Abstract

We propose and experimentally demonstrate a two-photon four-qubit cluster state generator using linear optics and a single polarization-entangled photon-pair source based on spontaneous parametric down-conversion (SPDC). Our novel scheme provides greater design flexibility compared to previous schemes that rely on hyperentanglement.

© 2007 Optical Society of America

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  1. 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]
  2. P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, "Experimental one-way quantum computing," Nature 434, 169-176 (2005).
    [CrossRef] [PubMed]
  3. Q1. C.-A. Lu, X.-Q. Zhou, O. Gühne, W.-B. Gao, J. Zhang, Z.-S. Yuan, A. Goebel, T. Yang, and J.-W. Pan, "Experimental entanglement of six photons in graph states," Nat. Phys. 3, 91-95 (2007).
    [CrossRef]
  4. G. Vallone, E. Pomarico, F. De Martini, and P. Mataloni, "One-way quantum computation via manipulation of polarization and momentum qubits in two-photon cluster states," e-print, arXiv:quant-ph/0707.1819 (2007).
  5. K. Chen, C.-M. Li, Q. Zhang, Y.-A. Chen, A. Goebel, S. Chen, A. Mair, and J.-W. Pan, "Experimental realization of one-way quantum computing with two-photon four-qubit cluster states," Phys. Rev. Lett. 99, 120503 (2007).
    [CrossRef] [PubMed]
  6. Y. Tokunaga, S. Kuwashiro, T. Yamamoto, M. Koashi, and N. Imoto, "Generation of high-fidelity four-photon cluster state and quantum-domain demonstration of one-way quantum computing," in Proceedings on Asian conference on Quantum Information Science2007, pp. 51-52.
  7. M. Barbieri, F. De Martini, P. Mataloni, G. Vallone, and A. Cabello, "Enhancing the violation of the Einstein-Podolsky-Rosen local realism by quantum hyperentanglement," Phys. Rev. Lett. 97, 140407 (2006).
    [CrossRef] [PubMed]
  8. N. Kiesel, C. Schmid, U. Weber, G. Tóth, O. Gühne, R. Ursin, and H. Weinfurter, "Experimental analysis of a four-qubit photon cluster state," Phys. Rev. Lett. 95, 210502 (2005).
    [CrossRef] [PubMed]
  9. Y.-H. Kim, "Single-photon two-qubit entangled states: Preparation and measurement," Phys. Rev. A 67, 040301(R) (2003).
    [CrossRef]
  10. G. Vallone, E. Pomarico, P. Mataloni, F. De Martini, and V. Berardi, "Realization and characterization of a two-photon four-qubit linear cluster state," Phys. Rev. Lett. 98, 180502 (2007).
    [CrossRef] [PubMed]
  11. P. G. Kwiat, "Hyper-entangled states," J. Mod. Opt. 44, 2173-2184 (1997).
  12. X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, "Optical fiber source of polarization-entangled photons in the 1550 nm telecom band," Phys. Rev. Lett. 94, 053601 (2005).
    [CrossRef] [PubMed]
  13. T. Kim, M. Fiorentino, and F. N. C. Wong, "Phase-stable source of polarization-entangled photons using a polarization Sagnac interferometer," Phys. Rev. A 73, 012316 (2006).
    [CrossRef]
  14. J. Fan and A. Migdall, "A broadband high spectral brightness fiber-based two-photon source," Opt. Express 15, 2915-2920 (2007).
    [CrossRef] [PubMed]
  15. H. J. Briegel and R. Raussendorf, "Persistent entanglement in arrays of interacting particles," Phys. Rev. Lett. 86, 910-913 (2001).
    [CrossRef] [PubMed]
  16. Y. Nambu, K. Usami, Y. Tsuda, K. Matsumoto, and K. Nakamura, "Generation of polarization-entangled photon pairs in a cascade of two type-I crystals pumped by femtosecond pulses," Phys. Rev. A 66, 033816 (2002).
    [CrossRef]
  17. R. Raussendorf and H. J. Briegel, "A one-way quantum computer," Phys. Rev. Lett. 86, 5188-5191 (2001).
    [CrossRef] [PubMed]
  18. G. Tóth and O. Gühne, "Entanglement detection in the stabilizer formalism," Phys. Rev. A 72, 022340 (2005).
    [CrossRef]

2007

Q1. C.-A. Lu, X.-Q. Zhou, O. Gühne, W.-B. Gao, J. Zhang, Z.-S. Yuan, A. Goebel, T. Yang, and J.-W. Pan, "Experimental entanglement of six photons in graph states," Nat. Phys. 3, 91-95 (2007).
[CrossRef]

K. Chen, C.-M. Li, Q. Zhang, Y.-A. Chen, A. Goebel, S. Chen, A. Mair, and J.-W. Pan, "Experimental realization of one-way quantum computing with two-photon four-qubit cluster states," Phys. Rev. Lett. 99, 120503 (2007).
[CrossRef] [PubMed]

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]

G. Vallone, E. Pomarico, P. Mataloni, F. De Martini, and V. Berardi, "Realization and characterization of a two-photon four-qubit linear cluster state," Phys. Rev. Lett. 98, 180502 (2007).
[CrossRef] [PubMed]

J. Fan and A. Migdall, "A broadband high spectral brightness fiber-based two-photon source," Opt. Express 15, 2915-2920 (2007).
[CrossRef] [PubMed]

2006

T. Kim, M. Fiorentino, and F. N. C. Wong, "Phase-stable source of polarization-entangled photons using a polarization Sagnac interferometer," Phys. Rev. A 73, 012316 (2006).
[CrossRef]

M. Barbieri, F. De Martini, P. Mataloni, G. Vallone, and A. Cabello, "Enhancing the violation of the Einstein-Podolsky-Rosen local realism by quantum hyperentanglement," Phys. Rev. Lett. 97, 140407 (2006).
[CrossRef] [PubMed]

2005

N. Kiesel, C. Schmid, U. Weber, G. Tóth, O. Gühne, R. Ursin, and H. Weinfurter, "Experimental analysis of a four-qubit photon cluster state," Phys. Rev. Lett. 95, 210502 (2005).
[CrossRef] [PubMed]

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, "Experimental one-way quantum computing," Nature 434, 169-176 (2005).
[CrossRef] [PubMed]

X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, "Optical fiber source of polarization-entangled photons in the 1550 nm telecom band," Phys. Rev. Lett. 94, 053601 (2005).
[CrossRef] [PubMed]

G. Tóth and O. Gühne, "Entanglement detection in the stabilizer formalism," Phys. Rev. A 72, 022340 (2005).
[CrossRef]

2002

Y. Nambu, K. Usami, Y. Tsuda, K. Matsumoto, and K. Nakamura, "Generation of polarization-entangled photon pairs in a cascade of two type-I crystals pumped by femtosecond pulses," Phys. Rev. A 66, 033816 (2002).
[CrossRef]

2001

R. Raussendorf and H. J. Briegel, "A one-way quantum computer," Phys. Rev. Lett. 86, 5188-5191 (2001).
[CrossRef] [PubMed]

H. J. Briegel and R. Raussendorf, "Persistent entanglement in arrays of interacting particles," Phys. Rev. Lett. 86, 910-913 (2001).
[CrossRef] [PubMed]

1997

P. G. Kwiat, "Hyper-entangled states," J. Mod. Opt. 44, 2173-2184 (1997).

Aspelmeyer, M.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, "Experimental one-way quantum computing," Nature 434, 169-176 (2005).
[CrossRef] [PubMed]

Barbieri, M.

M. Barbieri, F. De Martini, P. Mataloni, G. Vallone, and A. Cabello, "Enhancing the violation of the Einstein-Podolsky-Rosen local realism by quantum hyperentanglement," Phys. Rev. Lett. 97, 140407 (2006).
[CrossRef] [PubMed]

Berardi, V.

G. Vallone, E. Pomarico, P. Mataloni, F. De Martini, and V. Berardi, "Realization and characterization of a two-photon four-qubit linear cluster state," Phys. Rev. Lett. 98, 180502 (2007).
[CrossRef] [PubMed]

Briegel, H. J.

H. J. Briegel and R. Raussendorf, "Persistent entanglement in arrays of interacting particles," Phys. Rev. Lett. 86, 910-913 (2001).
[CrossRef] [PubMed]

R. Raussendorf and H. J. Briegel, "A one-way quantum computer," Phys. Rev. Lett. 86, 5188-5191 (2001).
[CrossRef] [PubMed]

Cabello, A.

M. Barbieri, F. De Martini, P. Mataloni, G. Vallone, and A. Cabello, "Enhancing the violation of the Einstein-Podolsky-Rosen local realism by quantum hyperentanglement," Phys. Rev. Lett. 97, 140407 (2006).
[CrossRef] [PubMed]

Chen, K.

K. Chen, C.-M. Li, Q. Zhang, Y.-A. Chen, A. Goebel, S. Chen, A. Mair, and J.-W. Pan, "Experimental realization of one-way quantum computing with two-photon four-qubit cluster states," Phys. Rev. Lett. 99, 120503 (2007).
[CrossRef] [PubMed]

Chen, S.

K. Chen, C.-M. Li, Q. Zhang, Y.-A. Chen, A. Goebel, S. Chen, A. Mair, and J.-W. Pan, "Experimental realization of one-way quantum computing with two-photon four-qubit cluster states," Phys. Rev. Lett. 99, 120503 (2007).
[CrossRef] [PubMed]

Chen, Y.-A.

K. Chen, C.-M. Li, Q. Zhang, Y.-A. Chen, A. Goebel, S. Chen, A. Mair, and J.-W. Pan, "Experimental realization of one-way quantum computing with two-photon four-qubit cluster states," Phys. Rev. Lett. 99, 120503 (2007).
[CrossRef] [PubMed]

De Martini, F.

G. Vallone, E. Pomarico, P. Mataloni, F. De Martini, and V. Berardi, "Realization and characterization of a two-photon four-qubit linear cluster state," Phys. Rev. Lett. 98, 180502 (2007).
[CrossRef] [PubMed]

M. Barbieri, F. De Martini, P. Mataloni, G. Vallone, and A. Cabello, "Enhancing the violation of the Einstein-Podolsky-Rosen local realism by quantum hyperentanglement," Phys. Rev. Lett. 97, 140407 (2006).
[CrossRef] [PubMed]

Dowling, J. P.

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]

Fan, J.

Fiorentino, M.

T. Kim, M. Fiorentino, and F. N. C. Wong, "Phase-stable source of polarization-entangled photons using a polarization Sagnac interferometer," Phys. Rev. A 73, 012316 (2006).
[CrossRef]

Gao, W.-B.

Q1. C.-A. Lu, X.-Q. Zhou, O. Gühne, W.-B. Gao, J. Zhang, Z.-S. Yuan, A. Goebel, T. Yang, and J.-W. Pan, "Experimental entanglement of six photons in graph states," Nat. Phys. 3, 91-95 (2007).
[CrossRef]

Goebel, A.

Q1. C.-A. Lu, X.-Q. Zhou, O. Gühne, W.-B. Gao, J. Zhang, Z.-S. Yuan, A. Goebel, T. Yang, and J.-W. Pan, "Experimental entanglement of six photons in graph states," Nat. Phys. 3, 91-95 (2007).
[CrossRef]

K. Chen, C.-M. Li, Q. Zhang, Y.-A. Chen, A. Goebel, S. Chen, A. Mair, and J.-W. Pan, "Experimental realization of one-way quantum computing with two-photon four-qubit cluster states," Phys. Rev. Lett. 99, 120503 (2007).
[CrossRef] [PubMed]

Gühne, O.

Q1. C.-A. Lu, X.-Q. Zhou, O. Gühne, W.-B. Gao, J. Zhang, Z.-S. Yuan, A. Goebel, T. Yang, and J.-W. Pan, "Experimental entanglement of six photons in graph states," Nat. Phys. 3, 91-95 (2007).
[CrossRef]

G. Tóth and O. Gühne, "Entanglement detection in the stabilizer formalism," Phys. Rev. A 72, 022340 (2005).
[CrossRef]

N. Kiesel, C. Schmid, U. Weber, G. Tóth, O. Gühne, R. Ursin, and H. Weinfurter, "Experimental analysis of a four-qubit photon cluster state," Phys. Rev. Lett. 95, 210502 (2005).
[CrossRef] [PubMed]

Kiesel, N.

N. Kiesel, C. Schmid, U. Weber, G. Tóth, O. Gühne, R. Ursin, and H. Weinfurter, "Experimental analysis of a four-qubit photon cluster state," Phys. Rev. Lett. 95, 210502 (2005).
[CrossRef] [PubMed]

Kim, T.

T. Kim, M. Fiorentino, and F. N. C. Wong, "Phase-stable source of polarization-entangled photons using a polarization Sagnac interferometer," Phys. Rev. A 73, 012316 (2006).
[CrossRef]

Kok, P.

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]

Kumar, P.

X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, "Optical fiber source of polarization-entangled photons in the 1550 nm telecom band," Phys. Rev. Lett. 94, 053601 (2005).
[CrossRef] [PubMed]

Kwiat, P. G.

P. G. Kwiat, "Hyper-entangled states," J. Mod. Opt. 44, 2173-2184 (1997).

Li, C.-M.

K. Chen, C.-M. Li, Q. Zhang, Y.-A. Chen, A. Goebel, S. Chen, A. Mair, and J.-W. Pan, "Experimental realization of one-way quantum computing with two-photon four-qubit cluster states," Phys. Rev. Lett. 99, 120503 (2007).
[CrossRef] [PubMed]

Li, X.

X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, "Optical fiber source of polarization-entangled photons in the 1550 nm telecom band," Phys. Rev. Lett. 94, 053601 (2005).
[CrossRef] [PubMed]

Lu, C.-A.

Q1. C.-A. Lu, X.-Q. Zhou, O. Gühne, W.-B. Gao, J. Zhang, Z.-S. Yuan, A. Goebel, T. Yang, and J.-W. Pan, "Experimental entanglement of six photons in graph states," Nat. Phys. 3, 91-95 (2007).
[CrossRef]

Mair, A.

K. Chen, C.-M. Li, Q. Zhang, Y.-A. Chen, A. Goebel, S. Chen, A. Mair, and J.-W. Pan, "Experimental realization of one-way quantum computing with two-photon four-qubit cluster states," Phys. Rev. Lett. 99, 120503 (2007).
[CrossRef] [PubMed]

Mataloni, P.

G. Vallone, E. Pomarico, P. Mataloni, F. De Martini, and V. Berardi, "Realization and characterization of a two-photon four-qubit linear cluster state," Phys. Rev. Lett. 98, 180502 (2007).
[CrossRef] [PubMed]

M. Barbieri, F. De Martini, P. Mataloni, G. Vallone, and A. Cabello, "Enhancing the violation of the Einstein-Podolsky-Rosen local realism by quantum hyperentanglement," Phys. Rev. Lett. 97, 140407 (2006).
[CrossRef] [PubMed]

Matsumoto, K.

Y. Nambu, K. Usami, Y. Tsuda, K. Matsumoto, and K. Nakamura, "Generation of polarization-entangled photon pairs in a cascade of two type-I crystals pumped by femtosecond pulses," Phys. Rev. A 66, 033816 (2002).
[CrossRef]

Migdall, A.

Milburn, G. J.

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]

Munro, W. J.

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]

Nakamura, K.

Y. Nambu, K. Usami, Y. Tsuda, K. Matsumoto, and K. Nakamura, "Generation of polarization-entangled photon pairs in a cascade of two type-I crystals pumped by femtosecond pulses," Phys. Rev. A 66, 033816 (2002).
[CrossRef]

Nambu, Y.

Y. Nambu, K. Usami, Y. Tsuda, K. Matsumoto, and K. Nakamura, "Generation of polarization-entangled photon pairs in a cascade of two type-I crystals pumped by femtosecond pulses," Phys. Rev. A 66, 033816 (2002).
[CrossRef]

Nemoto, K.

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]

Pan, J.-W.

K. Chen, C.-M. Li, Q. Zhang, Y.-A. Chen, A. Goebel, S. Chen, A. Mair, and J.-W. Pan, "Experimental realization of one-way quantum computing with two-photon four-qubit cluster states," Phys. Rev. Lett. 99, 120503 (2007).
[CrossRef] [PubMed]

Q1. C.-A. Lu, X.-Q. Zhou, O. Gühne, W.-B. Gao, J. Zhang, Z.-S. Yuan, A. Goebel, T. Yang, and J.-W. Pan, "Experimental entanglement of six photons in graph states," Nat. Phys. 3, 91-95 (2007).
[CrossRef]

Pomarico, E.

G. Vallone, E. Pomarico, P. Mataloni, F. De Martini, and V. Berardi, "Realization and characterization of a two-photon four-qubit linear cluster state," Phys. Rev. Lett. 98, 180502 (2007).
[CrossRef] [PubMed]

Ralph, T. C.

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]

Raussendorf, R.

H. J. Briegel and R. Raussendorf, "Persistent entanglement in arrays of interacting particles," Phys. Rev. Lett. 86, 910-913 (2001).
[CrossRef] [PubMed]

R. Raussendorf and H. J. Briegel, "A one-way quantum computer," Phys. Rev. Lett. 86, 5188-5191 (2001).
[CrossRef] [PubMed]

Resch, K. J.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, "Experimental one-way quantum computing," Nature 434, 169-176 (2005).
[CrossRef] [PubMed]

Rudolph, T.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, "Experimental one-way quantum computing," Nature 434, 169-176 (2005).
[CrossRef] [PubMed]

Schenck, E.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, "Experimental one-way quantum computing," Nature 434, 169-176 (2005).
[CrossRef] [PubMed]

Schmid, C.

N. Kiesel, C. Schmid, U. Weber, G. Tóth, O. Gühne, R. Ursin, and H. Weinfurter, "Experimental analysis of a four-qubit photon cluster state," Phys. Rev. Lett. 95, 210502 (2005).
[CrossRef] [PubMed]

Sharping, J. E.

X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, "Optical fiber source of polarization-entangled photons in the 1550 nm telecom band," Phys. Rev. Lett. 94, 053601 (2005).
[CrossRef] [PubMed]

Tóth, G.

N. Kiesel, C. Schmid, U. Weber, G. Tóth, O. Gühne, R. Ursin, and H. Weinfurter, "Experimental analysis of a four-qubit photon cluster state," Phys. Rev. Lett. 95, 210502 (2005).
[CrossRef] [PubMed]

G. Tóth and O. Gühne, "Entanglement detection in the stabilizer formalism," Phys. Rev. A 72, 022340 (2005).
[CrossRef]

Tsuda, Y.

Y. Nambu, K. Usami, Y. Tsuda, K. Matsumoto, and K. Nakamura, "Generation of polarization-entangled photon pairs in a cascade of two type-I crystals pumped by femtosecond pulses," Phys. Rev. A 66, 033816 (2002).
[CrossRef]

Ursin, R.

N. Kiesel, C. Schmid, U. Weber, G. Tóth, O. Gühne, R. Ursin, and H. Weinfurter, "Experimental analysis of a four-qubit photon cluster state," Phys. Rev. Lett. 95, 210502 (2005).
[CrossRef] [PubMed]

Usami, K.

Y. Nambu, K. Usami, Y. Tsuda, K. Matsumoto, and K. Nakamura, "Generation of polarization-entangled photon pairs in a cascade of two type-I crystals pumped by femtosecond pulses," Phys. Rev. A 66, 033816 (2002).
[CrossRef]

Vallone, G.

G. Vallone, E. Pomarico, P. Mataloni, F. De Martini, and V. Berardi, "Realization and characterization of a two-photon four-qubit linear cluster state," Phys. Rev. Lett. 98, 180502 (2007).
[CrossRef] [PubMed]

M. Barbieri, F. De Martini, P. Mataloni, G. Vallone, and A. Cabello, "Enhancing the violation of the Einstein-Podolsky-Rosen local realism by quantum hyperentanglement," Phys. Rev. Lett. 97, 140407 (2006).
[CrossRef] [PubMed]

Vedral, V.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, "Experimental one-way quantum computing," Nature 434, 169-176 (2005).
[CrossRef] [PubMed]

Voss, P. L.

X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, "Optical fiber source of polarization-entangled photons in the 1550 nm telecom band," Phys. Rev. Lett. 94, 053601 (2005).
[CrossRef] [PubMed]

Walther, P.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, "Experimental one-way quantum computing," Nature 434, 169-176 (2005).
[CrossRef] [PubMed]

Weber, U.

N. Kiesel, C. Schmid, U. Weber, G. Tóth, O. Gühne, R. Ursin, and H. Weinfurter, "Experimental analysis of a four-qubit photon cluster state," Phys. Rev. Lett. 95, 210502 (2005).
[CrossRef] [PubMed]

Weinfurter, H.

N. Kiesel, C. Schmid, U. Weber, G. Tóth, O. Gühne, R. Ursin, and H. Weinfurter, "Experimental analysis of a four-qubit photon cluster state," Phys. Rev. Lett. 95, 210502 (2005).
[CrossRef] [PubMed]

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, "Experimental one-way quantum computing," Nature 434, 169-176 (2005).
[CrossRef] [PubMed]

Wong, F. N. C.

T. Kim, M. Fiorentino, and F. N. C. Wong, "Phase-stable source of polarization-entangled photons using a polarization Sagnac interferometer," Phys. Rev. A 73, 012316 (2006).
[CrossRef]

Yang, T.

Q1. C.-A. Lu, X.-Q. Zhou, O. Gühne, W.-B. Gao, J. Zhang, Z.-S. Yuan, A. Goebel, T. Yang, and J.-W. Pan, "Experimental entanglement of six photons in graph states," Nat. Phys. 3, 91-95 (2007).
[CrossRef]

Yuan, Z.-S.

Q1. C.-A. Lu, X.-Q. Zhou, O. Gühne, W.-B. Gao, J. Zhang, Z.-S. Yuan, A. Goebel, T. Yang, and J.-W. Pan, "Experimental entanglement of six photons in graph states," Nat. Phys. 3, 91-95 (2007).
[CrossRef]

Zeilinger, A.

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of the two-photon four-qubit linear cluster state: (a) generation scheme, (b) configuration of the state. PBS, polarizing beam splitter; NPBS, non-polarizing beam splitter; HWP, half-wave plate; C-Z, controlled-Z operation.

Fig. 2.
Fig. 2.

Experimental setup for generation and measurement of the two-photon four-qubit cluster state. BBO, beta-barium borate; PBS, polarizing beam splitter; NPBS, non-polarizing beam splitter; HWP, half-wave plate; PZT, piezo-electric transducer; IF, interference filter.

Fig. 3.
Fig. 3.

Photon count rates as functions of the phases in path qubit projections: (a) coincidence count rate vs ϕ1, where the polarizers for photons 1 and 2 are H- and V-polarized, respectively, and shutters 1, 2, 3 are open; (b) single count rate of photon counter 2 vs ϕ2, where the polarizer for photon 2 is V-polarized and shutters 3, 4 are open.

Fig. 4.
Fig. 4.

Correlations between two entangled qubits selected from the cluster state |Ψ〉: (a) qubits 1 (polarization) and 3 (polarization) entangled as 1/21/2(|0〉1|0〉3+|1〉1|1〉3); (b) qubits 2 (path) and 3 (polarization) entangled as 1/21/2(|0〉2|+〉3+|1〉2|-〉3); (c) qubits 2 (path) and 4 (path) entangled as 1/21/2(|0〉2|0〉4+|1〉2|1〉4). The state for the i-th qubit is denoted as |Ψ〉 i .

Fig. 5.
Fig. 5.

Coincidence count measurements for the 32 projected states that evaluate the entanglement witness for the generated four-qubit state.

Equations (7)

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Φ trans = 1 2 ( H , a 1 H , c 2 + H , a 1 H , d 2 + V , b 1 V , c 2 + V , b 1 V , d 2 ) ,
Ψ = 1 2 ( D , a 1 D , c 2 + D , a 1 A , d 2 + A , b 1 A , c 2 + A , b 1 D , d 2 ) ,
Ψ = 1 2 ( + 0 + 0 + + 0 1 + 1 0 + 1 + 1 ) ,
Ψ meas = 1 2 ( D 1 ( D 2 + e i ϕ 2 A 2 ) + e i ϕ 1 A 1 ( A 2 + e i ϕ 2 D 2 ) ) .
W = 3 I 1 2 ( S ( 1 ) + I ) ( S ( 3 ) + I ) 1 2 ( S ( 2 ) + I ) ( S ( 4 ) + I ) ,
S ( 1 ) = X 1 Z 2 I 3 I 4 , S ( 2 ) = Z 1 X 2 Z 3 I 4 , S ( 3 ) = I 1 Z 2 X 3 Z 4 , S ( 4 ) = I 1 I 2 Z 3 X 4 ,
F = C 4 ρ exp C 4 1 2 1 2 W = 0.72 ± 0.02 ,

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