Abstract

High-dimensional entangled states have attracted attention because of their strong nonlocality and powerful capability for quantum information processing. By the methods presented in this paper, arbitrary forms-entangled qudits including symmetric and asymmetric forms could be generated with weak cross-Kerr nonlinearity. These schemes are heralded by the use of single-photon detectors. If all the detectors do not register any single photons, the generation is a success with the probability 1/nM determined by dimension n and partite M. Furthermore, these schemes work well even with the common photon number nonresolving detectors; therefore they are feasible with the current experimental technology.

© 2013 Optical Society of America

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  1. 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).
    [CrossRef]
  2. C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein–Podolsky–Rosen states,” Phys. Rev. Lett. 69, 2881–2884 (1992).
    [CrossRef]
  3. T. Monz, P. Schindler, J. T. Barreiro, M. Chwalla, D. Nigg, W. A. Coish, M. Harlander, W. Haensel, M. Hennrich, and R. Blatt, “14 qubit entanglement: creation and coherence,” Phys. Rev. Lett. 106, 130506 (2011).
    [CrossRef]
  4. X.-C. Yao, T.-X. Wang, P. Xu, H. Lu, G.-S. Pan, X.-H. Bao, C.-Z. Peng, C.-Y. Lu, Y.-A. Chen, and J.-W. Pan, “Observation of eight-photon entanglement,” Nat. Photonics 6, 225–228 (2012).
    [CrossRef]
  5. Y.-F. Huang, B.-H. Liu, L. Peng, Y.-H. Li, L. Li, C.-F. Li, and G.-C. Guo, “Experimental generation of an eight-photon Greenberger–Horne–Zeilinger state,” Nat. Commun. 2, 546–551 (2011).
    [CrossRef]
  6. A. Zeilinger, M. A. Horne, H. Weinfurter, and M. Żukowski, “Three-particle entanglements from two entangled airs,” Phys. Rev. Lett. 78, 3031–3034 (1997).
    [CrossRef]
  7. D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger–Horne–Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349(1999).
    [CrossRef]
  8. M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
    [CrossRef]
  9. M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
    [CrossRef]
  10. 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]
  11. R. W. Spekkens and T. Rudolph, “Degrees of concealment and bindingness in quantum bit commitment protocols,” Phys. Rev. A 65, 012310 (2001).
    [CrossRef]
  12. D. Bruß and C. Macchiavello, “Optimal eavesdropping in cryptography with three-dimensional quantum states,” Phys. Rev. Lett. 88, 127901 (2002).
    [CrossRef]
  13. N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
    [CrossRef]
  14. T. Durt, N. J. Cerf, N. Gisin, and M. Żukowski, “Security of quantum key distribution with entangled qutrits,” Phys. Rev. A 67, 012311 (2003).
    [CrossRef]
  15. G. M. Terriza, A. Vaziri, J. Řeháček, Z. Hradil, and A. Zeilinger, “Triggered qutrits for quantum communication protocols,” Phys. Rev. Lett. 92, 167903 (2004).
    [CrossRef]
  16. 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]
  17. S. Gröblacher, Y. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
    [CrossRef]
  18. T. C. Ralph, K. J. Resch, and A. Gilchrist, “Efficient Toffoli gates using qudits,” Phys. Rev. A 75, 022313 (2007).
    [CrossRef]
  19. B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
    [CrossRef]
  20. D. Gross and J. Eisert, “Novel schemes for measurement-based quantum computation,” Phys. Rev. Lett. 98, 220503 (2007).
    [CrossRef]
  21. J. M. Cai, W. Dür, M. Van den Nest, A. Miyake, and H. J. Briegel, “Quantum computation in correlation space and extremal entanglement,” Phys. Rev. Lett. 103, 050503 (2009).
    [CrossRef]
  22. J. M. Cai, A. Miyake, W. Dür, and H. J. Briegel, “Universal quantum computer from a quantum magnet,” Phys. Rev. A 82, 052309 (2010).
    [CrossRef]
  23. R. Kaltenbaek, J. Lavoie, B. Zeng, S. D. Bartlett, and K. J. Resch, “Optical one-way quantum computing with a simulated valence-bond solid,” Nat. Phys. 6, 850–854 (2010).
    [CrossRef]
  24. W. B. Gao, X. C. Yao, J. M. Cai, H. Lu, P. Xu, T. Yang, C. Y. Lu, Y. A. Chen, Z. B. Chen, and J. W. Pan, “Experimental measurement-based quantum computing beyond the cluster-state model,” Nat. Photonics 5, 117–123 (2011).
    [CrossRef]
  25. J. C. Howell, A. Lamas-Linares, and D. Bouwmeester, “Experimental violation of a spin-1 bell inequality using maximally entangled four-photon states,” Phys. Rev. Lett. 88, 030401 (2002).
    [CrossRef]
  26. Y. I. Bogdanov, M. V. Chekhova, S. P. Kulik, G. A. Maslennikov, A. A. Zhukov, C. H. Oh, and M. K. Tey, “Qutrit state engineering with biphotons,” Phys. Rev. Lett. 93, 230503 (2004).
    [CrossRef]
  27. Y. I. Bogdanov, M. V. Chekhova, L. A. Krivitsky, S. P. Kulik, A. N. Penin, A. A. Zhukov, L. C. Kwek, C. H. Oh, and M. K. Tey, “Statistical reconstruction of qutrits,” Phys. Rev. A 70, 042303 (2004).
    [CrossRef]
  28. Y. I. Bogdanov, M. V. Chekhova, S. P. Kulik, G. A. Maslennikov, C. H. Oh, and M. K. Tey, “Preparation of arbitrary qutrit state based on biphotons,” Proc. SPIE 5833, 202–212 (2005).
    [CrossRef]
  29. E. V. Moreva, G. A. Maslennikov, S. S. Straupe, and S. P. Kulik, “Realization of four-level qudits using biphotons,” Phys. Rev. Lett. 97, 023602 (2006).
    [CrossRef]
  30. H. Mikami and T. Kobayashi, “Remote preparation of qutrit states with biphotons,” Phys. Rev. A 75, 022325 (2007).
    [CrossRef]
  31. G. Vallone, E. Pomarico, F. De Martini, and P. Mataloni, “Experimental realization of polarization qutrits from nonmaximally entangled states,” Phys. Rev. A 76, 012319 (2007).
    [CrossRef]
  32. Y. M. Li, K. S. Zhang, and K. C. Peng, “Generation of qudits and entangled qudits,” Phys. Rev. A 77, 015802 (2008).
    [CrossRef]
  33. B. P. Lanyon, T. J. Weinhold, N. K. Langford, J. L. O’Brien, K. J. Resch, A. Gilchrist, and A. G. White, “Manipulating biphotonic qutrits,” Phys. Rev. Lett. 100, 060504 (2008).
    [CrossRef]
  34. J. Joo, T. Rudolph, and B. C. Sanders, “A heralded two-qutrit entangled state,” J. Phys. B 42, 114007 (2009).
    [CrossRef]
  35. A. Halevy, E. Megidish, T. Shacham, L. Dovrat, and H. S. Eisenberg, “Projection of two biphoton qutrits onto a maximally entangled state,” Phys. Rev. Lett. 106, 130502 (2011).
    [CrossRef]
  36. X. L. Ye and Q. Lin, “Efficient and flexible generation of entangled qudits with cross-phase modulation,” J. Opt. Soc. Am. B 29, 1810–1814 (2012).
    [CrossRef]
  37. Q. Lin, “Efficient generation of arbitrary multi-partite polarized entangled qudits,” Sci. Sin. Phys. Mech. Astron. 42, 842–851 (2012).
    [CrossRef]
  38. 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(R) (2005).
  39. K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502(2004).
    [CrossRef]
  40. W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
    [CrossRef]
  41. C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
    [CrossRef]
  42. Q. Lin and B. He, “Bi-directional mapping between polarization and spatially encoded photonic qutrits,” Phys. Rev. A 80, 062312 (2009).
    [CrossRef]
  43. M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73, 58–61 (1994).
    [CrossRef]
  44. L. M. Duan and R. Raussendorf, “Efficient quantum computation with probabilistic quantum gates,” Phys. Rev. Lett. 95, 080503 (2005).
    [CrossRef]
  45. B. He, Q. Lin, and C. Simon, “Cross-Kerr nonlinearity between continuous-mode coherent states and single photons,” Phys. Rev. A 83, 053826 (2011).
    [CrossRef]

2012 (3)

X.-C. Yao, T.-X. Wang, P. Xu, H. Lu, G.-S. Pan, X.-H. Bao, C.-Z. Peng, C.-Y. Lu, Y.-A. Chen, and J.-W. Pan, “Observation of eight-photon entanglement,” Nat. Photonics 6, 225–228 (2012).
[CrossRef]

Q. Lin, “Efficient generation of arbitrary multi-partite polarized entangled qudits,” Sci. Sin. Phys. Mech. Astron. 42, 842–851 (2012).
[CrossRef]

X. L. Ye and Q. Lin, “Efficient and flexible generation of entangled qudits with cross-phase modulation,” J. Opt. Soc. Am. B 29, 1810–1814 (2012).
[CrossRef]

2011 (5)

B. He, Q. Lin, and C. Simon, “Cross-Kerr nonlinearity between continuous-mode coherent states and single photons,” Phys. Rev. A 83, 053826 (2011).
[CrossRef]

A. Halevy, E. Megidish, T. Shacham, L. Dovrat, and H. S. Eisenberg, “Projection of two biphoton qutrits onto a maximally entangled state,” Phys. Rev. Lett. 106, 130502 (2011).
[CrossRef]

Y.-F. Huang, B.-H. Liu, L. Peng, Y.-H. Li, L. Li, C.-F. Li, and G.-C. Guo, “Experimental generation of an eight-photon Greenberger–Horne–Zeilinger state,” Nat. Commun. 2, 546–551 (2011).
[CrossRef]

T. Monz, P. Schindler, J. T. Barreiro, M. Chwalla, D. Nigg, W. A. Coish, M. Harlander, W. Haensel, M. Hennrich, and R. Blatt, “14 qubit entanglement: creation and coherence,” Phys. Rev. Lett. 106, 130506 (2011).
[CrossRef]

W. B. Gao, X. C. Yao, J. M. Cai, H. Lu, P. Xu, T. Yang, C. Y. Lu, Y. A. Chen, Z. B. Chen, and J. W. Pan, “Experimental measurement-based quantum computing beyond the cluster-state model,” Nat. Photonics 5, 117–123 (2011).
[CrossRef]

2010 (2)

J. M. Cai, A. Miyake, W. Dür, and H. J. Briegel, “Universal quantum computer from a quantum magnet,” Phys. Rev. A 82, 052309 (2010).
[CrossRef]

R. Kaltenbaek, J. Lavoie, B. Zeng, S. D. Bartlett, and K. J. Resch, “Optical one-way quantum computing with a simulated valence-bond solid,” Nat. Phys. 6, 850–854 (2010).
[CrossRef]

2009 (4)

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[CrossRef]

J. M. Cai, W. Dür, M. Van den Nest, A. Miyake, and H. J. Briegel, “Quantum computation in correlation space and extremal entanglement,” Phys. Rev. Lett. 103, 050503 (2009).
[CrossRef]

J. Joo, T. Rudolph, and B. C. Sanders, “A heralded two-qutrit entangled state,” J. Phys. B 42, 114007 (2009).
[CrossRef]

Q. Lin and B. He, “Bi-directional mapping between polarization and spatially encoded photonic qutrits,” Phys. Rev. A 80, 062312 (2009).
[CrossRef]

2008 (2)

Y. M. Li, K. S. Zhang, and K. C. Peng, “Generation of qudits and entangled qudits,” Phys. Rev. A 77, 015802 (2008).
[CrossRef]

B. P. Lanyon, T. J. Weinhold, N. K. Langford, J. L. O’Brien, K. J. Resch, A. Gilchrist, and A. G. White, “Manipulating biphotonic qutrits,” Phys. Rev. Lett. 100, 060504 (2008).
[CrossRef]

2007 (4)

H. Mikami and T. Kobayashi, “Remote preparation of qutrit states with biphotons,” Phys. Rev. A 75, 022325 (2007).
[CrossRef]

G. Vallone, E. Pomarico, F. De Martini, and P. Mataloni, “Experimental realization of polarization qutrits from nonmaximally entangled states,” Phys. Rev. A 76, 012319 (2007).
[CrossRef]

T. C. Ralph, K. J. Resch, and A. Gilchrist, “Efficient Toffoli gates using qudits,” Phys. Rev. A 75, 022313 (2007).
[CrossRef]

D. Gross and J. Eisert, “Novel schemes for measurement-based quantum computation,” Phys. Rev. Lett. 98, 220503 (2007).
[CrossRef]

2006 (2)

E. V. Moreva, G. A. Maslennikov, S. S. Straupe, and S. P. Kulik, “Realization of four-level qudits using biphotons,” Phys. Rev. Lett. 97, 023602 (2006).
[CrossRef]

S. Gröblacher, Y. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[CrossRef]

2005 (5)

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]

Y. I. Bogdanov, M. V. Chekhova, S. P. Kulik, G. A. Maslennikov, C. H. Oh, and M. K. Tey, “Preparation of arbitrary qutrit state based on biphotons,” Proc. SPIE 5833, 202–212 (2005).
[CrossRef]

W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
[CrossRef]

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(R) (2005).

L. M. Duan and R. Raussendorf, “Efficient quantum computation with probabilistic quantum gates,” Phys. Rev. Lett. 95, 080503 (2005).
[CrossRef]

2004 (7)

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502(2004).
[CrossRef]

Y. I. Bogdanov, M. V. Chekhova, S. P. Kulik, G. A. Maslennikov, A. A. Zhukov, C. H. Oh, and M. K. Tey, “Qutrit state engineering with biphotons,” Phys. Rev. Lett. 93, 230503 (2004).
[CrossRef]

Y. I. Bogdanov, M. V. Chekhova, L. A. Krivitsky, S. P. Kulik, A. N. Penin, A. A. Zhukov, L. C. Kwek, C. H. Oh, and M. K. Tey, “Statistical reconstruction of qutrits,” Phys. Rev. A 70, 042303 (2004).
[CrossRef]

G. M. Terriza, A. Vaziri, J. Řeháček, Z. Hradil, and A. Zeilinger, “Triggered qutrits for quantum communication protocols,” Phys. Rev. Lett. 92, 167903 (2004).
[CrossRef]

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]

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
[CrossRef]

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[CrossRef]

2003 (1)

T. Durt, N. J. Cerf, N. Gisin, and M. Żukowski, “Security of quantum key distribution with entangled qutrits,” Phys. Rev. A 67, 012311 (2003).
[CrossRef]

2002 (3)

D. Bruß and C. Macchiavello, “Optimal eavesdropping in cryptography with three-dimensional quantum states,” Phys. Rev. Lett. 88, 127901 (2002).
[CrossRef]

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[CrossRef]

J. C. Howell, A. Lamas-Linares, and D. Bouwmeester, “Experimental violation of a spin-1 bell inequality using maximally entangled four-photon states,” Phys. Rev. Lett. 88, 030401 (2002).
[CrossRef]

2001 (1)

R. W. Spekkens and T. Rudolph, “Degrees of concealment and bindingness in quantum bit commitment protocols,” Phys. Rev. A 65, 012310 (2001).
[CrossRef]

1999 (1)

D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger–Horne–Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349(1999).
[CrossRef]

1997 (1)

A. Zeilinger, M. A. Horne, H. Weinfurter, and M. Żukowski, “Three-particle entanglements from two entangled airs,” Phys. Rev. Lett. 78, 3031–3034 (1997).
[CrossRef]

1994 (1)

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73, 58–61 (1994).
[CrossRef]

1993 (1)

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).
[CrossRef]

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]

1987 (1)

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef]

Almeida, M. P.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[CrossRef]

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]

Bao, X.-H.

X.-C. Yao, T.-X. Wang, P. Xu, H. Lu, G.-S. Pan, X.-H. Bao, C.-Z. Peng, C.-Y. Lu, Y.-A. Chen, and J.-W. Pan, “Observation of eight-photon entanglement,” Nat. Photonics 6, 225–228 (2012).
[CrossRef]

Barbieri, M.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[CrossRef]

Barreiro, J. T.

T. Monz, P. Schindler, J. T. Barreiro, M. Chwalla, D. Nigg, W. A. Coish, M. Harlander, W. Haensel, M. Hennrich, and R. Blatt, “14 qubit entanglement: creation and coherence,” Phys. Rev. Lett. 106, 130506 (2011).
[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(R) (2005).

Bartlett, S. D.

R. Kaltenbaek, J. Lavoie, B. Zeng, S. D. Bartlett, and K. J. Resch, “Optical one-way quantum computing with a simulated valence-bond solid,” Nat. Phys. 6, 850–854 (2010).
[CrossRef]

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]

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(R) (2005).

Bennett, C. H.

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).
[CrossRef]

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

Bernstein, H. J.

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73, 58–61 (1994).
[CrossRef]

Bertani, P.

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73, 58–61 (1994).
[CrossRef]

Blatt, R.

T. Monz, P. Schindler, J. T. Barreiro, M. Chwalla, D. Nigg, W. A. Coish, M. Harlander, W. Haensel, M. Hennrich, and R. Blatt, “14 qubit entanglement: creation and coherence,” Phys. Rev. Lett. 106, 130506 (2011).
[CrossRef]

Bogdanov, Y. I.

Y. I. Bogdanov, M. V. Chekhova, S. P. Kulik, G. A. Maslennikov, C. H. Oh, and M. K. Tey, “Preparation of arbitrary qutrit state based on biphotons,” Proc. SPIE 5833, 202–212 (2005).
[CrossRef]

Y. I. Bogdanov, M. V. Chekhova, L. A. Krivitsky, S. P. Kulik, A. N. Penin, A. A. Zhukov, L. C. Kwek, C. H. Oh, and M. K. Tey, “Statistical reconstruction of qutrits,” Phys. Rev. A 70, 042303 (2004).
[CrossRef]

Y. I. Bogdanov, M. V. Chekhova, S. P. Kulik, G. A. Maslennikov, A. A. Zhukov, C. H. Oh, and M. K. Tey, “Qutrit state engineering with biphotons,” Phys. Rev. Lett. 93, 230503 (2004).
[CrossRef]

Bourennane, M.

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
[CrossRef]

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[CrossRef]

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[CrossRef]

Bouwmeester, D.

J. C. Howell, A. Lamas-Linares, and D. Bouwmeester, “Experimental violation of a spin-1 bell inequality using maximally entangled four-photon states,” Phys. Rev. Lett. 88, 030401 (2002).
[CrossRef]

D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger–Horne–Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349(1999).
[CrossRef]

Brassard, G.

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).
[CrossRef]

Briegel, H. J.

J. M. Cai, A. Miyake, W. Dür, and H. J. Briegel, “Universal quantum computer from a quantum magnet,” Phys. Rev. A 82, 052309 (2010).
[CrossRef]

J. M. Cai, W. Dür, M. Van den Nest, A. Miyake, and H. J. Briegel, “Quantum computation in correlation space and extremal entanglement,” Phys. Rev. Lett. 103, 050503 (2009).
[CrossRef]

Bruß, D.

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[CrossRef]

D. Bruß and C. Macchiavello, “Optimal eavesdropping in cryptography with three-dimensional quantum states,” Phys. Rev. Lett. 88, 127901 (2002).
[CrossRef]

Cai, J. M.

W. B. Gao, X. C. Yao, J. M. Cai, H. Lu, P. Xu, T. Yang, C. Y. Lu, Y. A. Chen, Z. B. Chen, and J. W. Pan, “Experimental measurement-based quantum computing beyond the cluster-state model,” Nat. Photonics 5, 117–123 (2011).
[CrossRef]

J. M. Cai, A. Miyake, W. Dür, and H. J. Briegel, “Universal quantum computer from a quantum magnet,” Phys. Rev. A 82, 052309 (2010).
[CrossRef]

J. M. Cai, W. Dür, M. Van den Nest, A. Miyake, and H. J. Briegel, “Quantum computation in correlation space and extremal entanglement,” Phys. Rev. Lett. 103, 050503 (2009).
[CrossRef]

Cerf, N. J.

T. Durt, N. J. Cerf, N. Gisin, and M. Żukowski, “Security of quantum key distribution with entangled qutrits,” Phys. Rev. A 67, 012311 (2003).
[CrossRef]

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[CrossRef]

Chekhova, M. V.

Y. I. Bogdanov, M. V. Chekhova, S. P. Kulik, G. A. Maslennikov, C. H. Oh, and M. K. Tey, “Preparation of arbitrary qutrit state based on biphotons,” Proc. SPIE 5833, 202–212 (2005).
[CrossRef]

Y. I. Bogdanov, M. V. Chekhova, L. A. Krivitsky, S. P. Kulik, A. N. Penin, A. A. Zhukov, L. C. Kwek, C. H. Oh, and M. K. Tey, “Statistical reconstruction of qutrits,” Phys. Rev. A 70, 042303 (2004).
[CrossRef]

Y. I. Bogdanov, M. V. Chekhova, S. P. Kulik, G. A. Maslennikov, A. A. Zhukov, C. H. Oh, and M. K. Tey, “Qutrit state engineering with biphotons,” Phys. Rev. Lett. 93, 230503 (2004).
[CrossRef]

Chen, Y. A.

W. B. Gao, X. C. Yao, J. M. Cai, H. Lu, P. Xu, T. Yang, C. Y. Lu, Y. A. Chen, Z. B. Chen, and J. W. Pan, “Experimental measurement-based quantum computing beyond the cluster-state model,” Nat. Photonics 5, 117–123 (2011).
[CrossRef]

Chen, Y.-A.

X.-C. Yao, T.-X. Wang, P. Xu, H. Lu, G.-S. Pan, X.-H. Bao, C.-Z. Peng, C.-Y. Lu, Y.-A. Chen, and J.-W. Pan, “Observation of eight-photon entanglement,” Nat. Photonics 6, 225–228 (2012).
[CrossRef]

Chen, Z. B.

W. B. Gao, X. C. Yao, J. M. Cai, H. Lu, P. Xu, T. Yang, C. Y. Lu, Y. A. Chen, Z. B. Chen, and J. W. Pan, “Experimental measurement-based quantum computing beyond the cluster-state model,” Nat. Photonics 5, 117–123 (2011).
[CrossRef]

Chwalla, M.

T. Monz, P. Schindler, J. T. Barreiro, M. Chwalla, D. Nigg, W. A. Coish, M. Harlander, W. Haensel, M. Hennrich, and R. Blatt, “14 qubit entanglement: creation and coherence,” Phys. Rev. Lett. 106, 130506 (2011).
[CrossRef]

Coish, W. A.

T. Monz, P. Schindler, J. T. Barreiro, M. Chwalla, D. Nigg, W. A. Coish, M. Harlander, W. Haensel, M. Hennrich, and R. Blatt, “14 qubit entanglement: creation and coherence,” Phys. Rev. Lett. 106, 130506 (2011).
[CrossRef]

Crépeau, C.

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).
[CrossRef]

Dalton, R. B.

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]

Daniell, M.

D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger–Horne–Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349(1999).
[CrossRef]

De Martini, F.

G. Vallone, E. Pomarico, F. De Martini, and P. Mataloni, “Experimental realization of polarization qutrits from nonmaximally entangled states,” Phys. Rev. A 76, 012319 (2007).
[CrossRef]

Dovrat, L.

A. Halevy, E. Megidish, T. Shacham, L. Dovrat, and H. S. Eisenberg, “Projection of two biphoton qutrits onto a maximally entangled state,” Phys. Rev. Lett. 106, 130502 (2011).
[CrossRef]

Duan, L. M.

L. M. Duan and R. Raussendorf, “Efficient quantum computation with probabilistic quantum gates,” Phys. Rev. Lett. 95, 080503 (2005).
[CrossRef]

Dür, W.

J. M. Cai, A. Miyake, W. Dür, and H. J. Briegel, “Universal quantum computer from a quantum magnet,” Phys. Rev. A 82, 052309 (2010).
[CrossRef]

J. M. Cai, W. Dür, M. Van den Nest, A. Miyake, and H. J. Briegel, “Quantum computation in correlation space and extremal entanglement,” Phys. Rev. Lett. 103, 050503 (2009).
[CrossRef]

Durt, T.

T. Durt, N. J. Cerf, N. Gisin, and M. Żukowski, “Security of quantum key distribution with entangled qutrits,” Phys. Rev. A 67, 012311 (2003).
[CrossRef]

Eibl, M.

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
[CrossRef]

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[CrossRef]

Eisenberg, H. S.

A. Halevy, E. Megidish, T. Shacham, L. Dovrat, and H. S. Eisenberg, “Projection of two biphoton qutrits onto a maximally entangled state,” Phys. Rev. Lett. 106, 130502 (2011).
[CrossRef]

Eisert, J.

D. Gross and J. Eisert, “Novel schemes for measurement-based quantum computation,” Phys. Rev. Lett. 98, 220503 (2007).
[CrossRef]

Gaertner, S.

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[CrossRef]

Gao, W. B.

W. B. Gao, X. C. Yao, J. M. Cai, H. Lu, P. Xu, T. Yang, C. Y. Lu, Y. A. Chen, Z. B. Chen, and J. W. Pan, “Experimental measurement-based quantum computing beyond the cluster-state model,” Nat. Photonics 5, 117–123 (2011).
[CrossRef]

Gilchrist, A.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[CrossRef]

B. P. Lanyon, T. J. Weinhold, N. K. Langford, J. L. O’Brien, K. J. Resch, A. Gilchrist, and A. G. White, “Manipulating biphotonic qutrits,” Phys. Rev. Lett. 100, 060504 (2008).
[CrossRef]

T. C. Ralph, K. J. Resch, and A. Gilchrist, “Efficient Toffoli gates using qudits,” Phys. Rev. A 75, 022313 (2007).
[CrossRef]

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]

Gisin, N.

T. Durt, N. J. Cerf, N. Gisin, and M. Żukowski, “Security of quantum key distribution with entangled qutrits,” Phys. Rev. A 67, 012311 (2003).
[CrossRef]

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[CrossRef]

Gröblacher, S.

S. Gröblacher, Y. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[CrossRef]

Gross, D.

D. Gross and J. Eisert, “Novel schemes for measurement-based quantum computation,” Phys. Rev. Lett. 98, 220503 (2007).
[CrossRef]

Gühne, O.

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[CrossRef]

Guo, G.-C.

Y.-F. Huang, B.-H. Liu, L. Peng, Y.-H. Li, L. Li, C.-F. Li, and G.-C. Guo, “Experimental generation of an eight-photon Greenberger–Horne–Zeilinger state,” Nat. Commun. 2, 546–551 (2011).
[CrossRef]

Haensel, W.

T. Monz, P. Schindler, J. T. Barreiro, M. Chwalla, D. Nigg, W. A. Coish, M. Harlander, W. Haensel, M. Hennrich, and R. Blatt, “14 qubit entanglement: creation and coherence,” Phys. Rev. Lett. 106, 130506 (2011).
[CrossRef]

Halevy, A.

A. Halevy, E. Megidish, T. Shacham, L. Dovrat, and H. S. Eisenberg, “Projection of two biphoton qutrits onto a maximally entangled state,” Phys. Rev. Lett. 106, 130502 (2011).
[CrossRef]

Harlander, M.

T. Monz, P. Schindler, J. T. Barreiro, M. Chwalla, D. Nigg, W. A. Coish, M. Harlander, W. Haensel, M. Hennrich, and R. Blatt, “14 qubit entanglement: creation and coherence,” Phys. Rev. Lett. 106, 130506 (2011).
[CrossRef]

Harvey, M. D.

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]

He, B.

B. He, Q. Lin, and C. Simon, “Cross-Kerr nonlinearity between continuous-mode coherent states and single photons,” Phys. Rev. A 83, 053826 (2011).
[CrossRef]

Q. Lin and B. He, “Bi-directional mapping between polarization and spatially encoded photonic qutrits,” Phys. Rev. A 80, 062312 (2009).
[CrossRef]

Hennrich, M.

T. Monz, P. Schindler, J. T. Barreiro, M. Chwalla, D. Nigg, W. A. Coish, M. Harlander, W. Haensel, M. Hennrich, and R. Blatt, “14 qubit entanglement: creation and coherence,” Phys. Rev. Lett. 106, 130506 (2011).
[CrossRef]

Hong, C. K.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef]

Horne, M. A.

A. Zeilinger, M. A. Horne, H. Weinfurter, and M. Żukowski, “Three-particle entanglements from two entangled airs,” Phys. Rev. Lett. 78, 3031–3034 (1997).
[CrossRef]

Howell, J. C.

J. C. Howell, A. Lamas-Linares, and D. Bouwmeester, “Experimental violation of a spin-1 bell inequality using maximally entangled four-photon states,” Phys. Rev. Lett. 88, 030401 (2002).
[CrossRef]

Hradil, Z.

G. M. Terriza, A. Vaziri, J. Řeháček, Z. Hradil, and A. Zeilinger, “Triggered qutrits for quantum communication protocols,” Phys. Rev. Lett. 92, 167903 (2004).
[CrossRef]

Huang, Y.-F.

Y.-F. Huang, B.-H. Liu, L. Peng, Y.-H. Li, L. Li, C.-F. Li, and G.-C. Guo, “Experimental generation of an eight-photon Greenberger–Horne–Zeilinger state,” Nat. Commun. 2, 546–551 (2011).
[CrossRef]

Hyllus, P.

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[CrossRef]

Jennewein, T.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[CrossRef]

Jennewein, Y.

S. Gröblacher, Y. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[CrossRef]

Joo, J.

J. Joo, T. Rudolph, and B. C. Sanders, “A heralded two-qutrit entangled state,” J. Phys. B 42, 114007 (2009).
[CrossRef]

Jozsa, R.

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).
[CrossRef]

Kaltenbaek, R.

R. Kaltenbaek, J. Lavoie, B. Zeng, S. D. Bartlett, and K. J. Resch, “Optical one-way quantum computing with a simulated valence-bond solid,” Nat. Phys. 6, 850–854 (2010).
[CrossRef]

Karlsson, A.

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[CrossRef]

Kiesel, N.

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
[CrossRef]

Kobayashi, T.

H. Mikami and T. Kobayashi, “Remote preparation of qutrit states with biphotons,” Phys. Rev. A 75, 022325 (2007).
[CrossRef]

Kok, P.

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(R) (2005).

Krivitsky, L. A.

Y. I. Bogdanov, M. V. Chekhova, L. A. Krivitsky, S. P. Kulik, A. N. Penin, A. A. Zhukov, L. C. Kwek, C. H. Oh, and M. K. Tey, “Statistical reconstruction of qutrits,” Phys. Rev. A 70, 042303 (2004).
[CrossRef]

Kulik, S. P.

E. V. Moreva, G. A. Maslennikov, S. S. Straupe, and S. P. Kulik, “Realization of four-level qudits using biphotons,” Phys. Rev. Lett. 97, 023602 (2006).
[CrossRef]

Y. I. Bogdanov, M. V. Chekhova, S. P. Kulik, G. A. Maslennikov, C. H. Oh, and M. K. Tey, “Preparation of arbitrary qutrit state based on biphotons,” Proc. SPIE 5833, 202–212 (2005).
[CrossRef]

Y. I. Bogdanov, M. V. Chekhova, L. A. Krivitsky, S. P. Kulik, A. N. Penin, A. A. Zhukov, L. C. Kwek, C. H. Oh, and M. K. Tey, “Statistical reconstruction of qutrits,” Phys. Rev. A 70, 042303 (2004).
[CrossRef]

Y. I. Bogdanov, M. V. Chekhova, S. P. Kulik, G. A. Maslennikov, A. A. Zhukov, C. H. Oh, and M. K. Tey, “Qutrit state engineering with biphotons,” Phys. Rev. Lett. 93, 230503 (2004).
[CrossRef]

Kurtsiefer, C.

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[CrossRef]

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
[CrossRef]

Kwek, L. C.

Y. I. Bogdanov, M. V. Chekhova, L. A. Krivitsky, S. P. Kulik, A. N. Penin, A. A. Zhukov, L. C. Kwek, C. H. Oh, and M. K. Tey, “Statistical reconstruction of qutrits,” Phys. Rev. A 70, 042303 (2004).
[CrossRef]

Lamas-Linares, A.

J. C. Howell, A. Lamas-Linares, and D. Bouwmeester, “Experimental violation of a spin-1 bell inequality using maximally entangled four-photon states,” Phys. Rev. Lett. 88, 030401 (2002).
[CrossRef]

Langford, N. K.

B. P. Lanyon, T. J. Weinhold, N. K. Langford, J. L. O’Brien, K. J. Resch, A. Gilchrist, and A. G. White, “Manipulating biphotonic qutrits,” Phys. Rev. Lett. 100, 060504 (2008).
[CrossRef]

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]

Lanyon, B. P.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[CrossRef]

B. P. Lanyon, T. J. Weinhold, N. K. Langford, J. L. O’Brien, K. J. Resch, A. Gilchrist, and A. G. White, “Manipulating biphotonic qutrits,” Phys. Rev. Lett. 100, 060504 (2008).
[CrossRef]

Lavoie, J.

R. Kaltenbaek, J. Lavoie, B. Zeng, S. D. Bartlett, and K. J. Resch, “Optical one-way quantum computing with a simulated valence-bond solid,” Nat. Phys. 6, 850–854 (2010).
[CrossRef]

Lewenstein, M.

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[CrossRef]

Li, C.-F.

Y.-F. Huang, B.-H. Liu, L. Peng, Y.-H. Li, L. Li, C.-F. Li, and G.-C. Guo, “Experimental generation of an eight-photon Greenberger–Horne–Zeilinger state,” Nat. Commun. 2, 546–551 (2011).
[CrossRef]

Li, L.

Y.-F. Huang, B.-H. Liu, L. Peng, Y.-H. Li, L. Li, C.-F. Li, and G.-C. Guo, “Experimental generation of an eight-photon Greenberger–Horne–Zeilinger state,” Nat. Commun. 2, 546–551 (2011).
[CrossRef]

Li, Y. M.

Y. M. Li, K. S. Zhang, and K. C. Peng, “Generation of qudits and entangled qudits,” Phys. Rev. A 77, 015802 (2008).
[CrossRef]

Li, Y.-H.

Y.-F. Huang, B.-H. Liu, L. Peng, Y.-H. Li, L. Li, C.-F. Li, and G.-C. Guo, “Experimental generation of an eight-photon Greenberger–Horne–Zeilinger state,” Nat. Commun. 2, 546–551 (2011).
[CrossRef]

Lin, Q.

Q. Lin, “Efficient generation of arbitrary multi-partite polarized entangled qudits,” Sci. Sin. Phys. Mech. Astron. 42, 842–851 (2012).
[CrossRef]

X. L. Ye and Q. Lin, “Efficient and flexible generation of entangled qudits with cross-phase modulation,” J. Opt. Soc. Am. B 29, 1810–1814 (2012).
[CrossRef]

B. He, Q. Lin, and C. Simon, “Cross-Kerr nonlinearity between continuous-mode coherent states and single photons,” Phys. Rev. A 83, 053826 (2011).
[CrossRef]

Q. Lin and B. He, “Bi-directional mapping between polarization and spatially encoded photonic qutrits,” Phys. Rev. A 80, 062312 (2009).
[CrossRef]

Liu, B.-H.

Y.-F. Huang, B.-H. Liu, L. Peng, Y.-H. Li, L. Li, C.-F. Li, and G.-C. Guo, “Experimental generation of an eight-photon Greenberger–Horne–Zeilinger state,” Nat. Commun. 2, 546–551 (2011).
[CrossRef]

Lu, C. Y.

W. B. Gao, X. C. Yao, J. M. Cai, H. Lu, P. Xu, T. Yang, C. Y. Lu, Y. A. Chen, Z. B. Chen, and J. W. Pan, “Experimental measurement-based quantum computing beyond the cluster-state model,” Nat. Photonics 5, 117–123 (2011).
[CrossRef]

Lu, C.-Y.

X.-C. Yao, T.-X. Wang, P. Xu, H. Lu, G.-S. Pan, X.-H. Bao, C.-Z. Peng, C.-Y. Lu, Y.-A. Chen, and J.-W. Pan, “Observation of eight-photon entanglement,” Nat. Photonics 6, 225–228 (2012).
[CrossRef]

Lu, H.

X.-C. Yao, T.-X. Wang, P. Xu, H. Lu, G.-S. Pan, X.-H. Bao, C.-Z. Peng, C.-Y. Lu, Y.-A. Chen, and J.-W. Pan, “Observation of eight-photon entanglement,” Nat. Photonics 6, 225–228 (2012).
[CrossRef]

W. B. Gao, X. C. Yao, J. M. Cai, H. Lu, P. Xu, T. Yang, C. Y. Lu, Y. A. Chen, Z. B. Chen, and J. W. Pan, “Experimental measurement-based quantum computing beyond the cluster-state model,” Nat. Photonics 5, 117–123 (2011).
[CrossRef]

Macchiavello, C.

D. Bruß and C. Macchiavello, “Optimal eavesdropping in cryptography with three-dimensional quantum states,” Phys. Rev. Lett. 88, 127901 (2002).
[CrossRef]

Mandel, L.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef]

Maslennikov, G. A.

E. V. Moreva, G. A. Maslennikov, S. S. Straupe, and S. P. Kulik, “Realization of four-level qudits using biphotons,” Phys. Rev. Lett. 97, 023602 (2006).
[CrossRef]

Y. I. Bogdanov, M. V. Chekhova, S. P. Kulik, G. A. Maslennikov, C. H. Oh, and M. K. Tey, “Preparation of arbitrary qutrit state based on biphotons,” Proc. SPIE 5833, 202–212 (2005).
[CrossRef]

Y. I. Bogdanov, M. V. Chekhova, S. P. Kulik, G. A. Maslennikov, A. A. Zhukov, C. H. Oh, and M. K. Tey, “Qutrit state engineering with biphotons,” Phys. Rev. Lett. 93, 230503 (2004).
[CrossRef]

Mataloni, P.

G. Vallone, E. Pomarico, F. De Martini, and P. Mataloni, “Experimental realization of polarization qutrits from nonmaximally entangled states,” Phys. Rev. A 76, 012319 (2007).
[CrossRef]

Megidish, E.

A. Halevy, E. Megidish, T. Shacham, L. Dovrat, and H. S. Eisenberg, “Projection of two biphoton qutrits onto a maximally entangled state,” Phys. Rev. Lett. 106, 130502 (2011).
[CrossRef]

Mikami, H.

H. Mikami and T. Kobayashi, “Remote preparation of qutrit states with biphotons,” Phys. Rev. A 75, 022325 (2007).
[CrossRef]

Miyake, A.

J. M. Cai, A. Miyake, W. Dür, and H. J. Briegel, “Universal quantum computer from a quantum magnet,” Phys. Rev. A 82, 052309 (2010).
[CrossRef]

J. M. Cai, W. Dür, M. Van den Nest, A. Miyake, and H. J. Briegel, “Quantum computation in correlation space and extremal entanglement,” Phys. Rev. Lett. 103, 050503 (2009).
[CrossRef]

Monz, T.

T. Monz, P. Schindler, J. T. Barreiro, M. Chwalla, D. Nigg, W. A. Coish, M. Harlander, W. Haensel, M. Hennrich, and R. Blatt, “14 qubit entanglement: creation and coherence,” Phys. Rev. Lett. 106, 130506 (2011).
[CrossRef]

Moreva, E. V.

E. V. Moreva, G. A. Maslennikov, S. S. Straupe, and S. P. Kulik, “Realization of four-level qudits using biphotons,” Phys. Rev. Lett. 97, 023602 (2006).
[CrossRef]

Munro, W. J.

W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
[CrossRef]

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(R) (2005).

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502(2004).
[CrossRef]

Nemoto, K.

W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
[CrossRef]

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(R) (2005).

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502(2004).
[CrossRef]

Nigg, D.

T. Monz, P. Schindler, J. T. Barreiro, M. Chwalla, D. Nigg, W. A. Coish, M. Harlander, W. Haensel, M. Hennrich, and R. Blatt, “14 qubit entanglement: creation and coherence,” Phys. Rev. Lett. 106, 130506 (2011).
[CrossRef]

O’Brien, J. L.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[CrossRef]

B. P. Lanyon, T. J. Weinhold, N. K. Langford, J. L. O’Brien, K. J. Resch, A. Gilchrist, and A. G. White, “Manipulating biphotonic qutrits,” Phys. Rev. Lett. 100, 060504 (2008).
[CrossRef]

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]

Oh, C. H.

Y. I. Bogdanov, M. V. Chekhova, S. P. Kulik, G. A. Maslennikov, C. H. Oh, and M. K. Tey, “Preparation of arbitrary qutrit state based on biphotons,” Proc. SPIE 5833, 202–212 (2005).
[CrossRef]

Y. I. Bogdanov, M. V. Chekhova, L. A. Krivitsky, S. P. Kulik, A. N. Penin, A. A. Zhukov, L. C. Kwek, C. H. Oh, and M. K. Tey, “Statistical reconstruction of qutrits,” Phys. Rev. A 70, 042303 (2004).
[CrossRef]

Y. I. Bogdanov, M. V. Chekhova, S. P. Kulik, G. A. Maslennikov, A. A. Zhukov, C. H. Oh, and M. K. Tey, “Qutrit state engineering with biphotons,” Phys. Rev. Lett. 93, 230503 (2004).
[CrossRef]

Ou, Z. Y.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef]

Pan, G.-S.

X.-C. Yao, T.-X. Wang, P. Xu, H. Lu, G.-S. Pan, X.-H. Bao, C.-Z. Peng, C.-Y. Lu, Y.-A. Chen, and J.-W. Pan, “Observation of eight-photon entanglement,” Nat. Photonics 6, 225–228 (2012).
[CrossRef]

Pan, J. W.

W. B. Gao, X. C. Yao, J. M. Cai, H. Lu, P. Xu, T. Yang, C. Y. Lu, Y. A. Chen, Z. B. Chen, and J. W. Pan, “Experimental measurement-based quantum computing beyond the cluster-state model,” Nat. Photonics 5, 117–123 (2011).
[CrossRef]

Pan, J.-W.

X.-C. Yao, T.-X. Wang, P. Xu, H. Lu, G.-S. Pan, X.-H. Bao, C.-Z. Peng, C.-Y. Lu, Y.-A. Chen, and J.-W. Pan, “Observation of eight-photon entanglement,” Nat. Photonics 6, 225–228 (2012).
[CrossRef]

D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger–Horne–Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349(1999).
[CrossRef]

Peng, C.-Z.

X.-C. Yao, T.-X. Wang, P. Xu, H. Lu, G.-S. Pan, X.-H. Bao, C.-Z. Peng, C.-Y. Lu, Y.-A. Chen, and J.-W. Pan, “Observation of eight-photon entanglement,” Nat. Photonics 6, 225–228 (2012).
[CrossRef]

Peng, K. C.

Y. M. Li, K. S. Zhang, and K. C. Peng, “Generation of qudits and entangled qudits,” Phys. Rev. A 77, 015802 (2008).
[CrossRef]

Peng, L.

Y.-F. Huang, B.-H. Liu, L. Peng, Y.-H. Li, L. Li, C.-F. Li, and G.-C. Guo, “Experimental generation of an eight-photon Greenberger–Horne–Zeilinger state,” Nat. Commun. 2, 546–551 (2011).
[CrossRef]

Penin, A. N.

Y. I. Bogdanov, M. V. Chekhova, L. A. Krivitsky, S. P. Kulik, A. N. Penin, A. A. Zhukov, L. C. Kwek, C. H. Oh, and M. K. Tey, “Statistical reconstruction of qutrits,” Phys. Rev. A 70, 042303 (2004).
[CrossRef]

Peres, A.

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).
[CrossRef]

Pomarico, E.

G. Vallone, E. Pomarico, F. De Martini, and P. Mataloni, “Experimental realization of polarization qutrits from nonmaximally entangled states,” Phys. Rev. A 76, 012319 (2007).
[CrossRef]

Pryde, G. J.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[CrossRef]

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]

Ralph, T. C.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[CrossRef]

T. C. Ralph, K. J. Resch, and A. Gilchrist, “Efficient Toffoli gates using qudits,” Phys. Rev. A 75, 022313 (2007).
[CrossRef]

Raussendorf, R.

L. M. Duan and R. Raussendorf, “Efficient quantum computation with probabilistic quantum gates,” Phys. Rev. Lett. 95, 080503 (2005).
[CrossRef]

Reck, M.

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73, 58–61 (1994).
[CrossRef]

Rehácek, J.

G. M. Terriza, A. Vaziri, J. Řeháček, Z. Hradil, and A. Zeilinger, “Triggered qutrits for quantum communication protocols,” Phys. Rev. Lett. 92, 167903 (2004).
[CrossRef]

Resch, K. J.

R. Kaltenbaek, J. Lavoie, B. Zeng, S. D. Bartlett, and K. J. Resch, “Optical one-way quantum computing with a simulated valence-bond solid,” Nat. Phys. 6, 850–854 (2010).
[CrossRef]

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[CrossRef]

B. P. Lanyon, T. J. Weinhold, N. K. Langford, J. L. O’Brien, K. J. Resch, A. Gilchrist, and A. G. White, “Manipulating biphotonic qutrits,” Phys. Rev. Lett. 100, 060504 (2008).
[CrossRef]

T. C. Ralph, K. J. Resch, and A. Gilchrist, “Efficient Toffoli gates using qudits,” Phys. Rev. A 75, 022313 (2007).
[CrossRef]

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]

Rudolph, T.

J. Joo, T. Rudolph, and B. C. Sanders, “A heralded two-qutrit entangled state,” J. Phys. B 42, 114007 (2009).
[CrossRef]

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]

R. W. Spekkens and T. Rudolph, “Degrees of concealment and bindingness in quantum bit commitment protocols,” Phys. Rev. A 65, 012310 (2001).
[CrossRef]

Sanders, B. C.

J. Joo, T. Rudolph, and B. C. Sanders, “A heralded two-qutrit entangled state,” J. Phys. B 42, 114007 (2009).
[CrossRef]

Sanpera, A.

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[CrossRef]

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]

Schindler, P.

T. Monz, P. Schindler, J. T. Barreiro, M. Chwalla, D. Nigg, W. A. Coish, M. Harlander, W. Haensel, M. Hennrich, and R. Blatt, “14 qubit entanglement: creation and coherence,” Phys. Rev. Lett. 106, 130506 (2011).
[CrossRef]

Shacham, T.

A. Halevy, E. Megidish, T. Shacham, L. Dovrat, and H. S. Eisenberg, “Projection of two biphoton qutrits onto a maximally entangled state,” Phys. Rev. Lett. 106, 130502 (2011).
[CrossRef]

Simon, C.

B. He, Q. Lin, and C. Simon, “Cross-Kerr nonlinearity between continuous-mode coherent states and single photons,” Phys. Rev. A 83, 053826 (2011).
[CrossRef]

Spekkens, R. W.

R. W. Spekkens and T. Rudolph, “Degrees of concealment and bindingness in quantum bit commitment protocols,” Phys. Rev. A 65, 012310 (2001).
[CrossRef]

Spiller, T. P.

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(R) (2005).

W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
[CrossRef]

Straupe, S. S.

E. V. Moreva, G. A. Maslennikov, S. S. Straupe, and S. P. Kulik, “Realization of four-level qudits using biphotons,” Phys. Rev. Lett. 97, 023602 (2006).
[CrossRef]

Terriza, G. M.

G. M. Terriza, A. Vaziri, J. Řeháček, Z. Hradil, and A. Zeilinger, “Triggered qutrits for quantum communication protocols,” Phys. Rev. Lett. 92, 167903 (2004).
[CrossRef]

Tey, M. K.

Y. I. Bogdanov, M. V. Chekhova, S. P. Kulik, G. A. Maslennikov, C. H. Oh, and M. K. Tey, “Preparation of arbitrary qutrit state based on biphotons,” Proc. SPIE 5833, 202–212 (2005).
[CrossRef]

Y. I. Bogdanov, M. V. Chekhova, L. A. Krivitsky, S. P. Kulik, A. N. Penin, A. A. Zhukov, L. C. Kwek, C. H. Oh, and M. K. Tey, “Statistical reconstruction of qutrits,” Phys. Rev. A 70, 042303 (2004).
[CrossRef]

Y. I. Bogdanov, M. V. Chekhova, S. P. Kulik, G. A. Maslennikov, A. A. Zhukov, C. H. Oh, and M. K. Tey, “Qutrit state engineering with biphotons,” Phys. Rev. Lett. 93, 230503 (2004).
[CrossRef]

Vallone, G.

G. Vallone, E. Pomarico, F. De Martini, and P. Mataloni, “Experimental realization of polarization qutrits from nonmaximally entangled states,” Phys. Rev. A 76, 012319 (2007).
[CrossRef]

Van den Nest, M.

J. M. Cai, W. Dür, M. Van den Nest, A. Miyake, and H. J. Briegel, “Quantum computation in correlation space and extremal entanglement,” Phys. Rev. Lett. 103, 050503 (2009).
[CrossRef]

Vaziri, A.

S. Gröblacher, Y. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[CrossRef]

G. M. Terriza, A. Vaziri, J. Řeháček, Z. Hradil, and A. Zeilinger, “Triggered qutrits for quantum communication protocols,” Phys. Rev. Lett. 92, 167903 (2004).
[CrossRef]

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]

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]

Wang, T.-X.

X.-C. Yao, T.-X. Wang, P. Xu, H. Lu, G.-S. Pan, X.-H. Bao, C.-Z. Peng, C.-Y. Lu, Y.-A. Chen, and J.-W. Pan, “Observation of eight-photon entanglement,” Nat. Photonics 6, 225–228 (2012).
[CrossRef]

Weihs, G.

S. Gröblacher, Y. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[CrossRef]

Weinfurter, H.

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]

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
[CrossRef]

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[CrossRef]

D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger–Horne–Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349(1999).
[CrossRef]

A. Zeilinger, M. A. Horne, H. Weinfurter, and M. Żukowski, “Three-particle entanglements from two entangled airs,” Phys. Rev. Lett. 78, 3031–3034 (1997).
[CrossRef]

Weinhold, T. J.

B. P. Lanyon, T. J. Weinhold, N. K. Langford, J. L. O’Brien, K. J. Resch, A. Gilchrist, and A. G. White, “Manipulating biphotonic qutrits,” Phys. Rev. Lett. 100, 060504 (2008).
[CrossRef]

White, A. G.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[CrossRef]

B. P. Lanyon, T. J. Weinhold, N. K. Langford, J. L. O’Brien, K. J. Resch, A. Gilchrist, and A. G. White, “Manipulating biphotonic qutrits,” Phys. Rev. Lett. 100, 060504 (2008).
[CrossRef]

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]

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).
[CrossRef]

Wootters, W. K.

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).
[CrossRef]

Xu, P.

X.-C. Yao, T.-X. Wang, P. Xu, H. Lu, G.-S. Pan, X.-H. Bao, C.-Z. Peng, C.-Y. Lu, Y.-A. Chen, and J.-W. Pan, “Observation of eight-photon entanglement,” Nat. Photonics 6, 225–228 (2012).
[CrossRef]

W. B. Gao, X. C. Yao, J. M. Cai, H. Lu, P. Xu, T. Yang, C. Y. Lu, Y. A. Chen, Z. B. Chen, and J. W. Pan, “Experimental measurement-based quantum computing beyond the cluster-state model,” Nat. Photonics 5, 117–123 (2011).
[CrossRef]

Yang, T.

W. B. Gao, X. C. Yao, J. M. Cai, H. Lu, P. Xu, T. Yang, C. Y. Lu, Y. A. Chen, Z. B. Chen, and J. W. Pan, “Experimental measurement-based quantum computing beyond the cluster-state model,” Nat. Photonics 5, 117–123 (2011).
[CrossRef]

Yao, X. C.

W. B. Gao, X. C. Yao, J. M. Cai, H. Lu, P. Xu, T. Yang, C. Y. Lu, Y. A. Chen, Z. B. Chen, and J. W. Pan, “Experimental measurement-based quantum computing beyond the cluster-state model,” Nat. Photonics 5, 117–123 (2011).
[CrossRef]

Yao, X.-C.

X.-C. Yao, T.-X. Wang, P. Xu, H. Lu, G.-S. Pan, X.-H. Bao, C.-Z. Peng, C.-Y. Lu, Y.-A. Chen, and J.-W. Pan, “Observation of eight-photon entanglement,” Nat. Photonics 6, 225–228 (2012).
[CrossRef]

Ye, X. L.

Zeilinger, A.

S. Gröblacher, Y. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[CrossRef]

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]

G. M. Terriza, A. Vaziri, J. Řeháček, Z. Hradil, and A. Zeilinger, “Triggered qutrits for quantum communication protocols,” Phys. Rev. Lett. 92, 167903 (2004).
[CrossRef]

D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger–Horne–Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349(1999).
[CrossRef]

A. Zeilinger, M. A. Horne, H. Weinfurter, and M. Żukowski, “Three-particle entanglements from two entangled airs,” Phys. Rev. Lett. 78, 3031–3034 (1997).
[CrossRef]

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73, 58–61 (1994).
[CrossRef]

Zeng, B.

R. Kaltenbaek, J. Lavoie, B. Zeng, S. D. Bartlett, and K. J. Resch, “Optical one-way quantum computing with a simulated valence-bond solid,” Nat. Phys. 6, 850–854 (2010).
[CrossRef]

Zhang, K. S.

Y. M. Li, K. S. Zhang, and K. C. Peng, “Generation of qudits and entangled qudits,” Phys. Rev. A 77, 015802 (2008).
[CrossRef]

Zhukov, A. A.

Y. I. Bogdanov, M. V. Chekhova, L. A. Krivitsky, S. P. Kulik, A. N. Penin, A. A. Zhukov, L. C. Kwek, C. H. Oh, and M. K. Tey, “Statistical reconstruction of qutrits,” Phys. Rev. A 70, 042303 (2004).
[CrossRef]

Y. I. Bogdanov, M. V. Chekhova, S. P. Kulik, G. A. Maslennikov, A. A. Zhukov, C. H. Oh, and M. K. Tey, “Qutrit state engineering with biphotons,” Phys. Rev. Lett. 93, 230503 (2004).
[CrossRef]

Zukowski, M.

T. Durt, N. J. Cerf, N. Gisin, and M. Żukowski, “Security of quantum key distribution with entangled qutrits,” Phys. Rev. A 67, 012311 (2003).
[CrossRef]

A. Zeilinger, M. A. Horne, H. Weinfurter, and M. Żukowski, “Three-particle entanglements from two entangled airs,” Phys. Rev. Lett. 78, 3031–3034 (1997).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. B (1)

J. Joo, T. Rudolph, and B. C. Sanders, “A heralded two-qutrit entangled state,” J. Phys. B 42, 114007 (2009).
[CrossRef]

Nat. Commun. (1)

Y.-F. Huang, B.-H. Liu, L. Peng, Y.-H. Li, L. Li, C.-F. Li, and G.-C. Guo, “Experimental generation of an eight-photon Greenberger–Horne–Zeilinger state,” Nat. Commun. 2, 546–551 (2011).
[CrossRef]

Nat. Photonics (2)

X.-C. Yao, T.-X. Wang, P. Xu, H. Lu, G.-S. Pan, X.-H. Bao, C.-Z. Peng, C.-Y. Lu, Y.-A. Chen, and J.-W. Pan, “Observation of eight-photon entanglement,” Nat. Photonics 6, 225–228 (2012).
[CrossRef]

W. B. Gao, X. C. Yao, J. M. Cai, H. Lu, P. Xu, T. Yang, C. Y. Lu, Y. A. Chen, Z. B. Chen, and J. W. Pan, “Experimental measurement-based quantum computing beyond the cluster-state model,” Nat. Photonics 5, 117–123 (2011).
[CrossRef]

Nat. Phys. (2)

R. Kaltenbaek, J. Lavoie, B. Zeng, S. D. Bartlett, and K. J. Resch, “Optical one-way quantum computing with a simulated valence-bond solid,” Nat. Phys. 6, 850–854 (2010).
[CrossRef]

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[CrossRef]

Nature (1)

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]

New J. Phys. (2)

S. Gröblacher, Y. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[CrossRef]

W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
[CrossRef]

Phys. Rev. A (11)

Q. Lin and B. He, “Bi-directional mapping between polarization and spatially encoded photonic qutrits,” Phys. Rev. A 80, 062312 (2009).
[CrossRef]

B. He, Q. Lin, and C. Simon, “Cross-Kerr nonlinearity between continuous-mode coherent states and single photons,” Phys. Rev. A 83, 053826 (2011).
[CrossRef]

T. C. Ralph, K. J. Resch, and A. Gilchrist, “Efficient Toffoli gates using qudits,” Phys. Rev. A 75, 022313 (2007).
[CrossRef]

T. Durt, N. J. Cerf, N. Gisin, and M. Żukowski, “Security of quantum key distribution with entangled qutrits,” Phys. Rev. A 67, 012311 (2003).
[CrossRef]

R. W. Spekkens and T. Rudolph, “Degrees of concealment and bindingness in quantum bit commitment protocols,” Phys. Rev. A 65, 012310 (2001).
[CrossRef]

Y. I. Bogdanov, M. V. Chekhova, L. A. Krivitsky, S. P. Kulik, A. N. Penin, A. A. Zhukov, L. C. Kwek, C. H. Oh, and M. K. Tey, “Statistical reconstruction of qutrits,” Phys. Rev. A 70, 042303 (2004).
[CrossRef]

J. M. Cai, A. Miyake, W. Dür, and H. J. Briegel, “Universal quantum computer from a quantum magnet,” Phys. Rev. A 82, 052309 (2010).
[CrossRef]

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(R) (2005).

H. Mikami and T. Kobayashi, “Remote preparation of qutrit states with biphotons,” Phys. Rev. A 75, 022325 (2007).
[CrossRef]

G. Vallone, E. Pomarico, F. De Martini, and P. Mataloni, “Experimental realization of polarization qutrits from nonmaximally entangled states,” Phys. Rev. A 76, 012319 (2007).
[CrossRef]

Y. M. Li, K. S. Zhang, and K. C. Peng, “Generation of qudits and entangled qudits,” Phys. Rev. A 77, 015802 (2008).
[CrossRef]

Phys. Rev. Lett. (22)

B. P. Lanyon, T. J. Weinhold, N. K. Langford, J. L. O’Brien, K. J. Resch, A. Gilchrist, and A. G. White, “Manipulating biphotonic qutrits,” Phys. Rev. Lett. 100, 060504 (2008).
[CrossRef]

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502(2004).
[CrossRef]

A. Halevy, E. Megidish, T. Shacham, L. Dovrat, and H. S. Eisenberg, “Projection of two biphoton qutrits onto a maximally entangled state,” Phys. Rev. Lett. 106, 130502 (2011).
[CrossRef]

J. C. Howell, A. Lamas-Linares, and D. Bouwmeester, “Experimental violation of a spin-1 bell inequality using maximally entangled four-photon states,” Phys. Rev. Lett. 88, 030401 (2002).
[CrossRef]

Y. I. Bogdanov, M. V. Chekhova, S. P. Kulik, G. A. Maslennikov, A. A. Zhukov, C. H. Oh, and M. K. Tey, “Qutrit state engineering with biphotons,” Phys. Rev. Lett. 93, 230503 (2004).
[CrossRef]

E. V. Moreva, G. A. Maslennikov, S. S. Straupe, and S. P. Kulik, “Realization of four-level qudits using biphotons,” Phys. Rev. Lett. 97, 023602 (2006).
[CrossRef]

D. Bruß and C. Macchiavello, “Optimal eavesdropping in cryptography with three-dimensional quantum states,” Phys. Rev. Lett. 88, 127901 (2002).
[CrossRef]

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[CrossRef]

A. Zeilinger, M. A. Horne, H. Weinfurter, and M. Żukowski, “Three-particle entanglements from two entangled airs,” Phys. Rev. Lett. 78, 3031–3034 (1997).
[CrossRef]

D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger–Horne–Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349(1999).
[CrossRef]

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
[CrossRef]

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[CrossRef]

G. M. Terriza, A. Vaziri, J. Řeháček, Z. Hradil, and A. Zeilinger, “Triggered qutrits for quantum communication protocols,” Phys. Rev. Lett. 92, 167903 (2004).
[CrossRef]

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]

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).
[CrossRef]

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

T. Monz, P. Schindler, J. T. Barreiro, M. Chwalla, D. Nigg, W. A. Coish, M. Harlander, W. Haensel, M. Hennrich, and R. Blatt, “14 qubit entanglement: creation and coherence,” Phys. Rev. Lett. 106, 130506 (2011).
[CrossRef]

D. Gross and J. Eisert, “Novel schemes for measurement-based quantum computation,” Phys. Rev. Lett. 98, 220503 (2007).
[CrossRef]

J. M. Cai, W. Dür, M. Van den Nest, A. Miyake, and H. J. Briegel, “Quantum computation in correlation space and extremal entanglement,” Phys. Rev. Lett. 103, 050503 (2009).
[CrossRef]

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73, 58–61 (1994).
[CrossRef]

L. M. Duan and R. Raussendorf, “Efficient quantum computation with probabilistic quantum gates,” Phys. Rev. Lett. 95, 080503 (2005).
[CrossRef]

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef]

Proc. SPIE (1)

Y. I. Bogdanov, M. V. Chekhova, S. P. Kulik, G. A. Maslennikov, C. H. Oh, and M. K. Tey, “Preparation of arbitrary qutrit state based on biphotons,” Proc. SPIE 5833, 202–212 (2005).
[CrossRef]

Sci. Sin. Phys. Mech. Astron. (1)

Q. Lin, “Efficient generation of arbitrary multi-partite polarized entangled qudits,” Sci. Sin. Phys. Mech. Astron. 42, 842–851 (2012).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Generation of single-photon qudit. A single photon in the state |H is injected into a series of proper unitary operations and PBSs. The balanced single-photon qudit encoded by the spatial modes could be generated.

Fig. 2.
Fig. 2.

Generation of asymmetric entangled qutrit. Introduce a balanced single-photon qudit as ancilla, which is coupled to two qubus beams through XPM processes, associated with two independent polarized qutrits. With the proper design of XPM phase shifts, the asymmetric entangled qutrits could be heralded, generated with the success probability 1/9. In addition, if more independent qutrits are introduced and we repeat the same processes, multipartite entangled qutrits could be generated as well.

Fig. 3.
Fig. 3.

Generation of asymmetric entangled qudit. Similar to the generation of asymmetric entangled qutrits, a balanced single-photon qudit is introduced as anciila. Two independent polarized qudits are coupled to the two qubus beams, associated with the ancilla single-photon qudit as depicted in Fig. 3. By the proper design of XPM phase shifts, the asymmetric entangled qudits could be heralded, generated with the success probability 1/n2 determined by the dimension n. Here we suppose k1, which corresponds to the case of asymmetric entangled qudits generation. If the XPM phase shifts induced to the two independent qudits are the same, the symmetric entangle qudits could be generated. Moreover, if more independent qudits are introduced and the similar processes are repeated, multipartite entangled qudits could be generated with the success probability 1/nM determined by the dimension n and partite M.

Equations (24)

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j=0n1cj|jn|jn,
j=0n1cj|jn|(j+k)modnn,
|ϕsn=1nj=0n1|js,
U0=(n1n1n1nn1n).
Uj=(nj1nj1nj1njnj1nj),(j=1,,n1)
13(a0|03|0s+a1|13|1s+a2|23|2s)|α|αei2θ+13(a0|03|1s+a1|13|2s)|α|αei3θ+13a0|03|2s|α|αei4θ+13(a1|13|0s+a2|23|1s)|α|αeiθ+13a2|23|0s|α|α.
13(a0|03|0s+a1|13|1s+a2|23|2s)|0|2α+13(a0|03|1s+a1|13|2s)|α1|α+1+13a0|03|2s|α2|α+2+13(a1|13|0s+a2|23|1s)|α1|α+1+13a2|23|0s|α2|α+2,
a0|03|0s+a1|13|1s+a2|23|2s,
PE=49e2|α|2sin2θ2+29e2|α|2sin2θ,
(a0b1|03|13|0s+a1b2|13|23|1s+a2b0|23|03|2s)|α|αei2θ+rest.,
(a0b1|03|13|0s+a1b2|13|23|1s+a2b0|23|03|2s)|0|2α+rest.
a0b1|03|13|0s+a1b2|13|23|1s+a2b0|23|03|2s,
|js=13k=02e2πijk/3|ks,
a0b1|03|13+a1b2|13|23+a2b0|23|03.
13(|03|13+τm|13|23+τ2m|23|03),
13(|03|23+τm|13|03+τ2m|23|13).
1nj=0n1aj|jn|js|α|αei(n1)θ+rest.,
1nj=0n1aj|jn|js|0|2α+rest.
j=0n1aj|jn|js,
j=0n1ajb(j+k)modn|jn|(j+k)modnn|js|α|αei(n1)θ+rest.
j=0n1ajb(j+k)modn|jn|(j+k)modnn|js.
|js=1nk=0n1e2πijk/n|ks,
j=0n1ajb(j+k)modn|jn|(j+k)modnn.
1nj=0n1τjm|jn|(j+k)modnn,

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