Abstract

A scheme is proposed to implement the optical quantum Fredkin gate with weak nonlinearities and feed-forward. The distinctive feature of the present scheme is that the present Fredkin gate has four sets of possible output ports, and the total success probability for each set of the output ports is near 1/4 without ancillary single-photon. The present scheme requires nonlinear strength of the order of 103 and mean photon number of the probe coherent beam of the order of 106 so that the discrimination error probability does not exceed 104. These features show that it is still possible to operate in the regime of weak cross-Kerr nonlinearities, and the amplitude of the probe coherent beam is physically reasonable with current technology. These facts make us more confident in the feasibility of the proposed scheme.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  32. P. Kok, “Effects of self-phase-modulation on weak nonlinear optical quantum gates,” Phys. Rev. A 77, 013808 (2008).
    [CrossRef]
  33. C. R. Zhao and L. Ye, “Efficient scheme for the preparation of symmetric Dicke states via cross-Kerr nonlinearity,” Phys. Lett. A 375, 401–405 (2011).
    [CrossRef]
  34. S. G. R. Louis, K. Nemoto, W. J. Munro, and T. P. Spiller, “The efficiencies of generating cluster states with weak nonlinearities,” New J. Phys. 9, 193 (2007).
    [CrossRef]
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    [CrossRef]
  38. J. H. Shapiro, “Single-photon Kerr nonlinearities do not help quantum computation,” Phys. Rev. A 73, 062305 (2006).
    [CrossRef]
  39. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
    [CrossRef]
  40. W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
    [CrossRef]
  41. B. He, M. Nadeem, and J. A. A. Bergou, “Scheme for generating coherent-state superpositions with realistic cross-Kerr nonlinearity,” Phys. Rev. A 79, 035802 (2009).
    [CrossRef]
  42. H. Jeong, “Quantum computation using weak nonlinearities: robustness against decoherence,” Phys. Rev. A 73, 052320 (2006).
    [CrossRef]
  43. T. Yamamoto, K. Hayashi, S. K. Ozdemir, M. Koashi, and N. Imoto, “Robust photonic entanglement distribution by state-independent encoding onto decoherence-free subspace,” Nat Photonics 2, 488–491 (2008).
    [CrossRef]
  44. B. He, Y. H. Ren, and J. A. Bergou, “Universal entangler with photon pairs in arbitrary states,” J. Phys. B 43, 025502 (2010).
    [CrossRef]
  45. Q. Lin and B. He, “Efficient generation of universal two-dimensional cluster states with hybrid systems,” Phys. Rev. A 82, 022331 (2010).
    [CrossRef]
  46. X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, “Optical-fiber source of polarization-entangled photons in the 1550 nm telecom band,” Phys. Rev. Lett. 94, 053601 (2005).
    [CrossRef]
  47. Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase shifts for quantum logic,” Phys. Rev. Lett. 75, 4710–4713 (1995).
    [CrossRef]
  48. S. E. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
    [CrossRef]

2012 (2)

M. Z. Zhu, C. R. Zhao, and L. Ye, “Highly efficient scheme for the implementation of optical controlled-Z gate via two-qubit polarization parity detector,” Opt. Commun. 285, 1576–1580 (2012).
[CrossRef]

Z. C. Shi, Y. Xia, J. Song, and H. S. Song, “One-step implementation of the Fredkin gate via quantum Zeno dynamics,” Quantum Inf. Comput. 12, 215–230 (2012).

2011 (2)

C. R. Zhao and L. Ye, “Robust scheme for the preparation of symmetric Dicke states with coherence state via cross-Kerr nonlinearity,” Opt. Commun. 284, 541–544 (2011).
[CrossRef]

C. R. Zhao and L. Ye, “Efficient scheme for the preparation of symmetric Dicke states via cross-Kerr nonlinearity,” Phys. Lett. A 375, 401–405 (2011).
[CrossRef]

2010 (2)

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

Q. Lin and B. He, “Efficient generation of universal two-dimensional cluster states with hybrid systems,” Phys. Rev. A 82, 022331 (2010).
[CrossRef]

2009 (3)

B. He, M. Nadeem, and J. A. A. Bergou, “Scheme for generating coherent-state superpositions with realistic cross-Kerr nonlinearity,” Phys. Rev. A 79, 035802 (2009).
[CrossRef]

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

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

2008 (5)

P. Kok, “Effects of self-phase-modulation on weak nonlinear optical quantum gates,” Phys. Rev. A 77, 013808 (2008).
[CrossRef]

Y. F. Xiao, S. K. Ozdemir, V. Gaddam, C. H. Dong, N. Imoto, and L. Yang, “Quantum nondemolition measurement of photon number via optical Kerr effect in an ultra-high-Q microtoroid cavity,” Opt. Express 16, 21462–21475 (2008).
[CrossRef]

J. Fiurášek, “Linear optical Fredkin gate based on partial-SWAP gate,” Phys. Rev. A 78, 032317 (2008).
[CrossRef]

Y. X. Gong, G. C. Guo, and T. C. Ralph, “Methods for a linear optical quantum Fredkin gate,” Phys. Rev. A 78, 012305(2008).
[CrossRef]

T. Yamamoto, K. Hayashi, S. K. Ozdemir, M. Koashi, and N. Imoto, “Robust photonic entanglement distribution by state-independent encoding onto decoherence-free subspace,” Nat Photonics 2, 488–491 (2008).
[CrossRef]

2007 (4)

S. G. R. Louis, K. Nemoto, W. J. Munro, and T. P. Spiller, “The efficiencies of generating cluster states with weak nonlinearities,” New J. Phys. 9, 193 (2007).
[CrossRef]

Z. J. Deng, X. L. Zhang, H. Wei, K. L. Gao, and M. Feng, “Implementation of a nonlocal N-qubit conditional phase gate by single-photon interference,” Phys. Rev. A 76, 044305 (2007).
[CrossRef]

G. S. Jin, Y. Lin, and B. Wu, “Generating multiphoton Greenberger–Horne–Zeilinger states with weak cross-Kerr nonlinearity,” Phys. Rev. A 75, 054302 (2007).
[CrossRef]

M. Gao, W. H. Hu, and C. Z. Li, “Generating polarization-entangled W states using weak nonlinearity,” J. Phys. B 40, 3525–3529 (2007).
[CrossRef]

2006 (4)

T. P. Spiller, K. Nemoto, S. L. Braunstein, W. J. Munro, P. van Loock, and G. J. Milburn, “Quantum computation by communication,” New J. Phys. 8, 30 (2006).
[CrossRef]

J. Fiurášek, “Linear-optics quantum Toffoli and Fredkin gates,” Phys. Rev. A 73, 062313 (2006).
[CrossRef]

J. H. Shapiro, “Single-photon Kerr nonlinearities do not help quantum computation,” Phys. Rev. A 73, 062305 (2006).
[CrossRef]

H. Jeong, “Quantum computation using weak nonlinearities: robustness against decoherence,” Phys. Rev. A 73, 052320 (2006).
[CrossRef]

2005 (7)

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

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (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 (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]

I. Friedler, G. Kurizki, and D. Petrosyan, “Deterministic quantum logic with photons via optically induced photonic band gaps,” Phys. Rev. A 71, 023803 (2005).
[CrossRef]

L. M. Duan, B. Wang, and H. J. Kimble, “Robust quantum gates on neutral atoms with cavity-assisted photon scattering,” Phys. Rev. A 72, 032333 (2005).
[CrossRef]

2004 (3)

H. Goto and K. Ichimura, “Multiqubit controlled unitary gate by adiabatic passage with an optical cavity,” Phys. Rev. A 70, 012305 (2004).
[CrossRef]

M. D. Barrett, J. Chiaverini, T. Schaetz, J. Britton, W. M. Itano, J. D. Jost, E. Knill, C. Langer, D. Leibfried, R. Ozeri, and D. J. Wineland, “Deterministic quantum teleportation of atomic qubits,” Nature 429, 737–739 (2004).
[CrossRef]

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

2001 (1)

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef]

2000 (1)

D. Vitali, M. Fortunato, and P. Tombesi, “Complete quantum teleportation with a Kerr nonlinearity,” Phys. Rev. Lett. 85, 445–448 (2000).
[CrossRef]

1999 (1)

S. E. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
[CrossRef]

1998 (2)

P. Grangier, J. A. Levenson, and J. Poizat, “Quantum non-demolition measurements in optics,” Nature 396, 537–542 (1998).
[CrossRef]

L. K. Grover, “Quantum computers can search rapidly by using almost any transformation,” Phys. Rev. Lett. 80, 4329–4332 (1998).
[CrossRef]

1995 (4)

A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, “Elementary gates for quantum computation,” Phys. Rev. A 52, 3457–3467 (1995).
[CrossRef]

T. Sleator and H. Weinfurter, “Realizable universal quantum logic gates,” Phys. Rev. Lett. 74, 4087–4090 (1995).
[CrossRef]

I. L. Chuang and Y. Yamamoto, “Simple quantum computer,” Phys. Rev. A 52, 3489–3496 (1995).
[CrossRef]

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase shifts for quantum logic,” Phys. Rev. Lett. 75, 4710–4713 (1995).
[CrossRef]

1989 (1)

G. J. Milburn, “Quantum optical Fredkin gate,” Phys. Rev. Lett. 62, 2124–2127 (1989).
[CrossRef]

1985 (1)

N. Imoto, H. A. Haus, and Y. Yamamoto, “Quantum nondemolition measurement of the photon number via the optical Kerr effect,” Phys. Rev. A 32, 2287–2292 (1985).
[CrossRef]

1982 (1)

E. Fredkin and T. Toffoli, “Conservative logic,” Int. J. Theor. Phys. 21, 219–253 (1982).
[CrossRef]

Bachor, H.

H. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics, 2nd ed. (Wiley-VCH, 2004).

Barenco, A.

A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, “Elementary gates for quantum computation,” Phys. Rev. A 52, 3457–3467 (1995).
[CrossRef]

Barnett, S. M.

S. M. Barnett, Quantum Information (Oxford University, 2009).

Barrett, M. D.

M. D. Barrett, J. Chiaverini, T. Schaetz, J. Britton, W. M. Itano, J. D. Jost, E. Knill, C. Langer, D. Leibfried, R. Ozeri, and D. J. Wineland, “Deterministic quantum teleportation of atomic qubits,” Nature 429, 737–739 (2004).
[CrossRef]

Barrett, S. D.

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

Beausoleil, R. G.

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

W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
[CrossRef]

Bennett, C. H.

A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, “Elementary gates for quantum computation,” Phys. Rev. A 52, 3457–3467 (1995).
[CrossRef]

Bergou, J. A.

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

Bergou, J. A. A.

B. He, M. Nadeem, and J. A. A. Bergou, “Scheme for generating coherent-state superpositions with realistic cross-Kerr nonlinearity,” Phys. Rev. A 79, 035802 (2009).
[CrossRef]

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

Braunstein, S. L.

T. P. Spiller, K. Nemoto, S. L. Braunstein, W. J. Munro, P. van Loock, and G. J. Milburn, “Quantum computation by communication,” New J. Phys. 8, 30 (2006).
[CrossRef]

Britton, J.

M. D. Barrett, J. Chiaverini, T. Schaetz, J. Britton, W. M. Itano, J. D. Jost, E. Knill, C. Langer, D. Leibfried, R. Ozeri, and D. J. Wineland, “Deterministic quantum teleportation of atomic qubits,” Nature 429, 737–739 (2004).
[CrossRef]

Chiaverini, J.

M. D. Barrett, J. Chiaverini, T. Schaetz, J. Britton, W. M. Itano, J. D. Jost, E. Knill, C. Langer, D. Leibfried, R. Ozeri, and D. J. Wineland, “Deterministic quantum teleportation of atomic qubits,” Nature 429, 737–739 (2004).
[CrossRef]

Chuang, I. L.

I. L. Chuang and Y. Yamamoto, “Simple quantum computer,” Phys. Rev. A 52, 3489–3496 (1995).
[CrossRef]

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

Cleve, R.

A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, “Elementary gates for quantum computation,” Phys. Rev. A 52, 3457–3467 (1995).
[CrossRef]

Deng, Z. J.

Z. J. Deng, X. L. Zhang, H. Wei, K. L. Gao, and M. Feng, “Implementation of a nonlocal N-qubit conditional phase gate by single-photon interference,” Phys. Rev. A 76, 044305 (2007).
[CrossRef]

DiVincenzo, D. P.

A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, “Elementary gates for quantum computation,” Phys. Rev. A 52, 3457–3467 (1995).
[CrossRef]

Dong, C. H.

Duan, L. M.

L. M. Duan, B. Wang, and H. J. Kimble, “Robust quantum gates on neutral atoms with cavity-assisted photon scattering,” Phys. Rev. A 72, 032333 (2005).
[CrossRef]

Feng, M.

Z. J. Deng, X. L. Zhang, H. Wei, K. L. Gao, and M. Feng, “Implementation of a nonlocal N-qubit conditional phase gate by single-photon interference,” Phys. Rev. A 76, 044305 (2007).
[CrossRef]

Fiurášek, J.

J. Fiurášek, “Linear optical Fredkin gate based on partial-SWAP gate,” Phys. Rev. A 78, 032317 (2008).
[CrossRef]

J. Fiurášek, “Linear-optics quantum Toffoli and Fredkin gates,” Phys. Rev. A 73, 062313 (2006).
[CrossRef]

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

Fortunato, M.

D. Vitali, M. Fortunato, and P. Tombesi, “Complete quantum teleportation with a Kerr nonlinearity,” Phys. Rev. Lett. 85, 445–448 (2000).
[CrossRef]

Fredkin, E.

E. Fredkin and T. Toffoli, “Conservative logic,” Int. J. Theor. Phys. 21, 219–253 (1982).
[CrossRef]

Friedler, I.

I. Friedler, G. Kurizki, and D. Petrosyan, “Deterministic quantum logic with photons via optically induced photonic band gaps,” Phys. Rev. A 71, 023803 (2005).
[CrossRef]

Gaddam, V.

Gao, K. L.

Z. J. Deng, X. L. Zhang, H. Wei, K. L. Gao, and M. Feng, “Implementation of a nonlocal N-qubit conditional phase gate by single-photon interference,” Phys. Rev. A 76, 044305 (2007).
[CrossRef]

Gao, M.

M. Gao, W. H. Hu, and C. Z. Li, “Generating polarization-entangled W states using weak nonlinearity,” J. Phys. B 40, 3525–3529 (2007).
[CrossRef]

Gong, Y. X.

Y. X. Gong, G. C. Guo, and T. C. Ralph, “Methods for a linear optical quantum Fredkin gate,” Phys. Rev. A 78, 012305(2008).
[CrossRef]

Goto, H.

H. Goto and K. Ichimura, “Multiqubit controlled unitary gate by adiabatic passage with an optical cavity,” Phys. Rev. A 70, 012305 (2004).
[CrossRef]

Grangier, P.

P. Grangier, J. A. Levenson, and J. Poizat, “Quantum non-demolition measurements in optics,” Nature 396, 537–542 (1998).
[CrossRef]

Grover, L. K.

L. K. Grover, “Quantum computers can search rapidly by using almost any transformation,” Phys. Rev. Lett. 80, 4329–4332 (1998).
[CrossRef]

Guo, G. C.

Y. X. Gong, G. C. Guo, and T. C. Ralph, “Methods for a linear optical quantum Fredkin gate,” Phys. Rev. A 78, 012305(2008).
[CrossRef]

Harris, S. E.

S. E. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
[CrossRef]

Hau, L. V.

S. E. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
[CrossRef]

Haus, H. A.

N. Imoto, H. A. Haus, and Y. Yamamoto, “Quantum nondemolition measurement of the photon number via the optical Kerr effect,” Phys. Rev. A 32, 2287–2292 (1985).
[CrossRef]

Hayashi, K.

T. Yamamoto, K. Hayashi, S. K. Ozdemir, M. Koashi, and N. Imoto, “Robust photonic entanglement distribution by state-independent encoding onto decoherence-free subspace,” Nat Photonics 2, 488–491 (2008).
[CrossRef]

He, B.

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

Q. Lin and B. He, “Efficient generation of universal two-dimensional cluster states with hybrid systems,” Phys. Rev. A 82, 022331 (2010).
[CrossRef]

B. He, M. Nadeem, and J. A. A. Bergou, “Scheme for generating coherent-state superpositions with realistic cross-Kerr nonlinearity,” Phys. Rev. A 79, 035802 (2009).
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B. He, Y. H. Ren, and J. A. A. Bergou, “Creation of high-quality long-distance entanglement with flexible resources,” Phys. Rev. A 79, 052323 (2009).
[CrossRef]

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Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase shifts for quantum logic,” Phys. Rev. Lett. 75, 4710–4713 (1995).
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Hu, W. H.

M. Gao, W. H. Hu, and C. Z. Li, “Generating polarization-entangled W states using weak nonlinearity,” J. Phys. B 40, 3525–3529 (2007).
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H. Goto and K. Ichimura, “Multiqubit controlled unitary gate by adiabatic passage with an optical cavity,” Phys. Rev. A 70, 012305 (2004).
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M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
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Imoto, N.

T. Yamamoto, K. Hayashi, S. K. Ozdemir, M. Koashi, and N. Imoto, “Robust photonic entanglement distribution by state-independent encoding onto decoherence-free subspace,” Nat Photonics 2, 488–491 (2008).
[CrossRef]

Y. F. Xiao, S. K. Ozdemir, V. Gaddam, C. H. Dong, N. Imoto, and L. Yang, “Quantum nondemolition measurement of photon number via optical Kerr effect in an ultra-high-Q microtoroid cavity,” Opt. Express 16, 21462–21475 (2008).
[CrossRef]

N. Imoto, H. A. Haus, and Y. Yamamoto, “Quantum nondemolition measurement of the photon number via the optical Kerr effect,” Phys. Rev. A 32, 2287–2292 (1985).
[CrossRef]

Itano, W. M.

M. D. Barrett, J. Chiaverini, T. Schaetz, J. Britton, W. M. Itano, J. D. Jost, E. Knill, C. Langer, D. Leibfried, R. Ozeri, and D. J. Wineland, “Deterministic quantum teleportation of atomic qubits,” Nature 429, 737–739 (2004).
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H. Jeong, “Quantum computation using weak nonlinearities: robustness against decoherence,” Phys. Rev. A 73, 052320 (2006).
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G. S. Jin, Y. Lin, and B. Wu, “Generating multiphoton Greenberger–Horne–Zeilinger states with weak cross-Kerr nonlinearity,” Phys. Rev. A 75, 054302 (2007).
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Jost, J. D.

M. D. Barrett, J. Chiaverini, T. Schaetz, J. Britton, W. M. Itano, J. D. Jost, E. Knill, C. Langer, D. Leibfried, R. Ozeri, and D. J. Wineland, “Deterministic quantum teleportation of atomic qubits,” Nature 429, 737–739 (2004).
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Kimble, H. J.

L. M. Duan, B. Wang, and H. J. Kimble, “Robust quantum gates on neutral atoms with cavity-assisted photon scattering,” Phys. Rev. A 72, 032333 (2005).
[CrossRef]

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase shifts for quantum logic,” Phys. Rev. Lett. 75, 4710–4713 (1995).
[CrossRef]

Knill, E.

M. D. Barrett, J. Chiaverini, T. Schaetz, J. Britton, W. M. Itano, J. D. Jost, E. Knill, C. Langer, D. Leibfried, R. Ozeri, and D. J. Wineland, “Deterministic quantum teleportation of atomic qubits,” Nature 429, 737–739 (2004).
[CrossRef]

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
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Koashi, M.

T. Yamamoto, K. Hayashi, S. K. Ozdemir, M. Koashi, and N. Imoto, “Robust photonic entanglement distribution by state-independent encoding onto decoherence-free subspace,” Nat Photonics 2, 488–491 (2008).
[CrossRef]

Kok, P.

P. Kok, “Effects of self-phase-modulation on weak nonlinear optical quantum gates,” Phys. Rev. A 77, 013808 (2008).
[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 (2005).
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P. Kok and B. Lovett, Introduction to Optical Quantum Information Processing (Cambridge University, 2010).

Kumar, P.

X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, “Optical-fiber source of polarization-entangled photons in the 1550 nm telecom band,” Phys. Rev. Lett. 94, 053601 (2005).
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Kurizki, G.

I. Friedler, G. Kurizki, and D. Petrosyan, “Deterministic quantum logic with photons via optically induced photonic band gaps,” Phys. Rev. A 71, 023803 (2005).
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E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
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Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase shifts for quantum logic,” Phys. Rev. Lett. 75, 4710–4713 (1995).
[CrossRef]

Langer, C.

M. D. Barrett, J. Chiaverini, T. Schaetz, J. Britton, W. M. Itano, J. D. Jost, E. Knill, C. Langer, D. Leibfried, R. Ozeri, and D. J. Wineland, “Deterministic quantum teleportation of atomic qubits,” Nature 429, 737–739 (2004).
[CrossRef]

Leibfried, D.

M. D. Barrett, J. Chiaverini, T. Schaetz, J. Britton, W. M. Itano, J. D. Jost, E. Knill, C. Langer, D. Leibfried, R. Ozeri, and D. J. Wineland, “Deterministic quantum teleportation of atomic qubits,” Nature 429, 737–739 (2004).
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Levenson, J. A.

P. Grangier, J. A. Levenson, and J. Poizat, “Quantum non-demolition measurements in optics,” Nature 396, 537–542 (1998).
[CrossRef]

Li, C. Z.

M. Gao, W. H. Hu, and C. Z. Li, “Generating polarization-entangled W states using weak nonlinearity,” J. Phys. B 40, 3525–3529 (2007).
[CrossRef]

Li, J.

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

Li, X.

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

Lin, Q.

Q. Lin and B. He, “Efficient generation of universal two-dimensional cluster states with hybrid systems,” Phys. Rev. A 82, 022331 (2010).
[CrossRef]

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

Lin, Y.

G. S. Jin, Y. Lin, and B. Wu, “Generating multiphoton Greenberger–Horne–Zeilinger states with weak cross-Kerr nonlinearity,” Phys. Rev. A 75, 054302 (2007).
[CrossRef]

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S. G. R. Louis, K. Nemoto, W. J. Munro, and T. P. Spiller, “The efficiencies of generating cluster states with weak nonlinearities,” New J. Phys. 9, 193 (2007).
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Lovett, B.

P. Kok and B. Lovett, Introduction to Optical Quantum Information Processing (Cambridge University, 2010).

Mabuchi, H.

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase shifts for quantum logic,” Phys. Rev. Lett. 75, 4710–4713 (1995).
[CrossRef]

Marangos, J. P.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

Margolus, N.

A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, “Elementary gates for quantum computation,” Phys. Rev. A 52, 3457–3467 (1995).
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Milburn, G. J.

T. P. Spiller, K. Nemoto, S. L. Braunstein, W. J. Munro, P. van Loock, and G. J. Milburn, “Quantum computation by communication,” New J. Phys. 8, 30 (2006).
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E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
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G. J. Milburn, “Quantum optical Fredkin gate,” Phys. Rev. Lett. 62, 2124–2127 (1989).
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Munro, W. J.

S. G. R. Louis, K. Nemoto, W. J. Munro, and T. P. Spiller, “The efficiencies of generating cluster states with weak nonlinearities,” New J. Phys. 9, 193 (2007).
[CrossRef]

T. P. Spiller, K. Nemoto, S. L. Braunstein, W. J. Munro, P. van Loock, and G. J. Milburn, “Quantum computation by communication,” New J. Phys. 8, 30 (2006).
[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 (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).
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W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
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K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
[CrossRef]

Nadeem, M.

B. He, M. Nadeem, and J. A. A. Bergou, “Scheme for generating coherent-state superpositions with realistic cross-Kerr nonlinearity,” Phys. Rev. A 79, 035802 (2009).
[CrossRef]

Nemoto, K.

S. G. R. Louis, K. Nemoto, W. J. Munro, and T. P. Spiller, “The efficiencies of generating cluster states with weak nonlinearities,” New J. Phys. 9, 193 (2007).
[CrossRef]

T. P. Spiller, K. Nemoto, S. L. Braunstein, W. J. Munro, P. van Loock, and G. J. Milburn, “Quantum computation by communication,” New J. Phys. 8, 30 (2006).
[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 (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]

W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
[CrossRef]

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

Nielsen, M. A.

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

Ozdemir, S. K.

T. Yamamoto, K. Hayashi, S. K. Ozdemir, M. Koashi, and N. Imoto, “Robust photonic entanglement distribution by state-independent encoding onto decoherence-free subspace,” Nat Photonics 2, 488–491 (2008).
[CrossRef]

Y. F. Xiao, S. K. Ozdemir, V. Gaddam, C. H. Dong, N. Imoto, and L. Yang, “Quantum nondemolition measurement of photon number via optical Kerr effect in an ultra-high-Q microtoroid cavity,” Opt. Express 16, 21462–21475 (2008).
[CrossRef]

Ozeri, R.

M. D. Barrett, J. Chiaverini, T. Schaetz, J. Britton, W. M. Itano, J. D. Jost, E. Knill, C. Langer, D. Leibfried, R. Ozeri, and D. J. Wineland, “Deterministic quantum teleportation of atomic qubits,” Nature 429, 737–739 (2004).
[CrossRef]

Petrosyan, D.

I. Friedler, G. Kurizki, and D. Petrosyan, “Deterministic quantum logic with photons via optically induced photonic band gaps,” Phys. Rev. A 71, 023803 (2005).
[CrossRef]

Poizat, J.

P. Grangier, J. A. Levenson, and J. Poizat, “Quantum non-demolition measurements in optics,” Nature 396, 537–542 (1998).
[CrossRef]

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Y. X. Gong, G. C. Guo, and T. C. Ralph, “Methods for a linear optical quantum Fredkin gate,” Phys. Rev. A 78, 012305(2008).
[CrossRef]

H. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics, 2nd ed. (Wiley-VCH, 2004).

Ren, Y. H.

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

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

Schaetz, T.

M. D. Barrett, J. Chiaverini, T. Schaetz, J. Britton, W. M. Itano, J. D. Jost, E. Knill, C. Langer, D. Leibfried, R. Ozeri, and D. J. Wineland, “Deterministic quantum teleportation of atomic qubits,” Nature 429, 737–739 (2004).
[CrossRef]

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J. H. Shapiro, “Single-photon Kerr nonlinearities do not help quantum computation,” Phys. Rev. A 73, 062305 (2006).
[CrossRef]

Sharping, J. E.

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

Shi, Z. C.

Z. C. Shi, Y. Xia, J. Song, and H. S. Song, “One-step implementation of the Fredkin gate via quantum Zeno dynamics,” Quantum Inf. Comput. 12, 215–230 (2012).

Shor, P.

A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, “Elementary gates for quantum computation,” Phys. Rev. A 52, 3457–3467 (1995).
[CrossRef]

Sleator, T.

A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, “Elementary gates for quantum computation,” Phys. Rev. A 52, 3457–3467 (1995).
[CrossRef]

T. Sleator and H. Weinfurter, “Realizable universal quantum logic gates,” Phys. Rev. Lett. 74, 4087–4090 (1995).
[CrossRef]

Smolin, J. A.

A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, “Elementary gates for quantum computation,” Phys. Rev. A 52, 3457–3467 (1995).
[CrossRef]

Song, H. S.

Z. C. Shi, Y. Xia, J. Song, and H. S. Song, “One-step implementation of the Fredkin gate via quantum Zeno dynamics,” Quantum Inf. Comput. 12, 215–230 (2012).

Song, J.

Z. C. Shi, Y. Xia, J. Song, and H. S. Song, “One-step implementation of the Fredkin gate via quantum Zeno dynamics,” Quantum Inf. Comput. 12, 215–230 (2012).

Spiller, T. P.

S. G. R. Louis, K. Nemoto, W. J. Munro, and T. P. Spiller, “The efficiencies of generating cluster states with weak nonlinearities,” New J. Phys. 9, 193 (2007).
[CrossRef]

T. P. Spiller, K. Nemoto, S. L. Braunstein, W. J. Munro, P. van Loock, and G. J. Milburn, “Quantum computation by communication,” New J. Phys. 8, 30 (2006).
[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 (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]

W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
[CrossRef]

Toffoli, T.

E. Fredkin and T. Toffoli, “Conservative logic,” Int. J. Theor. Phys. 21, 219–253 (1982).
[CrossRef]

Tombesi, P.

D. Vitali, M. Fortunato, and P. Tombesi, “Complete quantum teleportation with a Kerr nonlinearity,” Phys. Rev. Lett. 85, 445–448 (2000).
[CrossRef]

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Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase shifts for quantum logic,” Phys. Rev. Lett. 75, 4710–4713 (1995).
[CrossRef]

van Loock, P.

T. P. Spiller, K. Nemoto, S. L. Braunstein, W. J. Munro, P. van Loock, and G. J. Milburn, “Quantum computation by communication,” New J. Phys. 8, 30 (2006).
[CrossRef]

Vitali, D.

D. Vitali, M. Fortunato, and P. Tombesi, “Complete quantum teleportation with a Kerr nonlinearity,” Phys. Rev. Lett. 85, 445–448 (2000).
[CrossRef]

Voss, P. L.

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

Wang, B.

L. M. Duan, B. Wang, and H. J. Kimble, “Robust quantum gates on neutral atoms with cavity-assisted photon scattering,” Phys. Rev. A 72, 032333 (2005).
[CrossRef]

Wei, H.

Z. J. Deng, X. L. Zhang, H. Wei, K. L. Gao, and M. Feng, “Implementation of a nonlocal N-qubit conditional phase gate by single-photon interference,” Phys. Rev. A 76, 044305 (2007).
[CrossRef]

Weinfurter, H.

A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, “Elementary gates for quantum computation,” Phys. Rev. A 52, 3457–3467 (1995).
[CrossRef]

T. Sleator and H. Weinfurter, “Realizable universal quantum logic gates,” Phys. Rev. Lett. 74, 4087–4090 (1995).
[CrossRef]

Wineland, D. J.

M. D. Barrett, J. Chiaverini, T. Schaetz, J. Britton, W. M. Itano, J. D. Jost, E. Knill, C. Langer, D. Leibfried, R. Ozeri, and D. J. Wineland, “Deterministic quantum teleportation of atomic qubits,” Nature 429, 737–739 (2004).
[CrossRef]

Wu, B.

G. S. Jin, Y. Lin, and B. Wu, “Generating multiphoton Greenberger–Horne–Zeilinger states with weak cross-Kerr nonlinearity,” Phys. Rev. A 75, 054302 (2007).
[CrossRef]

Xia, Y.

Z. C. Shi, Y. Xia, J. Song, and H. S. Song, “One-step implementation of the Fredkin gate via quantum Zeno dynamics,” Quantum Inf. Comput. 12, 215–230 (2012).

Xiao, Y. F.

Yamamoto, T.

T. Yamamoto, K. Hayashi, S. K. Ozdemir, M. Koashi, and N. Imoto, “Robust photonic entanglement distribution by state-independent encoding onto decoherence-free subspace,” Nat Photonics 2, 488–491 (2008).
[CrossRef]

Yamamoto, Y.

I. L. Chuang and Y. Yamamoto, “Simple quantum computer,” Phys. Rev. A 52, 3489–3496 (1995).
[CrossRef]

N. Imoto, H. A. Haus, and Y. Yamamoto, “Quantum nondemolition measurement of the photon number via the optical Kerr effect,” Phys. Rev. A 32, 2287–2292 (1985).
[CrossRef]

Yang, L.

Ye, L.

M. Z. Zhu, C. R. Zhao, and L. Ye, “Highly efficient scheme for the implementation of optical controlled-Z gate via two-qubit polarization parity detector,” Opt. Commun. 285, 1576–1580 (2012).
[CrossRef]

C. R. Zhao and L. Ye, “Robust scheme for the preparation of symmetric Dicke states with coherence state via cross-Kerr nonlinearity,” Opt. Commun. 284, 541–544 (2011).
[CrossRef]

C. R. Zhao and L. Ye, “Efficient scheme for the preparation of symmetric Dicke states via cross-Kerr nonlinearity,” Phys. Lett. A 375, 401–405 (2011).
[CrossRef]

Zhang, X. L.

Z. J. Deng, X. L. Zhang, H. Wei, K. L. Gao, and M. Feng, “Implementation of a nonlocal N-qubit conditional phase gate by single-photon interference,” Phys. Rev. A 76, 044305 (2007).
[CrossRef]

Zhao, C. R.

M. Z. Zhu, C. R. Zhao, and L. Ye, “Highly efficient scheme for the implementation of optical controlled-Z gate via two-qubit polarization parity detector,” Opt. Commun. 285, 1576–1580 (2012).
[CrossRef]

C. R. Zhao and L. Ye, “Robust scheme for the preparation of symmetric Dicke states with coherence state via cross-Kerr nonlinearity,” Opt. Commun. 284, 541–544 (2011).
[CrossRef]

C. R. Zhao and L. Ye, “Efficient scheme for the preparation of symmetric Dicke states via cross-Kerr nonlinearity,” Phys. Lett. A 375, 401–405 (2011).
[CrossRef]

Zhu, M. Z.

M. Z. Zhu, C. R. Zhao, and L. Ye, “Highly efficient scheme for the implementation of optical controlled-Z gate via two-qubit polarization parity detector,” Opt. Commun. 285, 1576–1580 (2012).
[CrossRef]

Int. J. Theor. Phys. (1)

E. Fredkin and T. Toffoli, “Conservative logic,” Int. J. Theor. Phys. 21, 219–253 (1982).
[CrossRef]

J. Phys. B (2)

M. Gao, W. H. Hu, and C. Z. Li, “Generating polarization-entangled W states using weak nonlinearity,” J. Phys. B 40, 3525–3529 (2007).
[CrossRef]

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

Nat Photonics (1)

T. Yamamoto, K. Hayashi, S. K. Ozdemir, M. Koashi, and N. Imoto, “Robust photonic entanglement distribution by state-independent encoding onto decoherence-free subspace,” Nat Photonics 2, 488–491 (2008).
[CrossRef]

Nature (3)

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef]

P. Grangier, J. A. Levenson, and J. Poizat, “Quantum non-demolition measurements in optics,” Nature 396, 537–542 (1998).
[CrossRef]

M. D. Barrett, J. Chiaverini, T. Schaetz, J. Britton, W. M. Itano, J. D. Jost, E. Knill, C. Langer, D. Leibfried, R. Ozeri, and D. J. Wineland, “Deterministic quantum teleportation of atomic qubits,” Nature 429, 737–739 (2004).
[CrossRef]

New J. Phys. (3)

T. P. Spiller, K. Nemoto, S. L. Braunstein, W. J. Munro, P. van Loock, and G. J. Milburn, “Quantum computation by communication,” New J. Phys. 8, 30 (2006).
[CrossRef]

S. G. R. Louis, K. Nemoto, W. J. Munro, and T. P. Spiller, “The efficiencies of generating cluster states with weak nonlinearities,” New J. Phys. 9, 193 (2007).
[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]

Opt. Commun. (2)

M. Z. Zhu, C. R. Zhao, and L. Ye, “Highly efficient scheme for the implementation of optical controlled-Z gate via two-qubit polarization parity detector,” Opt. Commun. 285, 1576–1580 (2012).
[CrossRef]

C. R. Zhao and L. Ye, “Robust scheme for the preparation of symmetric Dicke states with coherence state via cross-Kerr nonlinearity,” Opt. Commun. 284, 541–544 (2011).
[CrossRef]

Opt. Express (1)

Phys. Lett. A (1)

C. R. Zhao and L. Ye, “Efficient scheme for the preparation of symmetric Dicke states via cross-Kerr nonlinearity,” Phys. Lett. A 375, 401–405 (2011).
[CrossRef]

Phys. Rev. A (20)

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

P. Kok, “Effects of self-phase-modulation on weak nonlinear optical quantum gates,” Phys. Rev. A 77, 013808 (2008).
[CrossRef]

I. L. Chuang and Y. Yamamoto, “Simple quantum computer,” Phys. Rev. A 52, 3489–3496 (1995).
[CrossRef]

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

I. Friedler, G. Kurizki, and D. Petrosyan, “Deterministic quantum logic with photons via optically induced photonic band gaps,” Phys. Rev. A 71, 023803 (2005).
[CrossRef]

J. Fiurášek, “Linear-optics quantum Toffoli and Fredkin gates,” Phys. Rev. A 73, 062313 (2006).
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Figures (2)

Fig. 1.
Fig. 1.

Schematic diagram of optical Fredkin gate via weak nonlinearities and feed-forward. CKN, cross-Kerr nonlinearities. QND, quantum nondemolition detector which can exactly check the number of photons in the Fock state but not destroy them [13]. Dashed line indicates classical information feed-forward. For a classical information feed-forward technique, the future operation depends on earlier measurement results made on the probe coherent beams. PS, phase-shifter. π -PS, phase-shifter with the phase shift angle Δ ϕ = π . PBS, polarization beam splitter that totally transmits horizontally polarized photons and reflects vertically polarized photons. BS, beam splitter. Each of BSs in the scheme is the balanced BS.

Fig. 2.
Fig. 2.

Coherent state photon number probability distributions in the probe beam of the t mode for α = 10 3 and θ = 3.14 × 10 3 .

Equations (12)

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( a r a t ) = 1 2 ( 1 1 1 1 ) ( a in a u ) .
( a o b o ) = e i Δ ϕ 2 ( cos Δ ϕ 2 i sin Δ ϕ 2 i sin Δ ϕ 2 cos Δ ϕ 2 ) ( a i b i ) ,
| φ in = ( β 1 | H | H | H + β 2 | H | H | V + β 3 | H | V | H + β 4 | H | V | V + β 5 | V | H | H + β 6 | V | H | V + β 7 | V | V | H + β 8 | V | V | V ) C in T 1 in T 2 in .
( | H C | φ 4 + | V C | φ 1 ) | α I | α II + | H C | φ 1 | α e i 2 θ I | α e i 2 θ II + | V C | φ 4 | α e i 2 θ I | α e i 2 θ II + | H C ( | φ 2 + | φ 3 ) | α e i θ I | α e i θ II + | V C ( | φ 2 + | φ 3 ) | α e i θ I | α e i θ II ,
| φ 1 1 2 ( β 1 | H | 0 | H | 0 + β 2 | H | 0 | V | 0 + β 3 | V | 0 | H | 0 + β 4 | V | 0 | V | 0 ) T 1 T 1 T 2 T 2 | φ 2 1 2 ( β 1 | 0 | H | H | 0 + β 2 | 0 | H | V | 0 + β 3 | 0 | V | H | 0 + β 4 | 0 | V | V | 0 ) T 1 T 1 T 2 T 2 | φ 3 1 2 ( β 1 | H | 0 | 0 | H + β 2 | H | 0 | 0 | V + β 3 | V | 0 | 0 | H + β 4 | V | 0 | 0 | V ) T 1 T 1 T 2 T 2 | φ 4 1 2 ( β 1 | 0 | H | 0 | H + β 2 | 0 | H | 0 | V + β 3 | 0 | V | 0 | H + β 4 | 0 | V | 0 | V ) T 1 T 1 T 2 T 2 | φ 1 1 2 ( β 5 | H | 0 | H | 0 + β 6 | H | 0 | V | 0 + β 7 | V | 0 | H | 0 + β 8 | V | 0 | V | 0 ) T 1 T 1 T 2 T 2 | φ 2 1 2 ( β 5 | 0 | H | H | 0 + β 6 | 0 | H | V | 0 + β 7 | 0 | V | H | 0 + β 8 | 0 | V | V | 0 ) T 1 T 1 T 2 T 2 | φ 3 1 2 ( β 5 | H | 0 | 0 | H + β 6 | H | 0 | 0 | V + β 7 | V | 0 | 0 | H + β 8 | V | 0 | 0 | V ) T 1 T 1 T 2 T 2 | φ 4 1 2 ( β 5 | 0 | H | 0 | H + β 6 | 0 | H | 0 | V + β 7 | 0 | V | 0 | H + β 8 | 0 | V | 0 | V ) T 1 T 1 T 2 T 2 .
( | H C | φ 4 + | V C | φ 1 ) | 2 α r | 0 t + ( | H C | φ 1 | i 2 α sin 2 θ t + | V C | φ 4 | i 2 α sin 2 θ t ) | 2 α cos 2 θ r + ( | H C ( | φ 2 + | φ 3 ) | i 2 α sin θ t + | V C ( | φ 2 + | φ 3 ) | i 2 α sin θ t ) | 2 α cos θ r .
1 4 { | H C [ β 1 ( | 0 | H | 0 | H + | H | 0 | 0 | H + | 0 | H | H | 0 + | H | 0 | H | 0 ) + β 2 ( | 0 | V | 0 | H + | V | 0 | 0 | H + | 0 | V | H | 0 + | V | 0 | H | 0 ) + β 3 ( | 0 | H | 0 | V + | H | 0 | 0 | V + | 0 | H | V | 0 + | H | 0 | V | 0 ) + β 4 ( | 0 | V | 0 | V + | V | 0 | 0 | V + | 0 | V | V | 0 + | V | 0 | V | 0 ) ] T 1 T 1 T 2 T 2 + | V C [ β 5 ( | 0 | H | 0 | H | H | 0 | 0 | H | 0 | H | H | 0 + | H | 0 | H | 0 ) + β 6 ( | 0 | H | 0 | V | H | 0 | 0 | V | 0 | H | V | 0 + | H | 0 | V | 0 ) + β 7 ( | 0 | V | 0 | H | V | 0 | 0 | H | 0 | V | H | 0 + | V | 0 | H | 0 ) + β 8 ( | 0 | V | 0 | V | V | 0 | 0 | V | 0 | V | V | 0 + | V | 0 | V | 0 ) ] T 1 T 1 T 2 T 2 } .
1 4 [ | H C ( β 1 | H | H + β 2 | V | H + β 3 | H | V + β 4 | V | V ) T 1 T 2 + | V C ( β 5 | H | H + β 6 | H | V + β 7 | V | H + β 8 | V | V ) T 1 T 2 ] .
1 4 [ | H C ( β 1 | H | H + β 2 | H | V + β 3 | V | H + β 4 | V | V ) T 1 T 2 + | V C ( β 5 | H | H + β 6 | V | H + β 7 | H | V + β 8 | V | V ) T 1 T 2 ] .
1 4 { | H C [ β 1 ( | 0 | H | 0 | H | H | 0 | 0 | H | 0 | H | H | 0 + | H | 0 | H | 0 ) + β 2 ( | 0 | H | 0 | V | H | 0 | 0 | V | 0 | H | V | 0 + | H | 0 | V | 0 ) + β 3 ( | 0 | V | 0 | H | V | 0 | 0 | H | 0 | V | H | 0 + | V | 0 | H | 0 ) + β 4 ( | 0 | V | 0 | V | V | 0 | 0 | V | 0 | V | V | 0 + | V | 0 | V | 0 ) ] T 1 T 1 T 2 T 2 + | V C [ β 5 ( | 0 | H | 0 | H + | H | 0 | 0 | H + | 0 | H | H | 0 + | H | 0 | H | 0 ) + β 6 ( | 0 | V | 0 | H + | V | 0 | 0 | H + | 0 | V | H | 0 + | V | 0 | H | 0 ) + β 7 ( | 0 | H | 0 | V + | H | 0 | 0 | V + | 0 | H | V | 0 + | H | 0 | V | 0 ) + β 8 ( | 0 | V | 0 | V + | V | 0 | 0 | V + | 0 | V | V | 0 + | V | 0 | V | 0 ) ] T 1 T 1 T 2 T 2 } .
( | H C | φ 2 + | V C | φ 3 ) | α III | α IV + | H C | φ 3 | α e i 2 θ III | α e i 2 θ IV + | V C | φ 2 | α e i 2 θ III | α e i 2 θ IV .
( | H C | φ 2 + | V C | φ 3 ) | 2 α r | 0 t + ( | H C | φ 3 | i 2 α sin 2 θ t + | V C | φ 2 | i 2 α sin 2 θ t ) | 2 α cos 2 θ r .

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