Abstract

We propose a polarization-controlled-NOT (P-CNOT) gate and an orbital-angular-momentum-controlled-NOT (OAM-CNOT) gate for single-photon two-qubit quantum logic. Both of the controlled-NOT (CNOT) gates are simple and deterministic. Moreover the entanglement swap between polarization and orbital angular momentum (OAM) can be realized using the P-CNOT gate and the OAM-CNOT gate.

© 2007 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. T. B. Pittman, B. C. Jacobs and J. D. Franson, "Probabilistic quantum logic operations using polarizing beam splitters," Phys. Rev. A 64, 062311 (2001).
    [CrossRef]
  4. T. C. Ralph, N. K. Langford, T. B. Bell, and A. G. White, "Linear optical controlled-NOT gate in the coincidence basis," Phys. Rev. A 65, 062324 (2002).
    [CrossRef]
  5. J. L. O'Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, "Demonstration of an all-optical quantum controlled-NOT gate," Nature 426, 264-267 (2003).
    [CrossRef] [PubMed]
  6. S. Gasparoni, J. Pan, P. Walther, T. Rudolph, and A. Zeilinger, "Realization of a photonic controlled-NOT gate sufficient for quantum computation," Phys. Rev. Lett. 93, 020504 (2004).
    [CrossRef] [PubMed]
  7. N. J. Cerf, C. Adami, and P. G. Kwiat, "Optical simulation of quantum logic," Phys. Rev. A 57, R1477 (1998).
    [CrossRef]
  8. J. C. Howell and J. A. Yeazell, "Reducing the complexity of linear optics quantum circuits," Phys. Rev. A 61, 052303 (2000).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  21. V. Y. Bazheov, M. S. Soskin, and M. V. Vasnetsov, "Screw dislocations in light wavefronts," J. Mod. Opt. 39, 985-990 (1992).
    [CrossRef]
  22. J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, "The production of multiringed Laguerre-Gaussian modes by computer-generated holograms," J. Mod. Opt. 45, 1231-1237 (1998).
    [CrossRef]
  23. A. Vaziri, G. Weihs, and A. Zeilinger, "Superpositions of the orbital angular momentum for applications in quantum experiments," J. Opt. B: Quantum Semiclassical Opt. 4, S47-S51 (2002).
    [CrossRef]
  24. S. Feng and H. G. Winful, "Physical origin of the Gouy phase shift," Opt. Lett. 26, 485-487 (2001).
    [CrossRef]
  25. J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, "Measuring the orbital angular momentum of a single photon," Phys. Rev. Lett. 88, 257901 (2002).
    [CrossRef] [PubMed]
  26. G. F. Calvo, A. Picón, and A. Bramon, "Measuring two-photon orbital angular momentum entanglement," Phys. Rev. A 75, 012319 (2007).
    [CrossRef]
  27. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001).
    [CrossRef] [PubMed]

2007

2006

L. Marrucci, C. Manzo, and D. Paparo, "Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media," Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef] [PubMed]

G. F. Calvo, A. Picón, and E. Bagan, "Quantum field theory of photons with orbital angular momentum," Phys. Rev. A 73, 013805 (2006).
[CrossRef]

2005

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, "Generation of hyperentangled photon pairs," Phys. Rev. Lett. 95, 260501 (2005).
[CrossRef]

A. N. de Oliveira, S. P. Walborn, and C. H. Monken, "Implementing the Deutsch algorithm with polarization and transverse spatial modes," J. Opt. Soc. Am. B 7, 288-292 (2005).

M. Fiorentino, T. Kim, and F. N. C. Wong, "Single-photon two-qubit SWAP gate for entanglement manipulation," Phys. Rev. A 72, 012318 (2005).
[CrossRef]

2004

M. Fiorentino and F. N. C. Wong, "Deterministic controlled-NOT gate for single-photon two-qubit quantum logic," Phys. Rev. Lett. 93, 070502 (2004).
[CrossRef] [PubMed]

S. Roychowdhury, V. K. Jaiswal, and R. P. Singh,"Implementing controlled NOT gate with optical vortex," Opt. Commun. 236, 419-424 (2004).
[CrossRef]

S. Gasparoni, J. Pan, P. Walther, T. Rudolph, and A. Zeilinger, "Realization of a photonic controlled-NOT gate sufficient for quantum computation," Phys. Rev. Lett. 93, 020504 (2004).
[CrossRef] [PubMed]

2003

J. L. O'Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, "Demonstration of an all-optical quantum controlled-NOT gate," Nature 426, 264-267 (2003).
[CrossRef] [PubMed]

Y.-H. Kim, "Single-photon two-qubit entangled states: Preparation and measurement," Phys. Rev. A 67, 040301 (2003).
[CrossRef]

2002

T. C. Ralph, N. K. Langford, T. B. Bell, and A. G. White, "Linear optical controlled-NOT gate in the coincidence basis," Phys. Rev. A 65, 062324 (2002).
[CrossRef]

A. Vaziri, G. Weihs, and A. Zeilinger, "Superpositions of the orbital angular momentum for applications in quantum experiments," J. Opt. B: Quantum Semiclassical Opt. 4, S47-S51 (2002).
[CrossRef]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, "Measuring the orbital angular momentum of a single photon," Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef] [PubMed]

2001

S. Feng and H. G. Winful, "Physical origin of the Gouy phase shift," Opt. Lett. 26, 485-487 (2001).
[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] [PubMed]

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

T. B. Pittman, B. C. Jacobs and J. D. Franson, "Probabilistic quantum logic operations using polarizing beam splitters," Phys. Rev. A 64, 062311 (2001).
[CrossRef]

B.-G. Englert, C. Kurtsiefer, and H. Weinfurter, "Universal unitary gate for single-photon two-qubit states," Phys. Rev. A 63, 032303 (2001).
[CrossRef]

2000

J. C. Howell and J. A. Yeazell, "Reducing the complexity of linear optics quantum circuits," Phys. Rev. A 61, 052303 (2000).
[CrossRef]

1998

N. J. Cerf, C. Adami, and P. G. Kwiat, "Optical simulation of quantum logic," Phys. Rev. A 57, R1477 (1998).
[CrossRef]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, "The production of multiringed Laguerre-Gaussian modes by computer-generated holograms," J. Mod. Opt. 45, 1231-1237 (1998).
[CrossRef]

1995

D. P. DiVincenzo, "Two-bit gates are universal for quantum computation," Phys. Rev. A 51, 1015 (1995).
[CrossRef] [PubMed]

1992

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, "Laser beams with phase singularities," Opt. Quantum Electron. 24, S951-S962 (1992).
[CrossRef]

V. Y. Bazheov, M. S. Soskin, and M. V. Vasnetsov, "Screw dislocations in light wavefronts," J. Mod. Opt. 39, 985-990 (1992).
[CrossRef]

J. Mod. Opt.

V. Y. Bazheov, M. S. Soskin, and M. V. Vasnetsov, "Screw dislocations in light wavefronts," J. Mod. Opt. 39, 985-990 (1992).
[CrossRef]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, "The production of multiringed Laguerre-Gaussian modes by computer-generated holograms," J. Mod. Opt. 45, 1231-1237 (1998).
[CrossRef]

J. Opt. B: Quantum Semiclassical Opt.

A. Vaziri, G. Weihs, and A. Zeilinger, "Superpositions of the orbital angular momentum for applications in quantum experiments," J. Opt. B: Quantum Semiclassical Opt. 4, S47-S51 (2002).
[CrossRef]

J. Opt. Soc. Am. B

Nature

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

J. L. O'Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, "Demonstration of an all-optical quantum controlled-NOT gate," Nature 426, 264-267 (2003).
[CrossRef] [PubMed]

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

Opt. Commun.

S. Roychowdhury, V. K. Jaiswal, and R. P. Singh,"Implementing controlled NOT gate with optical vortex," Opt. Commun. 236, 419-424 (2004).
[CrossRef]

Opt. Lett.

Opt. Quantum Electron.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, "Laser beams with phase singularities," Opt. Quantum Electron. 24, S951-S962 (1992).
[CrossRef]

Phys. Rev. A

G. F. Calvo, A. Picón, and A. Bramon, "Measuring two-photon orbital angular momentum entanglement," Phys. Rev. A 75, 012319 (2007).
[CrossRef]

D. P. DiVincenzo, "Two-bit gates are universal for quantum computation," Phys. Rev. A 51, 1015 (1995).
[CrossRef] [PubMed]

G. F. Calvo, A. Picón, and E. Bagan, "Quantum field theory of photons with orbital angular momentum," Phys. Rev. A 73, 013805 (2006).
[CrossRef]

T. B. Pittman, B. C. Jacobs and J. D. Franson, "Probabilistic quantum logic operations using polarizing beam splitters," Phys. Rev. A 64, 062311 (2001).
[CrossRef]

T. C. Ralph, N. K. Langford, T. B. Bell, and A. G. White, "Linear optical controlled-NOT gate in the coincidence basis," Phys. Rev. A 65, 062324 (2002).
[CrossRef]

N. J. Cerf, C. Adami, and P. G. Kwiat, "Optical simulation of quantum logic," Phys. Rev. A 57, R1477 (1998).
[CrossRef]

J. C. Howell and J. A. Yeazell, "Reducing the complexity of linear optics quantum circuits," Phys. Rev. A 61, 052303 (2000).
[CrossRef]

B.-G. Englert, C. Kurtsiefer, and H. Weinfurter, "Universal unitary gate for single-photon two-qubit states," Phys. Rev. A 63, 032303 (2001).
[CrossRef]

Y.-H. Kim, "Single-photon two-qubit entangled states: Preparation and measurement," Phys. Rev. A 67, 040301 (2003).
[CrossRef]

M. Fiorentino, T. Kim, and F. N. C. Wong, "Single-photon two-qubit SWAP gate for entanglement manipulation," Phys. Rev. A 72, 012318 (2005).
[CrossRef]

Phys. Rev. Lett.

M. Fiorentino and F. N. C. Wong, "Deterministic controlled-NOT gate for single-photon two-qubit quantum logic," Phys. Rev. Lett. 93, 070502 (2004).
[CrossRef] [PubMed]

S. Gasparoni, J. Pan, P. Walther, T. Rudolph, and A. Zeilinger, "Realization of a photonic controlled-NOT gate sufficient for quantum computation," Phys. Rev. Lett. 93, 020504 (2004).
[CrossRef] [PubMed]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, "Measuring the orbital angular momentum of a single photon," Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef] [PubMed]

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, "Generation of hyperentangled photon pairs," Phys. Rev. Lett. 95, 260501 (2005).
[CrossRef]

L. Marrucci, C. Manzo, and D. Paparo, "Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media," Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef] [PubMed]

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Figures (2)

Fig. 1
Fig. 1

Experimental setup of the optical P-CNOT gate. PBS, polarizing beam splitter. CGH, computer generated hologram with parameter Δ l = 1 , which can change the parity of the OAM’s quantum number.

Fig. 2
Fig. 2

Experimental setup of the optical OAM-CNOT gate. BS, 50 50 beam splitter. DP, Dove prism. HWP, half-wave plate, which is oriented at 45° relative to the horizontal direction. The even-l photon will exit port A, and the odd-l photon will exit port B.

Equations (16)

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T ( r , ϕ ) = exp ( i δ 1 2 π mod ( Δ m ϕ 2 π Λ r cos ϕ , 2 π ) ) ,
Ψ = α 0 P 0 O + β 0 P 1 O + γ 1 P 0 O + δ 1 P 1 O ,
Ψ α 0 P 0 O + β 0 P 1 O + γ 1 P 1 O + δ 1 P 0 O .
1 2 ( 1 1 1 1 ) .
( A B ) = 1 2 u ( r ) exp ( i l ϕ ) ( 1 + exp ( i l π ) 1 exp ( i l π ) ) .
Ψ α 0 P 0 O + β 1 P 1 O + γ 1 P 0 O + δ 0 P 1 O .
Ψ real l p = 0 = C 0 , 0 0 , 0 + C 1 , 1 1 , 1 + C 1 , 1 1 , 1 + C 2 , 2 2 , 2 + C 2 , 2 2 , 2 + ,
Ψ logical l p = 0 = C 0 , 0 0 , 0 + C 1 , 1 1 , 1 + C 1 , 1 1 , 1 + C 2 , 2 0 , 0 + C 2 , 2 0 , 0 + = α 0 , 0 + β 1 , 1 ,
Ψ real l = 1 = C 0 , 1 0 , 1 + C 1 , 0 1 , 0 + C 1 , 2 1 , 2 + C 2 , 1 2 , 1 + C 2 , 3 2 , 3 + .
Ψ logical l = 1 = C 0 , 1 0 , 1 + C 1 , 0 1 , 0 + C 1 , 2 1 , 0 + C 2 , 1 0 , 1 + C 2 , 3 0 , 1 + = γ 0 , 1 + δ 1 , 0 ,
Ψ in = 1 2 ( 0 O S 1 O I + 1 O S 0 O I ) 0 P S 1 P I = 1 2 ( 0 P S 0 O S 1 P I 1 O I + 0 P S 1 O S 1 P I 0 O I ) ,
Ψ GHZ = 1 2 ( 0 P S 0 O S 0 P I 1 O I + 1 P S 1 O S 1 P I 0 O I ) .
Ψ out = 1 2 ( 0 P S 0 O S 1 P I 1 O I + 1 P S 0 O S 0 P I 1 O I ) = 1 2 ( 0 O S 1 O I ) ( 0 P S 1 P I + 1 P S 0 P I ) .
Ψ out = 1 2 ( 0 O S 1 O I ) ( 0 P S 0 P I + 1 P S 1 P I ) .
Φ GHZ = 1 2 ( 0 P S 0 O S 1 P I 0 O I + 1 P S 1 O S 0 P I 1 O I ) .
Φ out = 1 2 ( 0 P S 1 P I ) ( 0 O S 0 O I + 1 O S 1 O I ) .

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