Abstract

We construct an error-detected block, assisted by the quantum-dot spins in double-sided optical microcavities. With this block, we propose three error-detected schemes for the deterministic generation, the complete analysis, and the complete nondestructive analysis of hyperentangled Bell states in both the polarization and spatial-mode degrees of freedom of two-photon systems. In these schemes, the errors can be detected, which can improve their fidelities largely, far different from other previous schemes assisted by the interaction between the photon and the QD-cavity system. Our scheme for the deterministic generation of hyperentangled two-photon systems can be performed by repeat until success. These features make our schemes more useful in high-capacity quantum communication with hyperentanglement in the future.

© 2016 Optical Society of America

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Complete hyperentangled-Bell-state analysis for photon systems assisted by quantum-dot spins in optical microcavities

Bao-Cang Ren, Hai-Rui Wei, Ming Hua, Tao Li, and Fu-Guo Deng
Opt. Express 20(22) 24664-24677 (2012)

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2016 (1)

X. H. Li and S. Ghose, “Self-assisted complete maximally hyperentangled state analysis via the cross-Kerr nonlinearity,”Phys. Rev. A 93,022302 (2016).
[Crossref]

2015 (3)

Q. Liu and M. Zhang, “Generation and complete nondestructive analysis of hyperentanglement assisted by nitrogen-vacancy centers in resonators,”Phys. Rev. A 91,062321 (2015).
[Crossref]

D. Bhatti, J. von Zanthier, and G. S. Agarwal, “Entanglement of polarization and orbital angular momentum,”Phys. Rev. A 91,062303 (2015).
[Crossref]

Y. B. Sheng and L. Zhou, “Two-step complete polarization logic Bell-state analysis,”Sci. Rep. 5,13453 (2015).
[Crossref] [PubMed]

2014 (1)

B. C. Ren and F. G. Deng, “Hyper-parallel photonic quantum computation with coupled quantum dots,”Sci. Rep. 4,4623 (2014).
[Crossref] [PubMed]

2012 (5)

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

I. J. Luxmoore, E. D. Ahmadi, B. J. Luxmoore, N. A. Wasley, A. I. Tartakovskii, M. Hugues, M. S. Skolnick, and A. M. Fox, “Restoring mode degeneracy in H1 photonic crystal cavities by uniaxial strain tuning,”Appl. Phys. Lett. 100,121116 (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]

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] [PubMed]

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]

2011 (5)

C. Bonato, E. van Nieuwenburg, J. Gudat, S. Thon, H. Kim, M. P. van Exter, and D. Bouwmeester, “Strain tuning of quantum dot optical transitions via laser-induced surface defects,”Phys. Rev. B 84,075306 (2011).
[Crossref]

Y. Eto, A. Noguchi, P. Zhang, M. Ueda, and M. Kozuma, “Projective measurement of a single nuclear spin qubit by using two-mode cavity QED,”Phys. Rev. Lett. 106,160501 (2011).
[Crossref] [PubMed]

M. J. Kastoryano, F. Reiter, and A. S. Sørensen, “Dissipative preparation of entanglement in optical cavities,”Phys. Rev. Lett. 106,090502 (2011).
[Crossref] [PubMed]

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]

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]

2010 (2)

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

2009 (6)

M. M. Wilde and D. B. Uskov, “Linear-optical hyperentanglement-assisted quantum error-correcting code,”Phys. Rev. A 79,022305 (2009).
[Crossref]

A. Rossi, G. Vallone, A. Chiuri, F. De Martini, and P. Mataloni, “Multipath entanglement of two photons,”Phys. Rev. Lett. 102,153902 (2009).
[Crossref] [PubMed]

G. Vallone, R. Ceccarelli, F. De Martini, and P. Mataloni, “Hyperentanglement of two photons in three degrees of freedom,”Phys. Rev. A 79,030301 (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]

J. H. An, M. Feng, and C. H. Oh, “Quantum-information processing with a single photon by an input-output process with respect to low-Q cavities,”Phys. Rev. A 79,032303 (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] [PubMed]

2008 (6)

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 451,441 (2008).
[Crossref] [PubMed]

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]

J. Berezovsky, M. H. Mikkelsen, N. G. Stoltz, L. A. Coldren, and D. D. Awschalom, “Picosecond coherent optical manipulation of a single electron spin in a quantum dot,”Science 320,349 (2008).
[Crossref] [PubMed]

D. Press, T. D. Ladd, B. Y. Zhang, and Y. Yamamoto, “Complete quantum control of a single quantum dot spin using ultrafast optical pulses,”Nature 456,218 (2008).
[Crossref] [PubMed]

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. B 78,085307 (2008).
[Crossref]

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]

2007 (2)

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]

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. B 76,241306 (2007).
[Crossref]

2006 (5)

M. Atatüre, J. Dreiser, A. Badolato, A. Högele, K. Karrai, and A. Imamoglu, “Quantum-dot spin-state preparation with near-unity fidelity,”Science 312,551 (2006).
[Crossref] [PubMed]

K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoğlu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,”Appl. Phys. Lett. 89,041118 (2006).
[Crossref]

A. Greilich, D. R. Yakovlev, A. Shabaev, A. L. Efros, I. A. Yugova, R. Oulton, V. Stavarache, D. Reuter, A. Wieck, and M. Bayer, “Mode locking of electron spin coherences in singly charged quantum dots,”Science 313,341 (2006).
[Crossref] [PubMed]

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)

S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,”Phys. Rev. A 71,060302 (2005).
[Crossref]

J. R. Petta, A. C. Johnson, J. M. Taylor, E. A. Laird, A. Yacoby, M. D. Lukin, C. M. Marcus, M. P. Hanson, and A. C. Gossard, “Coherent manipulation of coupled electron spins in semiconductor quantum dots,”Science 309,2180 (2005).
[Crossref] [PubMed]

M. Barbieri, C. Cinelli, P. Mataloni, and F. De Martini, “Polarization-momentum hyperentangled states: Realization and characterization,”Phys. Rev. A 72,052110 (2005).
[Crossref]

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]

2004 (4)

M. Barbieri, C. Cinelli, F. De Martini, and P. Mataloni, “Generation of (2×2) and (4×4) two-photon states with tunable degree of entanglement and mixedness,”Fortschr. Phys. 52,1102 (2004).
[Crossref]

J. M. Elzerman, R. Hanson, L. H. Willems van Beveren, B. Witkamp, L. M. K. Vandersypen, and L. P. Kouwenhoven, “Single-shot read-out of an individual electron spin in a quantum dot,”Nature 430,431 (2004).
[Crossref] [PubMed]

M. Kroutvar, Y. Ducommun, D. Heiss, M. Bichler, D. Schuh, G. Abstreiter, and J. J. Finley, “Optically programmable electron spin memory using semiconductor quantum dots,”Nature 432,81 (2004).
[Crossref] [PubMed]

W. Langbein, P. Borri, U. Woggon, V. Stavarache, D. Reuter, and A. D. Wieck, “Radiatively limited dephasing in InAs quantum dots,”Phys. Rev. B 70,033301 (2004).
[Crossref]

2003 (3)

G. Bester, S. Nair, and A. Zunger, “Pseudopotential calculation of the excitonic fine structure of million-atom self-assembled In1−x Gax As/Ga As quantum dots,”Phys. Rev. B 67,161306 (2003).
[Crossref]

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]

2002 (3)

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

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

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

2001 (2)

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]

D. Birkedal, K. Leosson, and J. M. Hvam, “Long lived coherence in self-assembled quantum dots,”Phys. Rev. Lett. 87,227401 (2001).
[Crossref] [PubMed]

1999 (3)

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

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]

1998 (1)

P. G. Kwiat and H. Weinfurter, “Embedded Bell-state analysis,”Phys. Rev. A 58,R2623–R2626 (1998).
[Crossref]

1996 (1)

K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,”Phys. Rev. Lett. 76,4656–4659 (1996).
[Crossref] [PubMed]

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 (1993).
[Crossref] [PubMed]

1992 (1)

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

1991 (1)

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

Abstreiter, G.

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. B 76,241306 (2007).
[Crossref]

M. Kroutvar, Y. Ducommun, D. Heiss, M. Bichler, D. Schuh, G. Abstreiter, and J. J. Finley, “Optically programmable electron spin memory using semiconductor quantum dots,”Nature 432,81 (2004).
[Crossref] [PubMed]

Agarwal, G. S.

D. Bhatti, J. von Zanthier, and G. S. Agarwal, “Entanglement of polarization and orbital angular momentum,”Phys. Rev. A 91,062303 (2015).
[Crossref]

Ahmadi, E. D.

I. J. Luxmoore, E. D. Ahmadi, B. J. Luxmoore, N. A. Wasley, A. I. Tartakovskii, M. Hugues, M. S. Skolnick, and A. M. Fox, “Restoring mode degeneracy in H1 photonic crystal cavities by uniaxial strain tuning,”Appl. Phys. Lett. 100,121116 (2012).
[Crossref]

An, J. H.

J. H. An, M. Feng, and C. H. Oh, “Quantum-information processing with a single photon by an input-output process with respect to low-Q cavities,”Phys. Rev. A 79,032303 (2009).
[Crossref]

Aolita, L.

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

Atatüre, M.

M. Atatüre, J. Dreiser, A. Badolato, A. Högele, K. Karrai, and A. Imamoglu, “Quantum-dot spin-state preparation with near-unity fidelity,”Science 312,551 (2006).
[Crossref] [PubMed]

Awschalom, D. D.

J. Berezovsky, M. H. Mikkelsen, N. G. Stoltz, L. A. Coldren, and D. D. Awschalom, “Picosecond coherent optical manipulation of a single electron spin in a quantum dot,”Science 320,349 (2008).
[Crossref] [PubMed]

Badolato, A.

M. Atatüre, J. Dreiser, A. Badolato, A. Högele, K. Karrai, and A. Imamoglu, “Quantum-dot spin-state preparation with near-unity fidelity,”Science 312,551 (2006).
[Crossref] [PubMed]

K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoğlu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,”Appl. Phys. Lett. 89,041118 (2006).
[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]

M. Barbieri, C. Cinelli, P. Mataloni, and F. De Martini, “Polarization-momentum hyperentangled states: Realization and characterization,”Phys. Rev. A 72,052110 (2005).
[Crossref]

M. Barbieri, C. Cinelli, F. De Martini, and P. Mataloni, “Generation of (2×2) and (4×4) two-photon states with tunable degree of entanglement and mixedness,”Fortschr. Phys. 52,1102 (2004).
[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]

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]

Barrett, S. D.

S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,”Phys. Rev. A 71,060302 (2005).
[Crossref]

Bayer, M.

A. Greilich, D. R. Yakovlev, A. Shabaev, A. L. Efros, I. A. Yugova, R. Oulton, V. Stavarache, D. Reuter, A. Wieck, and M. Bayer, “Mode locking of electron spin coherences in singly charged quantum dots,”Science 313,341 (2006).
[Crossref] [PubMed]

Beausoleil, R. G.

S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,”Phys. Rev. A 71,060302 (2005).
[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 (1993).
[Crossref] [PubMed]

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

Berezovsky, J.

J. Berezovsky, M. H. Mikkelsen, N. G. Stoltz, L. A. Coldren, and D. D. Awschalom, “Picosecond coherent optical manipulation of a single electron spin in a quantum dot,”Science 320,349 (2008).
[Crossref] [PubMed]

Berthiaume, A.

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

Bester, G.

G. Bester, S. Nair, and A. Zunger, “Pseudopotential calculation of the excitonic fine structure of million-atom self-assembled In1−x Gax As/Ga As quantum dots,”Phys. Rev. B 67,161306 (2003).
[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] [PubMed]

Bhatti, D.

D. Bhatti, J. von Zanthier, and G. S. Agarwal, “Entanglement of polarization and orbital angular momentum,”Phys. Rev. A 91,062303 (2015).
[Crossref]

Bichler, M.

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. B 76,241306 (2007).
[Crossref]

M. Kroutvar, Y. Ducommun, D. Heiss, M. Bichler, D. Schuh, G. Abstreiter, and J. J. Finley, “Optically programmable electron spin memory using semiconductor quantum dots,”Nature 432,81 (2004).
[Crossref] [PubMed]

Bimberg, D.

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]

Birkedal, D.

D. Birkedal, K. Leosson, and J. M. Hvam, “Long lived coherence in self-assembled quantum dots,”Phys. Rev. Lett. 87,227401 (2001).
[Crossref] [PubMed]

Bonato, C.

C. Bonato, E. van Nieuwenburg, J. Gudat, S. Thon, H. Kim, M. P. van Exter, and D. Bouwmeester, “Strain tuning of quantum dot optical transitions via laser-induced surface defects,”Phys. Rev. B 84,075306 (2011).
[Crossref]

Borri, P.

W. Langbein, P. Borri, U. Woggon, V. Stavarache, D. Reuter, and A. D. Wieck, “Radiatively limited dephasing in InAs quantum dots,”Phys. Rev. B 70,033301 (2004).
[Crossref]

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]

Bouwmeester, D.

C. Bonato, E. van Nieuwenburg, J. Gudat, S. Thon, H. Kim, M. P. van Exter, and D. Bouwmeester, “Strain tuning of quantum dot optical transitions via laser-induced surface defects,”Phys. Rev. B 84,075306 (2011).
[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 (1993).
[Crossref] [PubMed]

Brunner, 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).
[Crossref] [PubMed]

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 451,441 (2008).
[Crossref] [PubMed]

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] [PubMed]

Bulaev, D. V.

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. B 76,241306 (2007).
[Crossref]

Bužek, V.

M. Hillery, V. Bužek, and A. Berthiaume, “Quantum secret sharing,”Phys. Rev. A 59,1829 (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]

Ceccarelli, R.

G. Vallone, R. Ceccarelli, F. De Martini, and P. Mataloni, “Hyperentanglement of two photons in three degrees of freedom,”Phys. Rev. A 79,030301 (2009).
[Crossref]

Chang, D. E.

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

Chiuri, A.

A. Rossi, G. Vallone, A. Chiuri, F. De Martini, and P. Mataloni, “Multipath entanglement of two photons,”Phys. Rev. Lett. 102,153902 (2009).
[Crossref] [PubMed]

Chuang, I. L.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University,2000).

Cinelli, C.

M. Barbieri, C. Cinelli, P. Mataloni, and F. De Martini, “Polarization-momentum hyperentangled states: Realization and characterization,”Phys. Rev. A 72,052110 (2005).
[Crossref]

M. Barbieri, C. Cinelli, F. De Martini, and P. Mataloni, “Generation of (2×2) and (4×4) two-photon states with tunable degree of entanglement and mixedness,”Fortschr. Phys. 52,1102 (2004).
[Crossref]

Coldren, L. A.

J. Berezovsky, M. H. Mikkelsen, N. G. Stoltz, L. A. Coldren, and D. D. Awschalom, “Picosecond coherent optical manipulation of a single electron spin in a quantum dot,”Science 320,349 (2008).
[Crossref] [PubMed]

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 (1993).
[Crossref] [PubMed]

Dalgarno, P. A.

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] [PubMed]

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 451,441 (2008).
[Crossref] [PubMed]

De Martini, F.

A. Rossi, G. Vallone, A. Chiuri, F. De Martini, and P. Mataloni, “Multipath entanglement of two photons,”Phys. Rev. Lett. 102,153902 (2009).
[Crossref] [PubMed]

G. Vallone, R. Ceccarelli, F. De Martini, and P. Mataloni, “Hyperentanglement of two photons in three degrees of freedom,”Phys. Rev. A 79,030301 (2009).
[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]

M. Barbieri, C. Cinelli, P. Mataloni, and F. De Martini, “Polarization-momentum hyperentangled states: Realization and characterization,”Phys. Rev. A 72,052110 (2005).
[Crossref]

M. Barbieri, C. Cinelli, F. De Martini, and P. Mataloni, “Generation of (2×2) and (4×4) two-photon states with tunable degree of entanglement and mixedness,”Fortschr. Phys. 52,1102 (2004).
[Crossref]

Deng, F. G.

B. C. Ren and F. G. Deng, “Hyper-parallel photonic quantum computation with coupled quantum dots,”Sci. Rep. 4,4623 (2014).
[Crossref] [PubMed]

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] [PubMed]

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

Dreiser, J.

M. Atatüre, J. Dreiser, A. Badolato, A. Högele, K. Karrai, and A. Imamoglu, “Quantum-dot spin-state preparation with near-unity fidelity,”Science 312,551 (2006).
[Crossref] [PubMed]

Ducommun, Y.

M. Kroutvar, Y. Ducommun, D. Heiss, M. Bichler, D. Schuh, G. Abstreiter, and J. J. Finley, “Optically programmable electron spin memory using semiconductor quantum dots,”Nature 432,81 (2004).
[Crossref] [PubMed]

Efros, A. L.

A. Greilich, D. R. Yakovlev, A. Shabaev, A. L. Efros, I. A. Yugova, R. Oulton, V. Stavarache, D. Reuter, A. Wieck, and M. Bayer, “Mode locking of electron spin coherences in singly charged quantum dots,”Science 313,341 (2006).
[Crossref] [PubMed]

Ekert, A. K.

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

Elzerman, J. M.

J. M. Elzerman, R. Hanson, L. H. Willems van Beveren, B. Witkamp, L. M. K. Vandersypen, and L. P. Kouwenhoven, “Single-shot read-out of an individual electron spin in a quantum dot,”Nature 430,431 (2004).
[Crossref] [PubMed]

Eto, Y.

Y. Eto, A. Noguchi, P. Zhang, M. Ueda, and M. Kozuma, “Projective measurement of a single nuclear spin qubit by using two-mode cavity QED,”Phys. Rev. Lett. 106,160501 (2011).
[Crossref] [PubMed]

Feng, M.

J. H. An, M. Feng, and C. H. Oh, “Quantum-information processing with a single photon by an input-output process with respect to low-Q cavities,”Phys. Rev. A 79,032303 (2009).
[Crossref]

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. B 76,241306 (2007).
[Crossref]

M. Kroutvar, Y. Ducommun, D. Heiss, M. Bichler, D. Schuh, G. Abstreiter, and J. J. Finley, “Optically programmable electron spin memory using semiconductor quantum dots,”Nature 432,81 (2004).
[Crossref] [PubMed]

Fox, A. M.

I. J. Luxmoore, E. D. Ahmadi, B. J. Luxmoore, N. A. Wasley, A. I. Tartakovskii, M. Hugues, M. S. Skolnick, and A. M. Fox, “Restoring mode degeneracy in H1 photonic crystal cavities by uniaxial strain tuning,”Appl. Phys. Lett. 100,121116 (2012).
[Crossref]

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).
[Crossref] [PubMed]

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 451,441 (2008).
[Crossref] [PubMed]

Ghose, S.

X. H. Li and S. Ghose, “Self-assisted complete maximally hyperentangled state analysis via the cross-Kerr nonlinearity,”Phys. Rev. A 93,022302 (2016).
[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] [PubMed]

Gossard, A. C.

J. R. Petta, A. C. Johnson, J. M. Taylor, E. A. Laird, A. Yacoby, M. D. Lukin, C. M. Marcus, M. P. Hanson, and A. C. Gossard, “Coherent manipulation of coupled electron spins in semiconductor quantum dots,”Science 309,2180 (2005).
[Crossref] [PubMed]

Greilich, A.

A. Greilich, D. R. Yakovlev, A. Shabaev, A. L. Efros, I. A. Yugova, R. Oulton, V. Stavarache, D. Reuter, A. Wieck, and M. Bayer, “Mode locking of electron spin coherences in singly charged quantum dots,”Science 313,341 (2006).
[Crossref] [PubMed]

Gudat, J.

C. Bonato, E. van Nieuwenburg, J. Gudat, S. Thon, H. Kim, M. P. van Exter, and D. Bouwmeester, “Strain tuning of quantum dot optical transitions via laser-induced surface defects,”Phys. Rev. B 84,075306 (2011).
[Crossref]

Hanson, M. P.

J. R. Petta, A. C. Johnson, J. M. Taylor, E. A. Laird, A. Yacoby, M. D. Lukin, C. M. Marcus, M. P. Hanson, and A. C. Gossard, “Coherent manipulation of coupled electron spins in semiconductor quantum dots,”Science 309,2180 (2005).
[Crossref] [PubMed]

Hanson, R.

J. M. Elzerman, R. Hanson, L. H. Willems van Beveren, B. Witkamp, L. M. K. Vandersypen, and L. P. Kouwenhoven, “Single-shot read-out of an individual electron spin in a quantum dot,”Nature 430,431 (2004).
[Crossref] [PubMed]

Heiss, D.

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. B 76,241306 (2007).
[Crossref]

M. Kroutvar, Y. Ducommun, D. Heiss, M. Bichler, D. Schuh, G. Abstreiter, and J. J. Finley, “Optically programmable electron spin memory using semiconductor quantum dots,”Nature 432,81 (2004).
[Crossref] [PubMed]

Hennessy, K.

K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoğlu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,”Appl. Phys. Lett. 89,041118 (2006).
[Crossref]

Hillery, M.

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

Högele, A.

M. Atatüre, J. Dreiser, A. Badolato, A. Högele, K. Karrai, and A. Imamoglu, “Quantum-dot spin-state preparation with near-unity fidelity,”Science 312,551 (2006).
[Crossref] [PubMed]

Högerle, C.

K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoğlu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,”Appl. Phys. Lett. 89,041118 (2006).
[Crossref]

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).
[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]

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. 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]

Hu, E.

K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoğlu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,”Appl. Phys. Lett. 89,041118 (2006).
[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] [PubMed]

Huebl, H.

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. B 76,241306 (2007).
[Crossref]

Hugues, M.

I. J. Luxmoore, E. D. Ahmadi, B. J. Luxmoore, N. A. Wasley, A. I. Tartakovskii, M. Hugues, M. S. Skolnick, and A. M. Fox, “Restoring mode degeneracy in H1 photonic crystal cavities by uniaxial strain tuning,”Appl. Phys. Lett. 100,121116 (2012).
[Crossref]

Hvam, J. M.

D. Birkedal, K. Leosson, and J. M. Hvam, “Long lived coherence in self-assembled quantum dots,”Phys. Rev. Lett. 87,227401 (2001).
[Crossref] [PubMed]

Imamoglu, A.

M. Atatüre, J. Dreiser, A. Badolato, A. Högele, K. Karrai, and A. Imamoglu, “Quantum-dot spin-state preparation with near-unity fidelity,”Science 312,551 (2006).
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J. Berezovsky, M. H. Mikkelsen, N. G. Stoltz, L. A. Coldren, and D. D. Awschalom, “Picosecond coherent optical manipulation of a single electron spin in a quantum dot,”Science 320,349 (2008).
[Crossref] [PubMed]

Suominen, K. A.

N. Lütkenhaus, J. Calsamiglia, and K. A. Suominen, “Bell measurements for teleportation,”Phys. Rev. A 59,3295–3300 (1999).
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I. J. Luxmoore, E. D. Ahmadi, B. J. Luxmoore, N. A. Wasley, A. I. Tartakovskii, M. Hugues, M. S. Skolnick, and A. M. Fox, “Restoring mode degeneracy in H1 photonic crystal cavities by uniaxial strain tuning,”Appl. Phys. Lett. 100,121116 (2012).
[Crossref]

Taylor, J. M.

J. R. Petta, A. C. Johnson, J. M. Taylor, E. A. Laird, A. Yacoby, M. D. Lukin, C. M. Marcus, M. P. Hanson, and A. C. Gossard, “Coherent manipulation of coupled electron spins in semiconductor quantum dots,”Science 309,2180 (2005).
[Crossref] [PubMed]

Thon, S.

C. Bonato, E. van Nieuwenburg, J. Gudat, S. Thon, H. Kim, M. P. van Exter, and D. Bouwmeester, “Strain tuning of quantum dot optical transitions via laser-induced surface defects,”Phys. Rev. B 84,075306 (2011).
[Crossref]

Tong, D. M.

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

Ueda, M.

Y. Eto, A. Noguchi, P. Zhang, M. Ueda, and M. Kozuma, “Projective measurement of a single nuclear spin qubit by using two-mode cavity QED,”Phys. Rev. Lett. 106,160501 (2011).
[Crossref] [PubMed]

Uskov, D. B.

M. M. Wilde and D. B. Uskov, “Linear-optical hyperentanglement-assisted quantum error-correcting code,”Phys. Rev. A 79,022305 (2009).
[Crossref]

Vaidman, L.

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

G. Vallone, R. Ceccarelli, F. De Martini, and P. Mataloni, “Hyperentanglement of two photons in three degrees of freedom,”Phys. Rev. A 79,030301 (2009).
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A. Rossi, G. Vallone, A. Chiuri, F. De Martini, and P. Mataloni, “Multipath entanglement of two photons,”Phys. Rev. Lett. 102,153902 (2009).
[Crossref] [PubMed]

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]

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C. Bonato, E. van Nieuwenburg, J. Gudat, S. Thon, H. Kim, M. P. van Exter, and D. Bouwmeester, “Strain tuning of quantum dot optical transitions via laser-induced surface defects,”Phys. Rev. B 84,075306 (2011).
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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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van Nieuwenburg, E.

C. Bonato, E. van Nieuwenburg, J. Gudat, S. Thon, H. Kim, M. P. van Exter, and D. Bouwmeester, “Strain tuning of quantum dot optical transitions via laser-induced surface defects,”Phys. Rev. B 84,075306 (2011).
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Vandersypen, L. M. K.

J. M. Elzerman, R. Hanson, L. H. Willems van Beveren, B. Witkamp, L. M. K. Vandersypen, and L. P. Kouwenhoven, “Single-shot read-out of an individual electron spin in a quantum dot,”Nature 430,431 (2004).
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D. Bhatti, J. von Zanthier, and G. S. Agarwal, “Entanglement of polarization and orbital angular momentum,”Phys. Rev. A 91,062303 (2015).
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S. P. Walborn, S. Pádua, and C. H. Monken, “Hyperentanglement-assisted Bell-state analysis,”Phys. Rev. A 68,042313 (2003).
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Wang, C.

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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Wang, T. J.

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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Warburton, R. J.

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. 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 (2008).
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Wasley, N. A.

I. J. Luxmoore, E. D. Ahmadi, B. J. Luxmoore, N. A. Wasley, A. I. Tartakovskii, M. Hugues, M. S. Skolnick, and A. M. Fox, “Restoring mode degeneracy in H1 photonic crystal cavities by uniaxial strain tuning,”Appl. Phys. Lett. 100,121116 (2012).
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Wei, H. R.

Wei, T. C.

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).
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A. Greilich, D. R. Yakovlev, A. Shabaev, A. L. Efros, I. A. Yugova, R. Oulton, V. Stavarache, D. Reuter, A. Wieck, and M. Bayer, “Mode locking of electron spin coherences in singly charged quantum dots,”Science 313,341 (2006).
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Wieck, A. D.

W. Langbein, P. Borri, U. Woggon, V. Stavarache, D. Reuter, and A. D. Wieck, “Radiatively limited dephasing in InAs quantum dots,”Phys. Rev. B 70,033301 (2004).
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Wiesner, S. J.

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

M. M. Wilde and D. B. Uskov, “Linear-optical hyperentanglement-assisted quantum error-correcting code,”Phys. Rev. A 79,022305 (2009).
[Crossref]

Willems van Beveren, L. H.

J. M. Elzerman, R. Hanson, L. H. Willems van Beveren, B. Witkamp, L. M. K. Vandersypen, and L. P. Kouwenhoven, “Single-shot read-out of an individual electron spin in a quantum dot,”Nature 430,431 (2004).
[Crossref] [PubMed]

Witkamp, B.

J. M. Elzerman, R. Hanson, L. H. Willems van Beveren, B. Witkamp, L. M. K. Vandersypen, and L. P. Kouwenhoven, “Single-shot read-out of an individual electron spin in a quantum dot,”Nature 430,431 (2004).
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Woggon, U.

W. Langbein, P. Borri, U. Woggon, V. Stavarache, D. Reuter, and A. D. Wieck, “Radiatively limited dephasing in InAs quantum dots,”Phys. Rev. B 70,033301 (2004).
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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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Wootters, W. K.

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 (1993).
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Wüst, G.

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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Yacoby, A.

J. R. Petta, A. C. Johnson, J. M. Taylor, E. A. Laird, A. Yacoby, M. D. Lukin, C. M. Marcus, M. P. Hanson, and A. C. Gossard, “Coherent manipulation of coupled electron spins in semiconductor quantum dots,”Science 309,2180 (2005).
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Yakovlev, D. R.

A. Greilich, D. R. Yakovlev, A. Shabaev, A. L. Efros, I. A. Yugova, R. Oulton, V. Stavarache, D. Reuter, A. Wieck, and M. Bayer, “Mode locking of electron spin coherences in singly charged quantum dots,”Science 313,341 (2006).
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Yamamoto, Y.

D. Press, T. D. Ladd, B. Y. Zhang, and Y. Yamamoto, “Complete quantum control of a single quantum dot spin using ultrafast optical pulses,”Nature 456,218 (2008).
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Yoran, N.

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

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. B 78,085307 (2008).
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Yugova, I. A.

A. Greilich, D. R. Yakovlev, A. Shabaev, A. L. Efros, I. A. Yugova, R. Oulton, V. Stavarache, D. Reuter, A. Wieck, and M. Bayer, “Mode locking of electron spin coherences in singly charged quantum dots,”Science 313,341 (2006).
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Zbinden, H.

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]

Zeilinger, A.

K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,”Phys. Rev. Lett. 76,4656–4659 (1996).
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Zhang, B. Y.

D. Press, T. D. Ladd, B. Y. Zhang, and Y. Yamamoto, “Complete quantum control of a single quantum dot spin using ultrafast optical pulses,”Nature 456,218 (2008).
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Zhang, M.

Q. Liu and M. Zhang, “Generation and complete nondestructive analysis of hyperentanglement assisted by nitrogen-vacancy centers in resonators,”Phys. Rev. A 91,062321 (2015).
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Zhang, P.

Y. Eto, A. Noguchi, P. Zhang, M. Ueda, and M. Kozuma, “Projective measurement of a single nuclear spin qubit by using two-mode cavity QED,”Phys. Rev. Lett. 106,160501 (2011).
[Crossref] [PubMed]

Zhang, Y.

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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Zhou, L.

Y. B. Sheng and L. Zhou, “Two-step complete polarization logic Bell-state analysis,”Sci. Rep. 5,13453 (2015).
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Zunger, A.

G. Bester, S. Nair, and A. Zunger, “Pseudopotential calculation of the excitonic fine structure of million-atom self-assembled In1−x Gax As/Ga As quantum dots,”Phys. Rev. B 67,161306 (2003).
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Appl. Phys. Lett. (2)

I. J. Luxmoore, E. D. Ahmadi, B. J. Luxmoore, N. A. Wasley, A. I. Tartakovskii, M. Hugues, M. S. Skolnick, and A. M. Fox, “Restoring mode degeneracy in H1 photonic crystal cavities by uniaxial strain tuning,”Appl. Phys. Lett. 100,121116 (2012).
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K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoğlu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,”Appl. Phys. Lett. 89,041118 (2006).
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Fortschr. Phys. (1)

M. Barbieri, C. Cinelli, F. De Martini, and P. Mataloni, “Generation of (2×2) and (4×4) two-photon states with tunable degree of entanglement and mixedness,”Fortschr. Phys. 52,1102 (2004).
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Nat. Phys. (1)

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]

Nature (4)

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 451,441 (2008).
[Crossref] [PubMed]

J. M. Elzerman, R. Hanson, L. H. Willems van Beveren, B. Witkamp, L. M. K. Vandersypen, and L. P. Kouwenhoven, “Single-shot read-out of an individual electron spin in a quantum dot,”Nature 430,431 (2004).
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M. Kroutvar, Y. Ducommun, D. Heiss, M. Bichler, D. Schuh, G. Abstreiter, and J. J. Finley, “Optically programmable electron spin memory using semiconductor quantum dots,”Nature 432,81 (2004).
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D. Press, T. D. Ladd, B. Y. Zhang, and Y. Yamamoto, “Complete quantum control of a single quantum dot spin using ultrafast optical pulses,”Nature 456,218 (2008).
[Crossref] [PubMed]

Opt. Express (1)

Phys. Rev. A (23)

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]

Q. Liu and M. Zhang, “Generation and complete nondestructive analysis of hyperentanglement assisted by nitrogen-vacancy centers in resonators,”Phys. Rev. A 91,062321 (2015).
[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]

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]

G. Vallone, R. Ceccarelli, F. De Martini, and P. Mataloni, “Hyperentanglement of two photons in three degrees of freedom,”Phys. Rev. A 79,030301 (2009).
[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]

X. H. Li and S. Ghose, “Self-assisted complete maximally hyperentangled state analysis via the cross-Kerr nonlinearity,”Phys. Rev. A 93,022302 (2016).
[Crossref]

M. M. Wilde and D. B. Uskov, “Linear-optical hyperentanglement-assisted quantum error-correcting code,”Phys. Rev. A 79,022305 (2009).
[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]

M. Barbieri, C. Cinelli, P. Mataloni, and F. De Martini, “Polarization-momentum hyperentangled states: Realization and characterization,”Phys. Rev. A 72,052110 (2005).
[Crossref]

D. Bhatti, J. von Zanthier, and G. S. Agarwal, “Entanglement of polarization and orbital angular momentum,”Phys. Rev. A 91,062303 (2015).
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M. Hillery, V. Bužek, and A. Berthiaume, “Quantum secret sharing,”Phys. Rev. A 59,1829 (1999).
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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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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]

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]

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

X. S. Liu, G. L. Long, D. M. Tong, and F. Li, “General scheme for superdense coding between multiparties,”Phys. Rev. A 65,022304 (2002).
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S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,”Phys. Rev. A 71,060302 (2005).
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P. G. Kwiat and H. Weinfurter, “Embedded Bell-state analysis,”Phys. Rev. A 58,R2623–R2626 (1998).
[Crossref]

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

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

J. H. An, M. Feng, and C. H. Oh, “Quantum-information processing with a single photon by an input-output process with respect to low-Q cavities,”Phys. Rev. A 79,032303 (2009).
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Phys. Rev. B (8)

W. Langbein, P. Borri, U. Woggon, V. Stavarache, D. Reuter, and A. D. Wieck, “Radiatively limited dephasing in InAs quantum dots,”Phys. Rev. B 70,033301 (2004).
[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. B 76,241306 (2007).
[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. B 78,085307 (2008).
[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).
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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).
[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]

G. Bester, S. Nair, and A. Zunger, “Pseudopotential calculation of the excitonic fine structure of million-atom self-assembled In1−x Gax As/Ga As quantum dots,”Phys. Rev. B 67,161306 (2003).
[Crossref]

C. Bonato, E. van Nieuwenburg, J. Gudat, S. Thon, H. Kim, M. P. van Exter, and D. Bouwmeester, “Strain tuning of quantum dot optical transitions via laser-induced surface defects,”Phys. Rev. B 84,075306 (2011).
[Crossref]

Phys. Rev. Lett. (13)

Y. Eto, A. Noguchi, P. Zhang, M. Ueda, and M. Kozuma, “Projective measurement of a single nuclear spin qubit by using two-mode cavity QED,”Phys. Rev. Lett. 106,160501 (2011).
[Crossref] [PubMed]

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]

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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M. J. Kastoryano, F. Reiter, and A. S. Sørensen, “Dissipative preparation of entanglement in optical cavities,”Phys. Rev. Lett. 106,090502 (2011).
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Y. Li, L. Aolita, D. E. Chang, and L. C. Kwek, “Robust-fidelity atom-photon entangling gates in the weak-coupling regime,”Phys. Rev. Lett. 109,160504 (2012).
[Crossref] [PubMed]

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

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

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 (1993).
[Crossref] [PubMed]

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

K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,”Phys. Rev. Lett. 76,4656–4659 (1996).
[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]

A. Rossi, G. Vallone, A. Chiuri, F. De Martini, and P. Mataloni, “Multipath entanglement of two photons,”Phys. Rev. Lett. 102,153902 (2009).
[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]

Sci. Rep. (2)

Y. B. Sheng and L. Zhou, “Two-step complete polarization logic Bell-state analysis,”Sci. Rep. 5,13453 (2015).
[Crossref] [PubMed]

B. C. Ren and F. G. Deng, “Hyper-parallel photonic quantum computation with coupled quantum dots,”Sci. Rep. 4,4623 (2014).
[Crossref] [PubMed]

Science (5)

M. Atatüre, J. Dreiser, A. Badolato, A. Högele, K. Karrai, and A. Imamoglu, “Quantum-dot spin-state preparation with near-unity fidelity,”Science 312,551 (2006).
[Crossref] [PubMed]

J. Berezovsky, M. H. Mikkelsen, N. G. Stoltz, L. A. Coldren, and D. D. Awschalom, “Picosecond coherent optical manipulation of a single electron spin in a quantum dot,”Science 320,349 (2008).
[Crossref] [PubMed]

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] [PubMed]

J. R. Petta, A. C. Johnson, J. M. Taylor, E. A. Laird, A. Yacoby, M. D. Lukin, C. M. Marcus, M. P. Hanson, and A. C. Gossard, “Coherent manipulation of coupled electron spins in semiconductor quantum dots,”Science 309,2180 (2005).
[Crossref] [PubMed]

A. Greilich, D. R. Yakovlev, A. Shabaev, A. L. Efros, I. A. Yugova, R. Oulton, V. Stavarache, D. Reuter, A. Wieck, and M. Bayer, “Mode locking of electron spin coherences in singly charged quantum dots,”Science 313,341 (2006).
[Crossref] [PubMed]

Other (2)

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University,2000).

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

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Figures (8)

Fig. 1
Fig. 1 (a) A schematic diagram for a singly charged QD inside a double-sided optical microcavity. (b) Schematic description of the relevant exciton energy levels and the spin selection rules for optical transition of negatively charged excitons. |R〉 (|R〉) and |L〉 (|L〉) represent the right-circularly polarized photon and the left-circularly polarized photon propagating along (against) the normal direction of the cavity Z axis (the quantization axis), respectively.
Fig. 2
Fig. 2 Schematic diagram of the error-detected block. BS is a 50 : 50 beam splitter which performs the spatial-mode Hadamard operation [ | i 1 1 2 ( | j 1 + | j 2 ) , | i 2 1 2 ( | j 1 | j 2 ) ] on the photon. H pi (i = 1, 2) is a half-wave plate which performs the polarization Hadamard operation [ | R 1 2 ( | R + | L ) , | L 1 2 ( | R | L ) ] on the photon. M i (i = 1, 2) is a mirror. D is a single-photon detector.
Fig. 3
Fig. 3 (a) The blue solid line and the red dashed line are the reflection coefficient |D| of the error-detected block vs the normalized coupling strength g/κ for the leakage rates κs = 0.1κ and κs = 0.2κ, respectively. (b) The blue solid line and the red dashed line are the transmission coefficient |T| of the error-heralded block vs g/κ for κs = 0.1κ and κs = 0.2κ, respectively. γ = 0.1κ, which is experimentally achievable, and ω = ωc = ωX− are taken here.
Fig. 4
Fig. 4 Schematic diagram for two-photon polarization-spatial HBSG. CPBS i (i = 1, 2, 3) is a circularly polarized beam splitter which transmits the photon in the left-circular polarization |L〉 and reflects the photon in the right-circular polarization |R〉, respectively. X i (i = 1, 2, 3) is a half-wave plate which performs a polarization bit-flip operation σ x p = | R L | + | L R | on the photon.
Fig. 5
Fig. 5 Schematic diagram of the complete polarization-spatial HBSA. D i (i = 1, 2, 3), D Li (i = 1, 2) and D Ri (i = 1, 2) are single-photon detectors. SW is an optical switch which lets the wave-packets of a photon in different spatial-mode pass into and out of the error-detected block sequentially.
Fig. 6
Fig. 6 Schematic diagram of the complete nondestructive polarization-spatial HBSA.
Fig. 7
Fig. 7 The performance of our deterministic HBSG scheme. The bule dashed line, the red solid line, and the black solid line describe the performance of our deterministic HBSG scheme for generating hyperentangled Bell states |ϕ+ P |ϕ+ S , |ϕ P |ψ+ S , |ψ+ P |ϕ S , and |ψ P |ψ S , respectively. (a) The fidelities of our deterministic HBSG scheme. (b) The efficiencies of our deterministic HBSG. γ = 0.1κ and κs = 0.2κ, which are experimentally achievable, are taken here.
Fig. 8
Fig. 8 The performance of our complete HBSA scheme and complete nondestructive HBSA scheme for the hyperentangled Bell state |ϕ+ P |ϕ+ S . The blue solid line and the red dashed line describe the performance of our complete HBSA and complete nondestructive HBSA schemes, respectively. (a) The fidelities of our complete HBSA scheme and complete nondestructive HBSA scheme. (b) The efficiencies of our complete HBSA scheme and complete nondestructive HBSA scheme. γ = 0.1κ and κs = 0.2κ, which are experimentally achievable, are taken here.

Tables (2)

Tables Icon

Table 1 The relationship between the measurement outcomes of the states of the two-photon systems in the polarization and spatial-mode DOFs and the two QDs and the initial hyperentangled states of the two-photon system |Ψ〉 PS .

Tables Icon

Table 2 The relationship between the measurement outcomes of the states of the four QDs and the initial hyperentangled states of the two-photon system |Ψ PS .

Equations (20)

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d a ^ d t = [ i ( ω c ω ) + κ + κ s 2 ] a ^ g σ κ a ^ i n κ a ^ i n + H ^ , d σ d t = [ i ( ω X ω ) + γ 2 ] σ g σ z a ^ + G ^ , a ^ r = a ^ i n + κ a ^ , a ^ t = a ^ i n + κ a ^ ,
r ( ω ) = 1 + t ( ω ) , t ( ω ) = κ [ i ( ω X ω ) + γ 2 ] [ i ( ω X ω ) + γ 2 ] [ i ( ω c ω ) + κ + κ s 2 ] + g 2 .
r 0 ( ω ) = i ( ω c ω ) + κ s 2 i ( ω c ω ) + κ + κ s 2 , t 0 ( ω ) = κ i ( ω c ω ) + κ + κ s 2 .
r = 1 + t , t = γ 2 κ γ 2 ( κ + κ s 2 ) + g 2 , r 0 = κ s 2 κ + κ s 2 , t 0 = κ κ + κ s 2 .
| R r | L + t | R , | L r | R + t | L , | R t 0 | R + r 0 | L , | L t 0 | L + r 0 | R , | R r | L + t | R , | L r | R + t | L , | R t 0 | R + r 0 | L , | L t 0 | L + r 0 | R .
| Φ 1 = 1 2 [ ( | R + | L ) | j 1 + ( | R + | L ) | j 2 ] 1 2 ( | + | ) .
| Φ 2 = 1 2 2 [ ( t 0 + r 0 ) | R | j 2 + ( t + r ) | L | j 2 + ( t + r ) | R | j 1 + ( r 0 + t 0 ) | L | j 1 ] | + 1 2 2 [ ( t 0 + r 0 ) | R | j 1 + ( t + r ) | L | j 1 + ( t + r ) | R | j 2 + ( t 0 + r 0 ) | L | j 2 ] | .
| Φ 3 = 1 4 [ ( t + r + t 0 + r 0 ) | R | j 2 + ( t + r + t 0 + r 0 ) | R | j 1 ( t + r t 0 r 0 ) | L | j 2 + ( t + r t 0 r 0 ) | L | j 1 ] | + 1 4 [ ( t + r + t 0 + r 0 ) | R | j 2 + ( t + r + t 0 + r 0 ) | R | j 1 + ( t + r t 0 r 0 ) | L | j 2 ( t + r t 0 r 0 ) | L | j 1 ] | .
| Φ 4 = D | R | i 1 | φ + + T | L | i 2 | φ .
| Φ 5 = D | R | i 1 | φ + T | L | i 2 | φ + .
| Ψ P S = 1 2 ( | R R + | L L ) A B ( | a 1 b 1 + | a 2 b 2 ) A B .
| ϕ ± P = 1 2 ( | R R ± | L L ) , | ψ ± P = 1 2 ( | R L ± | L R ) .
| ϕ ± S = 1 2 ( | a 1 b 1 ± | a 2 b 2 ) , | ψ ± S = 1 2 ( | a 1 b 2 ± | a 2 b 1 ) .
Ω 1 = 1 2 ( | L L | a 1 b 1 | φ + 1 + ( | L R | a 1 b 2 | φ 1 + | R L | a 2 b 1 | φ 1 + | R R | a 2 b 2 | φ + 1 ) | φ + 2 .
Ω 2 = 1 2 ( | ϕ + P | ϕ + S | φ + 1 | φ + 2 | ϕ P | ψ + S | φ + 1 | φ 2 + | ψ + P | ϕ S | φ 1 | φ + 2 + | ψ P | ψ S | φ 1 | φ 2 .
| ϕ + P ( | ψ + P ) | ϕ + S | φ + 1 | φ + 2 | ϕ + P ( | ψ + P ) | ϕ + S | φ + 1 | φ + 2 , | ϕ + P ( | ψ + P ) | ψ + S | φ + 1 | φ + 2 | ϕ + P ( | ψ + P ) | ψ + S | φ + 1 | φ + 2 , | ϕ + P ( | ψ + P ) | ϕ S | φ + 1 | φ + 2 | ϕ + P ( | ψ + P ) | ϕ S | φ + 1 | φ 2 , | ϕ + P ( | ψ + P ) | ψ S | φ + 1 | φ + 2 | ϕ + P ( | ψ + P ) | ψ S | φ + 1 | φ 2 , | ϕ P ( | ψ P ) | ϕ + S | φ + 1 | φ + 2 | ϕ P ( | ψ P ) | ϕ + S | φ 1 | φ + 2 , | ϕ P ( | ψ P ) | ψ + S | φ + 1 | φ + 2 | ϕ P ( | ψ P ) | ψ + S | φ 1 | φ + 2 , | ϕ P ( | ψ P ) | ϕ S | φ + 1 | φ + 2 | ϕ P ( | ψ P ) | ϕ S | φ 1 | φ 2 , | ϕ P ( | ψ P ) | ψ S | φ + 1 | φ + 2 | ϕ P ( | ψ P ) | ψ S | φ 1 | φ 2 .
F 1 = ( T 2 + 1 ) 4 4 ( T 4 + 1 ) 2 , F 2 = F 3 = ( 1 + T 2 ) 2 2 ( 1 + T 4 ) , F 4 = 1 .
η 1 = 1 4 ( T 4 + 1 ) , η 2 = η 3 = 1 2 ( T 2 + T 6 ) , η 4 = T 4 .
F H B S A 1 = ( T 2 + 1 ) 4 ( T 2 + 1 ) 4 + 2 ( 1 T 4 ) 2 + ( 1 T 2 ) 4 , η H B S A 1 = 1 16 [ ( T 2 + 1 ) 4 + 2 ( 1 T 4 ) 2 + ( 1 T 2 ) 4 ] .
F H B S A 2 = ( 1 + T 2 ) 8 [ ( 1 + T 2 ) 4 + ( 1 T 4 ) 2 + 4 T 2 ( 1 T 2 ) 2 ] 2 , η H B S A 2 = 1 256 [ ( 1 + T 2 ) 4 + ( 1 T 4 ) 2 + 4 T 2 ( 1 T 2 ) 2 ] 2 .

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