Abstract

In this paper, we provide a simple but powerful module to generate entangled qudits. This module, assisted with cross-Kerr nonlinearity, is flexible for generation of entangled qudits with arbitrary dimensions. Since the generation is still probabilistic, we modify the simple module in order to increase efficiency and save resources. With the modified module, the input independent qudits could be transformed into different entangled forms, which include the possible maximal entangled form and the less entangled forms. The corresponding total success probability could reach 1.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  4. D. Bruß and C. Macchiavello, “Optimal eavesdropping in cryptography with three-dimensional quantum states,” Phys. Rev. Lett. 88, 127901 (2002).
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  5. 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).
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    [CrossRef]
  7. G. M. Terriza, A. Vaziri, J. Řeháček, Z. Hradil, and A. Zeilinger, “Triggered qutrits for quantum communication protocols,” Phys. Rev. Lett. 92, 167903 (2004).
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  15. L. Neves, S. Pádua, and C. Saavedra, “Controlled generation of maximally entangled qudits using twin photons,” Phys. Rev. A 69, 042305 (2004).
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    [CrossRef]
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    [CrossRef]
  33. K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
    [CrossRef]
  34. 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]
  35. Q. Lin and J. Li, “Quantum control gates with weak cross-Kerr nonlinearity,” Phys. Rev. A 79, 022301 (2009).
    [CrossRef]
  36. Q. Lin and B. He, “Single-photon logic gates using minimal resources,” Phys. Rev. A 80, 042310 (2009).
    [CrossRef]
  37. Q. Lin, B. He, J. A. Bergou, and Y. H. Ren, “Processing multiphoton states through operation on a single photon: methods and applications,” Phys. Rev. A 80, 042311 (2009).
    [CrossRef]
  38. B. He, Y.-H. Ren, and J. A. Bergou, “Creation of high-quality long-distance entanglement with flexible resources,” Phys. Rev. A 79, 052323 (2009).
    [CrossRef]
  39. B. He, Y.-H. Ren, and J. A. Bergou, “Universal entangler with photon pairs in arbitrary states,” J. Phys. B At. Mol. Opt. Phys. 43, 025502 (2010).
    [CrossRef]
  40. Q. Lin and B. He, “Bi-directional mapping between polarization and spatially encoded photonic qutrits,” Phys. Rev. A 80, 062312 (2009).
    [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. 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]

2011 (2)

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]

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]

2010 (1)

B. He, Y.-H. Ren, and J. A. Bergou, “Universal entangler with photon pairs in arbitrary states,” J. Phys. B At. Mol. Opt. Phys. 43, 025502 (2010).
[CrossRef]

2009 (6)

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

Q. Lin and J. Li, “Quantum control gates with weak cross-Kerr nonlinearity,” Phys. Rev. A 79, 022301 (2009).
[CrossRef]

Q. Lin and B. He, “Single-photon logic gates using minimal resources,” Phys. Rev. A 80, 042310 (2009).
[CrossRef]

Q. Lin, B. He, J. A. Bergou, and Y. H. Ren, “Processing multiphoton states through operation on a single photon: methods and applications,” Phys. Rev. A 80, 042311 (2009).
[CrossRef]

B. He, Y.-H. Ren, and J. A. Bergou, “Creation of high-quality long-distance entanglement with flexible resources,” Phys. Rev. A 79, 052323 (2009).
[CrossRef]

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

2008 (4)

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]

I. Bregman, D. Aharonov, M. Ben-Or, and H. S. Eisenberg, “Simple and secure quantum key distribution with biphotons,” Phys. Rev. A 77, 050301 (2008).
[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 (2008).
[CrossRef]

2007 (4)

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

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[CrossRef]

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]

2006 (2)

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

2005 (5)

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).
[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]

L. Neves, G. Lima, J. G. Aguirre Gómez, C. H. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
[CrossRef]

M. N. O’Sullivan-Hale, I. A. Khan, R. W. Boyd, and J. C. Howell, “Pixel entanglement: experimental realization of optically entangled d=3 and d=6 qudits,” Phys. Rev. Lett. 94, 220501 (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]

2004 (8)

R. T. Thew, A. Acín, H. Zbinden, and N. Gisin, “Bell-type test of energy-time entangled qutrits,” Phys. Rev. Lett. 93, 010503 (2004).
[CrossRef]

H. de Riedmatten, I. Marcikic, V. Scarani, W. Tittel, H. Zbinden, and N. Gisin, “Tailoring photonic entanglement in high-dimensional Hilbert spaces,” Phys. Rev. A 69, 050304(R) (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]

L. Neves, S. Pádua, and C. Saavedra, “Controlled generation of maximally entangled qudits using twin photons,” Phys. Rev. A 69, 042305 (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]

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (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 (4)

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]

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89, 240401 (2002).
[CrossRef]

2001 (2)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[CrossRef]

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

Acín, A.

R. T. Thew, A. Acín, H. Zbinden, and N. Gisin, “Bell-type test of energy-time entangled qutrits,” Phys. Rev. Lett. 93, 010503 (2004).
[CrossRef]

Aguirre Gómez, J. G.

L. Neves, G. Lima, J. G. Aguirre Gómez, C. H. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
[CrossRef]

Aharonov, D.

I. Bregman, D. Aharonov, M. Ben-Or, and H. S. Eisenberg, “Simple and secure quantum key distribution with biphotons,” Phys. Rev. A 77, 050301 (2008).
[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 (2008).
[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 (2008).
[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).
[CrossRef]

Bartlett, S. 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]

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).
[CrossRef]

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]

Ben-Or, M.

I. Bregman, D. Aharonov, M. Ben-Or, and H. S. Eisenberg, “Simple and secure quantum key distribution with biphotons,” Phys. Rev. A 77, 050301 (2008).
[CrossRef]

Bergou, J. A.

B. He, Y.-H. Ren, and J. A. Bergou, “Universal entangler with photon pairs in arbitrary states,” J. Phys. B At. Mol. Opt. Phys. 43, 025502 (2010).
[CrossRef]

B. He, Y.-H. Ren, and J. A. Bergou, “Creation of high-quality long-distance entanglement with flexible resources,” Phys. Rev. A 79, 052323 (2009).
[CrossRef]

Q. Lin, B. He, J. A. Bergou, and Y. H. Ren, “Processing multiphoton states through operation on a single photon: methods and applications,” Phys. Rev. A 80, 042311 (2009).
[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.

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]

Boyd, R. W.

M. N. O’Sullivan-Hale, I. A. Khan, R. W. Boyd, and J. C. Howell, “Pixel entanglement: experimental realization of optically entangled d=3 and d=6 qudits,” Phys. Rev. Lett. 94, 220501 (2005).
[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]

Bregman, I.

I. Bregman, D. Aharonov, M. Ben-Or, and H. S. Eisenberg, “Simple and secure quantum key distribution with biphotons,” Phys. Rev. A 77, 050301 (2008).
[CrossRef]

Bruß, D.

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

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.

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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).
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N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, “Measuring entangled qutrits and their use for quantum bit commitment,” Phys. Rev. Lett. 93, 053601 (2004).
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J. Joo, T. Rudolph, and B. C. Sanders, “A heralded two-qutrit entangled state,” J. Phys. B At. Mol. Opt. Phys. 42, 114007 (2009).
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C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
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N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
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M. N. O’Sullivan-Hale, I. A. Khan, R. W. Boyd, and J. C. Howell, “Pixel entanglement: experimental realization of optically entangled d=3 and d=6 qudits,” Phys. Rev. Lett. 94, 220501 (2005).
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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).
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S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302(R)(2005).
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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).
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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).
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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).
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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).
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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).
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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).
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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).
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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).
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N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, “Measuring entangled qutrits and their use for quantum bit commitment,” Phys. Rev. Lett. 93, 053601 (2004).
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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 (2008).
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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).
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Y. M. Li, K. S. Zhang, and K. C. Peng, “Generation of qudits and entangled qudits,” Phys. Rev. A 77, 015802 (2008).
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L. Neves, G. Lima, J. G. Aguirre Gómez, C. H. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
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B. He, Q. Lin, and C. Simon, “Cross-Kerr nonlinearity between continuous-mode coherent states and single photons,” Phys. Rev. A 83, 053826 (2011).
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Q. Lin and B. He, “Single-photon logic gates using minimal resources,” Phys. Rev. A 80, 042310 (2009).
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Q. Lin and J. Li, “Quantum control gates with weak cross-Kerr nonlinearity,” Phys. Rev. A 79, 022301 (2009).
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Q. Lin, B. He, J. A. Bergou, and Y. H. Ren, “Processing multiphoton states through operation on a single photon: methods and applications,” Phys. Rev. A 80, 042311 (2009).
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Q. Lin and B. He, “Bi-directional mapping between polarization and spatially encoded photonic qutrits,” Phys. Rev. A 80, 062312 (2009).
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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).
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H. de Riedmatten, I. Marcikic, V. Scarani, W. Tittel, H. Zbinden, and N. Gisin, “Tailoring photonic entanglement in high-dimensional Hilbert spaces,” Phys. Rev. A 69, 050304(R) (2004).
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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).
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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).
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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).
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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).
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H. Mikami and T. Kobayashi, “Remote preparation of qutrit states with biphotons,” Phys. Rev. A 75, 022325 (2007).
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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).
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L. Neves, G. Lima, J. G. Aguirre Gómez, C. H. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
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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).
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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).
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S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302(R)(2005).
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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).
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S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302(R)(2005).
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W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
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K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
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L. Neves, G. Lima, J. G. Aguirre Gómez, C. H. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
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L. Neves, S. Pádua, and C. Saavedra, “Controlled generation of maximally entangled qudits using twin photons,” Phys. Rev. A 69, 042305 (2004).
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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 (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]

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]

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M. N. O’Sullivan-Hale, I. A. Khan, R. W. Boyd, and J. C. Howell, “Pixel entanglement: experimental realization of optically entangled d=3 and d=6 qudits,” Phys. Rev. Lett. 94, 220501 (2005).
[CrossRef]

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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]

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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]

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L. Neves, G. Lima, J. G. Aguirre Gómez, C. H. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
[CrossRef]

L. Neves, S. Pádua, and C. Saavedra, “Controlled generation of maximally entangled qudits using twin photons,” Phys. Rev. A 69, 042305 (2004).
[CrossRef]

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

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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]

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C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef]

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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]

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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 (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]

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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 (2008).
[CrossRef]

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

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[CrossRef]

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]

Ren, Y. H.

Q. Lin, B. He, J. A. Bergou, and Y. H. Ren, “Processing multiphoton states through operation on a single photon: methods and applications,” Phys. Rev. A 80, 042311 (2009).
[CrossRef]

Ren, Y.-H.

B. He, Y.-H. Ren, and J. A. Bergou, “Universal entangler with photon pairs in arbitrary states,” J. Phys. B At. Mol. Opt. Phys. 43, 025502 (2010).
[CrossRef]

B. He, Y.-H. Ren, and J. A. Bergou, “Creation of high-quality long-distance entanglement with flexible resources,” Phys. Rev. A 79, 052323 (2009).
[CrossRef]

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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 (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]

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

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

Saavedra, C.

L. Neves, G. Lima, J. G. Aguirre Gómez, C. H. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
[CrossRef]

L. Neves, S. Pádua, and C. Saavedra, “Controlled generation of maximally entangled qudits using twin photons,” Phys. Rev. A 69, 042305 (2004).
[CrossRef]

Sanders, B. C.

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

Scarani, V.

H. de Riedmatten, I. Marcikic, V. Scarani, W. Tittel, H. Zbinden, and N. Gisin, “Tailoring photonic entanglement in high-dimensional Hilbert spaces,” Phys. Rev. A 69, 050304(R) (2004).
[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).
[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]

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, 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]

Thew, R. T.

R. T. Thew, A. Acín, H. Zbinden, and N. Gisin, “Bell-type test of energy-time entangled qutrits,” Phys. Rev. Lett. 93, 010503 (2004).
[CrossRef]

Tittel, W.

H. de Riedmatten, I. Marcikic, V. Scarani, W. Tittel, H. Zbinden, and N. Gisin, “Tailoring photonic entanglement in high-dimensional Hilbert spaces,” Phys. Rev. A 69, 050304(R) (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]

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]

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89, 240401 (2002).
[CrossRef]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[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]

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89, 240401 (2002).
[CrossRef]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[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, 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]

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 (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]

Zbinden, H.

H. de Riedmatten, I. Marcikic, V. Scarani, W. Tittel, H. Zbinden, and N. Gisin, “Tailoring photonic entanglement in high-dimensional Hilbert spaces,” Phys. Rev. A 69, 050304(R) (2004).
[CrossRef]

R. T. Thew, A. Acín, H. Zbinden, and N. Gisin, “Bell-type test of energy-time entangled qutrits,” Phys. Rev. Lett. 93, 010503 (2004).
[CrossRef]

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]

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]

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89, 240401 (2002).
[CrossRef]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[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, 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]

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]

J. Phys. B At. Mol. Opt. Phys. (2)

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

B. He, Y.-H. Ren, and J. A. Bergou, “Universal entangler with photon pairs in arbitrary states,” J. Phys. B At. Mol. Opt. Phys. 43, 025502 (2010).
[CrossRef]

Nat. Phys. (1)

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 (2008).
[CrossRef]

Nature (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[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 (17)

Q. Lin and J. Li, “Quantum control gates with weak cross-Kerr nonlinearity,” Phys. Rev. A 79, 022301 (2009).
[CrossRef]

Q. Lin and B. He, “Single-photon logic gates using minimal resources,” Phys. Rev. A 80, 042310 (2009).
[CrossRef]

Q. Lin, B. He, J. A. Bergou, and Y. H. Ren, “Processing multiphoton states through operation on a single photon: methods and applications,” Phys. Rev. A 80, 042311 (2009).
[CrossRef]

B. He, Y.-H. Ren, and J. A. Bergou, “Creation of high-quality long-distance entanglement with flexible resources,” Phys. Rev. A 79, 052323 (2009).
[CrossRef]

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

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]

I. Bregman, D. Aharonov, M. Ben-Or, and H. S. Eisenberg, “Simple and secure quantum key distribution with biphotons,” Phys. Rev. A 77, 050301 (2008).
[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]

H. de Riedmatten, I. Marcikic, V. Scarani, W. Tittel, H. Zbinden, and N. Gisin, “Tailoring photonic entanglement in high-dimensional Hilbert spaces,” Phys. Rev. A 69, 050304(R) (2004).
[CrossRef]

L. Neves, S. Pádua, and C. Saavedra, “Controlled generation of maximally entangled qudits using twin photons,” Phys. Rev. A 69, 042305 (2004).
[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]

Phys. Rev. Lett. (17)

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]

L. Neves, G. Lima, J. G. Aguirre Gómez, C. H. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
[CrossRef]

M. N. O’Sullivan-Hale, I. A. Khan, R. W. Boyd, and J. C. Howell, “Pixel entanglement: experimental realization of optically entangled d=3 and d=6 qudits,” Phys. Rev. Lett. 94, 220501 (2005).
[CrossRef]

R. T. Thew, A. Acín, H. Zbinden, and N. Gisin, “Bell-type test of energy-time entangled qutrits,” Phys. Rev. Lett. 93, 010503 (2004).
[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]

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89, 240401 (2002).
[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]

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]

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]

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]

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]

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

Rev. Mod. Phys. (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]

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Figures (2)

Fig. 1.
Fig. 1.

Simple module and its application to the entangled qutrits generation. Two independent qutrits are injected into two PBSs and interact with two qubus beams |α|α as indicated. After one more 5050 BS, a common PNND is used to distinguish the vacuum state from the nonvacuum state. If the detection is n=0, the entangled qutrits are finally created. This scheme is suitable for the generation of entangled qudits, as well. For details, see text.

Fig. 2.
Fig. 2.

Generation of entangled qutrits with two cascade modified generation modules. In the modified generation module shown in the dashed–dotted box, an additional phase shift 2θ is applied to two qubus beams after the interactions. To improve the generation efficiency of entangled qutrits, we replace the PNND by a QND module, which is used to realize the projection |nn|, and the detections are used to control the switch (S) through the classical feed forward. If the detection is n=0, the generation is successful and the output modes are switched into spatial modes 1 and 4. If the detection is n0, the output modes are switched into spatial modes 2 and 3 to be operated further by the second generation module associated with a bit flip operation placed on spatial mode 3. Finally, the entangled qutrits with other forms [see Eq. (17) and Eq. (18)] are achieved in output modes 5 and 8 or 6 and 7.

Equations (18)

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

|ψ1=α0|03+α1|13+α2|23,|ψ2=β0|03+β1|13+β2|23,
|03|α|α|03|α|αei2θ,|13|α|α|13|αeiθ|αeiθ,|23|α|α|23|αei2θ|α.
(α0β0|03|03+α1β1|13|13+α2β2|23|23)|αei2θ|αei2θ+(α0β1|03|13+α1β2|13|23)|αeiθ|αei3θ+(α1β0|13|03+α2β1|23|13)|αei3θ|αeiθ+α0β2|03|23|α|αei4θ+α2β0|23|03|αei4θ|α.
(α0β0|03|03+α1β1|13|13+α2β2|23|23)|0|2αei2θ+(α0β1|03|13+α1β2|13|23)|α|α++(α1β0|13|03+α2β1|23|13)|α|α++α0β2|03|23|α|α++α2β0|23|03|α|α+,
α0β0|03|03+α1β1|13|13+α2β2|23|23,
PE=49e|α|2sin2θ+29e|α|2sin22θ.
i=0n1αi|ini=0n1βj|jn.
i=0n1αiβi|in|in|αeinθ|αeinθ+C,
i=0n1αiβi|in|in.
(α0β0|03|03+α1β1|13|13+α2β2|23|23)|α|α+(α0β1|03|13+α1β2|13|23)|αeiθ|αeiθ+(α1β0|13|03+α2β1|23|13)|αeiθ|αeiθ+α0β2|03|23|αei2θ|αei2θ+α2β0|23|03|αei2θ|αei2θ.
(α0β0|03|03+α1β1|13|13+α2β2|23|23)|0|2α+(α0β1|03|13+α1β2|13|23)|i2αsinθ|2αcosθ+(α1β0|13|03+α2β1|23|13)|i2αsinθ|2αcosθ+α0β2|03|23|i2αsin2θ|2αcos2θ+α2β0|23|03|i2αsin2θ|2αcos2θ.
α0β0|03|03+α1β1|13|13+α2β2|23|23.
c1(α0β1|03|13+α1β2|13|23)|2γ+c2(α1β0|13|03+α2β1|23|13)|2γ+(c3α0β2|03|23+c4α2β0|23|03)|2γ,
|03|23,|13|13,|23|03.
c1(α0β1|03|13+α1β2|13|03)|2γ+c2(α1β0|13|23+α2β1|23|13)|2γ+(c3α0β2|03|03+c4α2β0|23|23)|2γ.
(c1α0β1|03|13+c2α1β0|13|23)|i2γsinθ|2γcosθ+(c1α1β2|13|03+c2α2β1|23|13)|i2γsinθ|2γcosθ+(c3α0β2|03|03+c4α2β0|23|23)|0|2γ.
c3α0β2|03|03+c4α2β0|23|23,
c1α0β1|03|13+c2α1β0|13|23+einπ(c1α1β2|13|03+c2α2β1|23|13),

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