|42+|rh|42)3(|r0|22+|rh|22)4,

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