Abstract

Bell-state analysis (BSA) is essential in quantum communication, but it is impossible to distinguish unambiguously the four Bell states in the polarization degree of freedom (DOF) of two-photon systems with only linear optical elements, except for the case in which the BSA is assisted with hyperentangled states, the simultaneous entanglement in more than one DOF. Here, we propose a scheme to distinguish completely the 16 hyperentangled Bell states in both the polarization and the spatial-mode DOFs of two-photon systems, by using the giant nonlinear optics in quantum dot-cavity systems. This scheme can be applied to increase the channel capacity of long-distance quantum communication based on hyperentanglement, such as entanglement swapping, teleportation, and superdense coding. We use hyperentanglement swapping as an example to show the application of this HBSA.

© 2012 OSA

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2011 (4)

N. Pisenti, C. P. E. Gaebler, and T. W. Lynn, “Distinguishability of hyperentangled Bell states by linear evolution and local projective measurement,” Phys. Rev. A84, 022340 (2011).
[CrossRef]

F. G. Deng, “One-step error correction for multipartite polarization entanglement,” Phys. Rev. A83, 062316 (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. B83, 115303 (2011).
[CrossRef]

A. B. Young, R. Oulton, C. Y. Hu, A. C. T. Thijssen, C. Schneider, S. Reitzenstein, M. Kamp, S. Höfling, L. Worschech, A. Forchel, and J. G. Rarity, “Quantum-dot-induced phase shift in a pillar microcavity,” Phys. Rev. A84, 011803 (2011).
[CrossRef]

2010 (8)

V. Loo, L. Lanco, A. Lemaître, I. Sagnes, O. Krebs, P. Voisin, and P. Senellart, “Quantum dot-cavity strong-coupling regime measured through coherent reflection spectroscopy in a very high-Q micropillar,” Appl. Phys. Lett.97, 241110 (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] [PubMed]

Y. B. Sheng and F. G. Deng, “Efficient quantum entanglement distribution over an arbitrary collective-noise channel,” Phys. Rev. A81, 042332 (2010).
[CrossRef]

J. Gea-Banacloche, “Impossibility of large phase shifts via the giant Kerr effect with single-photon wave packets,” Phys. Rev. A81, 043823 (2010).
[CrossRef]

Y. B. Sheng, F. G. Deng, and G. L. Long, “Complete hyperentangled-Bell-state analysis for quantum communication,” Phys. Rev. A82, 032318 (2010).
[CrossRef]

Y. B. Sheng and F. G. Deng, “Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement,” Phys. Rev. A81, 032307 (2010).
[CrossRef]

Y. B. Sheng and F. G. Deng, “One-step deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A82, 044305 (2010).
[CrossRef]

X. H. Li, “Deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A82, 044304 (2010).
[CrossRef]

2009 (2)

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,” Science325, 70–72 (2009).
[CrossRef] [PubMed]

G. Vallone, R. Ceccarelli, F. De Martini, and P. Mataloni, “Hyperentanglement of two photons in three degrees of freedom,” Phys. Rev. A79, 030301(R) (2009).
[CrossRef]

2008 (5)

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

B. D. Gerardot, D. Brunner, P. A. Dalgarno, P. Öhberg, 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 (London)451, 441–444 (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. A77, 042308 (2008).
[CrossRef]

C. Y. Hu, A. Young, J. L. O’Brien, 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. B78, 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. B78, 125318 (2008).
[CrossRef]

2007 (5)

T. C. Wei, J. T. Barreiro, and P. G. Kwiat, “Hyperentangled Bell-state analysis,” Phys. Rev. A75, 060305(R) (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. A75, 042317 (2007).
[CrossRef]

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys.79, 135–174 (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]

D. Heiss, S. Schaeck, H. Huebl, M. Bichler, G. Abstreiter, J. J. Finley, D. V. Bulaev, and D. Loss, “Observation of extremely slow hole spin relaxation in self-assembled quantum dots,” Phys. Rev. B76, 241306(R) (2007).
[CrossRef]

2006 (3)

J. H. Shapiro, “Single-photon Kerr nonlinearities do not help quantum computation,” Phys. Rev. A73, 062305 (2006).
[CrossRef]

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

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] [PubMed]

2005 (4)

T. Yang, Q. Zhang, J. Zhang, J. Yin, Z. Zhao, M. Żukowski, Z. B. Chen, and J. W. Pan, “All-versus-nothing violation of local realism by two-photon, four-dimensional entanglement,” Phys. Rev. Lett.95, 240406 (2005)
[CrossRef] [PubMed]

C. Cinelli, M. Barbieri, R. Perris, P. Mataloni, and F. De Martini, “All-versus-nothing nonlocality test of quantum mechanics by two-photon hyperentanglement,” Phys. Rev. Lett.95, 240405 (2005).
[CrossRef] [PubMed]

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of hyperentangled photon pairs,” Phys. Rev. Lett.95, 260501 (2005).
[CrossRef]

M. Barbieri, C. Cinelli, P. Mataloni, and F. De Martini, “Polarization-momentum hyperentangled states: realization and characterization,” Phys. Rev. A72, 052110 (2005).
[CrossRef]

2004 (5)

N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, “Measuring entangled qutrits and their use for quantum bit commitment,” Phys. Rev. Lett.93, 053601 (2004).
[CrossRef] [PubMed]

R. Ursin, T. Jennewein, M. Aspelmeyer, R. Kaltenbaek, M. Lindenthal, P. Walther, and A. Zeilinger, “Communications: quantum teleportation across the danube,” Nature (London)430, 849 (2004).
[CrossRef]

W. Langbein, P. Borri, U. Woggon, V. Stavarache, D. Reuter, and A. D. Wieck, “Radiatively limited dephasing in InAs quantum dots,” Phys. Rev. B70, 033301 (2004).
[CrossRef]

J. P. Reithmaier, G. Sȩk, 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 (London)432, 197–200 (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 (London)432, 200–203 (2004).
[CrossRef]

2003 (3)

G. Bester, S. Nair, and A. Zunger, “Pseudopotential calculation of the excitonic fine structure of million-atom self-assembled In1−xGaxAs/GaAs quantum dots,” Phys. Rev. B67, 161306 (R) (2003).
[CrossRef]

F. G. Deng and G. L. Long, “Controlled order rearrangement encryption for quantum key distribution,” Phys. Rev. A68, 042315 (2003).
[CrossRef]

S. P. Walborn, S. Ṕadua, and C. H. Monken, “Hyperentanglement-assisted Bell-state analysis,” Phys. Rev. A68, 042313 (2003).
[CrossRef]

2002 (6)

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

X. S. Liu, G. L. Long, D. M. Tong, and F. Li, “General scheme for superdense coding between multiparties,” Phys. Rev. A65, 022304 (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. A65, 032302 (2002).
[CrossRef]

J. Calsamiglia, “Generalized measurements by linear elements,” Phys. Rev. A65, 030301(R) (2002).
[CrossRef]

J. J. Finley, D. J. Mowbray, M. S. Skolnick, A. D. Ashmore, C. Baker, A. F. G. Monte, and M. Hopkinson, “Fine structure of charged and neutral excitons in InAs-Al0.6Ga0.4As quantum dots,” Phys. Rev. B66, 153316 (2002).
[CrossRef]

2001 (3)

P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, “Ultralong dephasing time in InGaAs quantum dots,” Phys. Rev. Lett.87, 157401 (2001).
[CrossRef] [PubMed]

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1999 (3)

J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed energy-time entangled twin-photon source for quantum communication,” Phys. Rev. Lett.82, 2594–2597 (1999).
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1998 (2)

P. G. Kwiat and H. Weinfurter, “Embedded Bell-state analysis,” Phys. Rev. A58, R2623–R2626 (1998).
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R. J. Warburton, C. S. Dürr, K. Karrai, J. P. Kotthaus, G. Medeiros-Ribeiro, and P. M. Petroff, “Charged excitons in self-assembled semiconductor quantum dots,” Phys. Rev. Lett.79, 5282–5285 (1997).
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1996 (2)

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1993 (2)

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1992 (2)

C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Enstein-Podolsky-Rosen states,” Phys. Rev. Lett.69, 2881–2884 (1992).
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1991 (1)

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1990 (1)

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1989 (1)

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1988 (2)

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D. Heiss, S. Schaeck, H. Huebl, M. Bichler, G. Abstreiter, J. J. Finley, D. V. Bulaev, and D. Loss, “Observation of extremely slow hole spin relaxation in self-assembled quantum dots,” Phys. Rev. B76, 241306(R) (2007).
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Y. H. Shih and C. O. Alley, “New type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion,” Phys. Rev. Lett.61, 2921–2924 (1988).
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M. Barbieri, G. Vallone, P. Mataloni, and F. De Martini, “Complete and deterministic discrimination of polarization Bell states assisted by momentum entanglement,” Phys. Rev. A75, 042317 (2007).
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C. Cinelli, M. Barbieri, R. Perris, P. Mataloni, and F. De Martini, “All-versus-nothing nonlocality test of quantum mechanics by two-photon hyperentanglement,” Phys. Rev. Lett.95, 240405 (2005).
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M. Barbieri, C. Cinelli, P. Mataloni, and F. De Martini, “Polarization-momentum hyperentangled states: realization and characterization,” Phys. Rev. A72, 052110 (2005).
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C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett.70, 1895–1899 (1993).
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C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bell’s theorem,” Phys. Rev. Lett.68, 557–559 (1992).
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C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Enstein-Podolsky-Rosen states,” Phys. Rev. Lett.69, 2881–2884 (1992).
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P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, “Ultralong dephasing time in InGaAs quantum dots,” Phys. Rev. Lett.87, 157401 (2001).
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D. Birkedal, K. Leosson, and J. M. Hvam, “Long lived coherence in self-assembled quantum dots,” Phys. Rev. Lett.87, 227401 (2001).
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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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P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, “Ultralong dephasing time in InGaAs quantum dots,” Phys. Rev. Lett.87, 157401 (2001).
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C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett.70, 1895–1899 (1993).
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C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bell’s theorem,” Phys. Rev. Lett.68, 557–559 (1992).
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J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed energy-time entangled twin-photon source for quantum communication,” Phys. Rev. Lett.82, 2594–2597 (1999).
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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,” Science325, 70–72 (2009).
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B. D. Gerardot, D. Brunner, P. A. Dalgarno, P. Öhberg, 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 (London)451, 441–444 (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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D. Heiss, S. Schaeck, H. Huebl, M. Bichler, G. Abstreiter, J. J. Finley, D. V. Bulaev, and D. Loss, “Observation of extremely slow hole spin relaxation in self-assembled quantum dots,” Phys. Rev. B76, 241306(R) (2007).
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J. Calsamiglia, “Generalized measurements by linear elements,” Phys. Rev. A65, 030301(R) (2002).
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N. Lütkenhaus, J. Calsamiglia, and K. A. Suominen, “Bell measurements for teleportation,” Phys. Rev. A59, 3295–3300 (1999).
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G. Vallone, R. Ceccarelli, F. De Martini, and P. Mataloni, “Hyperentanglement of two photons in three degrees of freedom,” Phys. Rev. A79, 030301(R) (2009).
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T. Yang, Q. Zhang, J. Zhang, J. Yin, Z. Zhao, M. Żukowski, Z. B. Chen, and J. W. Pan, “All-versus-nothing violation of local realism by two-photon, four-dimensional entanglement,” Phys. Rev. Lett.95, 240406 (2005)
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C. Cinelli, M. Barbieri, R. Perris, P. Mataloni, and F. De Martini, “All-versus-nothing nonlocality test of quantum mechanics by two-photon hyperentanglement,” Phys. Rev. Lett.95, 240405 (2005).
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M. Barbieri, C. Cinelli, P. Mataloni, and F. De Martini, “Polarization-momentum hyperentangled states: realization and characterization,” Phys. Rev. A72, 052110 (2005).
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C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett.70, 1895–1899 (1993).
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N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, “Measuring entangled qutrits and their use for quantum bit commitment,” Phys. Rev. Lett.93, 053601 (2004).
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G. Vallone, R. Ceccarelli, F. De Martini, and P. Mataloni, “Hyperentanglement of two photons in three degrees of freedom,” Phys. Rev. A79, 030301(R) (2009).
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M. Barbieri, G. Vallone, P. Mataloni, and F. De Martini, “Complete and deterministic discrimination of polarization Bell states assisted by momentum entanglement,” Phys. Rev. A75, 042317 (2007).
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M. Barbieri, C. Cinelli, P. Mataloni, and F. De Martini, “Polarization-momentum hyperentangled states: realization and characterization,” Phys. Rev. A72, 052110 (2005).
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C. Cinelli, M. Barbieri, R. Perris, P. Mataloni, and F. De Martini, “All-versus-nothing nonlocality test of quantum mechanics by two-photon hyperentanglement,” Phys. Rev. Lett.95, 240405 (2005).
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F. G. Deng, “One-step error correction for multipartite polarization entanglement,” Phys. Rev. A83, 062316 (2011).
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Y. B. Sheng and F. G. Deng, “Efficient quantum entanglement distribution over an arbitrary collective-noise channel,” Phys. Rev. A81, 042332 (2010).
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Y. B. Sheng, F. G. Deng, and G. L. Long, “Complete hyperentangled-Bell-state analysis for quantum communication,” Phys. Rev. A82, 032318 (2010).
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Y. B. Sheng and F. G. Deng, “Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement,” Phys. Rev. A81, 032307 (2010).
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Y. B. Sheng and F. G. Deng, “One-step deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A82, 044305 (2010).
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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. A77, 042308 (2008).
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F. G. Deng and G. L. Long, “Controlled order rearrangement encryption for quantum key distribution,” Phys. Rev. A68, 042315 (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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R. J. Warburton, C. S. Dürr, K. Karrai, J. P. Kotthaus, G. Medeiros-Ribeiro, and P. M. Petroff, “Charged excitons in self-assembled semiconductor quantum dots,” Phys. Rev. Lett.79, 5282–5285 (1997).
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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).
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A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett.67, 661–663 (1991).
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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 (London)432, 200–203 (2004).
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M. Bayer, G. Ortner, O. Stern, A. Kuther, A. A. Gorbunov, A. Forchel, P. Hawrylak, S. Fafard, K. Hinzer, T. L. Reinecke, S. N. Walck, J. P. Reithmaier, F. Klopf, and F. Schäfer, “Fine structure of neutral and charged excitons in self-assembled In(Ga)As/(Al)GaAs quantum dots,” Phys. Rev. B65, 195315 (2002).

Finley, J. J.

D. Heiss, S. Schaeck, H. Huebl, M. Bichler, G. Abstreiter, J. J. Finley, D. V. Bulaev, and D. Loss, “Observation of extremely slow hole spin relaxation in self-assembled quantum dots,” Phys. Rev. B76, 241306(R) (2007).
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J. J. Finley, D. J. Mowbray, M. S. Skolnick, A. D. Ashmore, C. Baker, A. F. G. Monte, and M. Hopkinson, “Fine structure of charged and neutral excitons in InAs-Al0.6Ga0.4As quantum dots,” Phys. Rev. B66, 153316 (2002).
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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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J. P. Reithmaier, G. Sȩk, 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 (London)432, 197–200 (2004).
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M. Bayer, G. Ortner, O. Stern, A. Kuther, A. A. Gorbunov, A. Forchel, P. Hawrylak, S. Fafard, K. Hinzer, T. L. Reinecke, S. N. Walck, J. P. Reithmaier, F. Klopf, and F. Schäfer, “Fine structure of neutral and charged excitons in self-assembled In(Ga)As/(Al)GaAs quantum dots,” Phys. Rev. B65, 195315 (2002).

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J. D. Franson, “Bell inequality for position and time,” Phys. Rev. Lett.62, 2205–2208 (1989).
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N. Pisenti, C. P. E. Gaebler, and T. W. Lynn, “Distinguishability of hyperentangled Bell states by linear evolution and local projective measurement,” Phys. Rev. A84, 022340 (2011).
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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,” Science325, 70–72 (2009).
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B. D. Gerardot, D. Brunner, P. A. Dalgarno, P. Öhberg, 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 (London)451, 441–444 (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 (London)432, 200–203 (2004).
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N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, “Measuring entangled qutrits and their use for quantum bit commitment,” Phys. Rev. Lett.93, 053601 (2004).
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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).
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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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J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed energy-time entangled twin-photon source for quantum communication,” Phys. Rev. Lett.82, 2594–2597 (1999).
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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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M. Bayer, G. Ortner, O. Stern, A. Kuther, A. A. Gorbunov, A. Forchel, P. Hawrylak, S. Fafard, K. Hinzer, T. L. Reinecke, S. N. Walck, J. P. Reithmaier, F. Klopf, and F. Schäfer, “Fine structure of neutral and charged excitons in self-assembled In(Ga)As/(Al)GaAs quantum dots,” Phys. Rev. B65, 195315 (2002).

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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Figures (5)

Fig. 1
Fig. 1

The spin-dependent transitions for negatively charged exciton X. (a) A charged QD inside a micropillar microcavity with circular cross section. (b) Spin selection rule for optical transitions of negatively charged exciton X due to the Pauli’s exclusion principle. L and R represent the left and the right circularly polarized lights, respectively.

Fig. 2
Fig. 2

Schematic diagram of the present HBSA protocol for the spatial-mode entangled Bell states, without destroying the polarization Bell states of the photon pair AB. (a) The QND is used to distinguish the odd-parity states | ψ ± S A B from the even-parity states | ϕ ± S A B. (b) The QND is used to distinguish the ”+” phase state | ψ + S A B ( | ϕ + S A B ) from the “−” phase states | ψ S A B ( | ϕ S A B ). The dashed line presents the case that the photons A coming from the spatial mode |a1〉 and B coming from |b2〉 pass through QD1 in sequence. The small mirror is used to reflect the photon for interacting with the cavity twice. HWP represents a half-wave plate which is used to perform a phase-flip operation Z = |R〉〈R| − |L〉〈L| in the polarization DOF, while HWP1 represents another half-wave plate which is used to perform a bit-flip operation X = |R〉〈L| + |L〉〈R| in the polarization DOF. BS represents a 50:50 beam splitter.

Fig. 3
Fig. 3

Schematic diagram of the present BSA protocol for polarization Bell states. The two spatial modes a and b are sent into the cavity in sequence.

Fig. 4
Fig. 4

Schematic diagram for the hyperentanglement swapping in both the polarization and the spatial-mode DOFs. The initial hyperentangled states are prepared in nodes AB and CD (also the four photons). After Alice performs the HBSA on the two photons BC, Bob and Charlie can get the hyperentangled state between nodes A and D.

Fig. 5
Fig. 5

The fidelity (a) and the efficiency (b) of the present HBSA protocol for the hyperentangled-Bell state |ϕ+P|ϕ+S vs the coupling strength g/(κ + κs) and the side leakage rate κs/κ with γ = 0.1κ.

Tables (2)

Tables Icon

Table 1 Relation between the four Bell states in the spatial-mode DOF and the output results of the measurements on electron-spin states.

Tables Icon

Table 2 The relation between the initial Bell states in the polarization DOF and the output results of the QD4 and the single-photon detections.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

d a d t = [ i ( ω c ω ) + κ 2 + κ s 2 ] a g σ κ a in , d σ d t = [ i ( ω X ω ) + γ 2 ] σ g σ z a , a out = a in + κ a ,
r ( ω ) = 1 κ [ i ( ω X ω ) + γ 2 ] [ i ( ω X ω ) + γ 2 ] [ i ( ω c ω ) + κ 2 + κ s 2 ] + g 2 .
r 0 ( ω ) = i ( ω c ω ) κ 2 + κ s 2 i ( ω c ω ) + κ 2 + κ s 2 .
1 2 ( | R + | L ) ( | + | ) 1 2 e i φ 0 [ ( | R + e i Δ φ | L ) | + ( e i Δ φ | R + | L ) | ] ,
| Φ + P S A B = 1 2 ( | R R + | L L ) P A B ( | a 1 b 1 + | a 2 b 2 ) S A B .
| ϕ ± P A B = 1 2 ( | R R ± | L L ) P A B , | ψ ± P A B = 1 2 ( | R L ± | L R ) P A B ,
| ϕ ± S A B = 1 2 ( | a 1 b 1 ± | a 2 b 2 ) S A B , | ψ ± S A B = 1 2 ( | a 1 b 2 ± | a 2 b 1 ) S A B .
( α | R + β | L ) 1 2 ( | + | ) e 2 i φ 0 ( α | R β | L ) 1 2 ( | | ) .
1 2 ( | R + | L ) | 1 2 e i φ 0 ( | R + i | L ) | , 1 2 ( | R + | L ) | 1 2 e i φ 0 ( | R i | L ) | .
| a 1 1 2 ( | c 1 + | c 2 ) , | a 2 1 2 ( | c 1 | c 2 ) , | b 1 1 2 ( | d 1 + | d 2 ) | b 2 1 2 ( | d 1 | d 2 ) ,
| ϕ ± S A B = 1 2 ( | a 1 b 1 + | a 2 b 2 ) S A B | φ + S A B = 1 2 ( | c 1 d 1 + | c 2 d 2 ) S A B , | φ S A B = 1 2 ( | a 1 b 1 + | a 2 b 2 ) S A B | ψ + S A B = 1 2 ( | c 1 d 2 + | c 2 d 1 ) S A B , | ψ + S A B = 1 2 ( | a 1 b 2 + | a 2 b 1 ) S A B | φ S A B = 1 2 ( | c 1 d 1 | c 2 d 2 ) S A B , | ψ S A B = 1 2 ( | a 1 b 2 | a 2 b 1 ) S A B | ψ S A B = 1 2 ( | c 1 d 2 | c 2 d 1 ) S A B .
1 2 ( | R R ± | L L ) ( | + | ) 1 2 e 2 i φ 0 [ ( | R R | L L ) ( | | ) ] , 1 2 ( | R L ± | L R ) ( | + | ) 1 2 e i ( φ 0 + φ h ) [ ( | R L ± | L R ) ( | + | ) ] .
| Φ + P S A B = 1 2 ( | R R + | L L ) P A B ( | a 1 b 1 + | a 2 b 2 ) S A B , | Φ + P S C D = 1 2 ( | R R + | L L ) P C D ( | c 1 d 1 + | c 2 d 2 ) S C D .
| Φ + P S A B | Φ + P S C D = 1 4 [ ( | ϕ + P A D | ϕ + P B C + | ϕ P A D | ϕ P B C + | ψ + P A D | ψ + P B C + | ψ P A D | ψ P B C ) ( | ϕ + S A D | ϕ + S B C + | ϕ S A D | ϕ S B C + | ψ + S A D | ψ + S B C + | ψ S A D | ψ S B C ) ] .
F = [ ( ζ 5 + ξ 5 ) 2 + 22 ɛ 4 ( ζ + ξ ) 2 + 4 ɛ ( ζ 4 ξ 4 ) 2 + 16 ɛ 3 ( ζ 2 ξ 2 ) 2 + 9 ɛ 2 ( ζ 3 + ξ 3 ) 2 ] 2 ( ζ 10 + ξ 10 ) 2 + 22 ɛ 8 ( ζ 2 + ξ 2 ) 2 + 4 ɛ 2 ( ζ 8 ξ 8 ) 2 + 16 ɛ 6 ( ζ 4 ξ 4 ) 2 + 9 ɛ 4 ( ζ 6 + ξ 6 ) 2 × 1 128 ,
η = ( 1 2 ζ 4 + 1 2 ξ 4 ) 2 ( 1 2 ζ 2 + 1 2 ξ 2 ) 2 ,

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