Abstract

We propose a feasible scheme to remotely prepare three-dimensional (3D) optical vortex lines. Our scheme relies on the complete description of high-dimensional orbital angular momentum (OAM) entanglement in terms of the Laguerre-Gaussian modes. It is theoretically demonstrated that by simply changing the pump beam waist, we can remotely prepare the target photons in the vortex states of 3D interesting morphology, appearing as twisted vortex strands, separated vortex loops, and vortex link or knot. Furthermore, we employ the biphoton Klyshko picture to illustrate the conservation law of the OAM index and the spreading effect of the radial mode index p, where the Schmidt numbers are calculated to show the high-dimensional capacity of the quantum channels involved in the present remote state preparation.

© 2014 Optical Society of America

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  1. C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, W. K. Wootters, “Teleporting an unknown quantum state via dual classical and einstein-podolsky-rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
    [CrossRef] [PubMed]
  2. C. H. Bennett, D. P. DiVincenzo, P. W. Shor, J. A. Smolin, B. M. Terhal, W. K. Wootters, “Remote state preparation,” Phys. Rev. Lett. 87, 077902 (2001).
    [CrossRef] [PubMed]
  3. H.-K. Lo, “Classical-communication cost in distributed quantum-information processing: A generalization of quantum-communication complexity,” Phys. Rev. A 62, 012313 (2000).
    [CrossRef]
  4. A. K. Pati, “Minimum classical bit for remote preparation and measurement of a qubit,” Phys. Rev. A 63, 014302 (2000).
    [CrossRef]
  5. S. A. Babichev, B. Brezger, A. I. Lvovsky, “Remote preparation of a single-mode photonic qubit by measuring field quadrature noise,” Phys. Rev. Lett. 92, 047903 (2004).
    [CrossRef] [PubMed]
  6. I. Devetak, T. Berger, “Low-entanglement remote state preparation,” Phys. Rev. Lett. 87, 197901 (2001).
    [CrossRef] [PubMed]
  7. D. W. Berry, B. C. Sanders, “Optimal remote state preparation,” Phys. Rev. Lett. 90, 057901 (2003).
    [CrossRef] [PubMed]
  8. B. Zeng, P. Zhang, “Remote-state preparation in higher dimension and the parallelizable manifold sn−1,” Phys. Rev. A 65, 022316 (2002).
    [CrossRef]
  9. Z. Kurucz, P. Adam, Z. Kis, J. Janszky, “Continuous variable remote state preparation,” Phys. Rev. A 72, 052315 (2005).
    [CrossRef]
  10. N. A. Peters, J. T. Barreiro, M. E. Goggin, T.-C. Wei, P. G. Kwiat, “Remote state preparation: Arbitrary remote control of photon polarization,” Phys. Rev. Lett. 94, 150502 (2005).
    [CrossRef] [PubMed]
  11. J. T. Barreiro, T.-C. Wei, P. G. Kwiat, “Remote preparation of single-photon “hybrid” entangled and vector-polarization states,” Phys. Rev. Lett. 105, 030407 (2010).
    [CrossRef]
  12. M. R. Dennis, K. O’Holleran, M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293 (2009).
    [CrossRef]
  13. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, J. P. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
    [CrossRef] [PubMed]
  14. M. Berry, M. Dennis, “Knotted and linked phase singularities in monochromatic waves,” Proc. Roy. Soc. A 457, 2251–2263 (2001).
    [CrossRef]
  15. M. Berry, M. Dennis, “Knotting and unknotting of phase singularities: Helmholtz waves, paraxial waves and waves in 2+ 1 spacetime,” J. Phys. A: Math. Gen. 34, 8877 (2001).
    [CrossRef]
  16. J. Leach, M. Dennis, J. Courtial, M. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
    [CrossRef]
  17. J. Leach, M. R. Dennis, J. Courtial, M. J. Padgett, “Laser beams: knotted threads of darkness,” Nature 432, 165 (2004).
    [CrossRef] [PubMed]
  18. M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 118–121 (2010).
    [CrossRef]
  19. J. Romero, J. Leach, B. Jack, M. R. Dennis, S. Franke-Arnold, S. M. Barnett, M. J. Padgett, “Entangled optical vortex links,” Phys. Rev. Lett. 106, 100407 (2011).
    [CrossRef] [PubMed]
  20. J. P. Torres, Y. Deyanova, L. Torner, G. Molina-Terriza, “Preparation of engineered two-photon entangled states for multidimensional quantum information,” Phys. Rev. A 67, 052313 (2003).
    [CrossRef]
  21. F. M. Miatto, A. M. Yao, S. M. Barnett, “Full characterization of the quantum spiral bandwidth of entangled biphotons,” Phys. Rev. A 83, 033816 (2011).
    [CrossRef]
  22. A. M. Yao, “Angular momentum decomposition of entangled photons with an arbitrary pump,” New J. Phys. 13, 053048 (2011).
    [CrossRef]
  23. H. Bechmann-Pasquinucci, W. Tittel, “Quantum cryptography using larger alphabets,” Phys. Rev. A 61, 062308 (2000).
    [CrossRef]
  24. P. B. Dixon, G. A. Howland, J. Schneeloch, J. C. Howell, “Quantum mutual information capacity for high-dimensional entangled states,” Phys. Rev. Lett. 108, 143603 (2012).
    [CrossRef] [PubMed]
  25. C. K. Law, J. H. Eberly, “Analysis and interpretation of high transverse entanglement in optical parametric down conversion,” Phys. Rev. Lett. 92, 127903 (2004).
    [CrossRef] [PubMed]
  26. J. B. Pors, A. Aiello, S. S. R. Oemrawsingh, M. P. van Exter, E. R. Eliel, J. P. Woerdman, “Angular phase-plate analyzers for measuring the dimensionality of multimode fields,” Phys. Rev. A 77, 033845 (2008).
    [CrossRef]
  27. M. D’Angelo, Y. Shih, “Quantum imaging,” Laser Phys. Lett. 2, 567–596 (2005).
    [CrossRef]
  28. L. Chen, J. Leach, B. Jack, M. J. Padgett, S. Franke-Arnold, W. She, “High-dimensional quantum nature of ghost angular Young’s diffraction,” Phys. Rev. A 82, 033822 (2010).
    [CrossRef]
  29. L. Chen, J. Lei, J. Romero, “Quantum digital spiral imaging,” Light: Sci. Appl. 3, e153 (2014).
    [CrossRef]

2014

L. Chen, J. Lei, J. Romero, “Quantum digital spiral imaging,” Light: Sci. Appl. 3, e153 (2014).
[CrossRef]

2012

P. B. Dixon, G. A. Howland, J. Schneeloch, J. C. Howell, “Quantum mutual information capacity for high-dimensional entangled states,” Phys. Rev. Lett. 108, 143603 (2012).
[CrossRef] [PubMed]

2011

J. Romero, J. Leach, B. Jack, M. R. Dennis, S. Franke-Arnold, S. M. Barnett, M. J. Padgett, “Entangled optical vortex links,” Phys. Rev. Lett. 106, 100407 (2011).
[CrossRef] [PubMed]

F. M. Miatto, A. M. Yao, S. M. Barnett, “Full characterization of the quantum spiral bandwidth of entangled biphotons,” Phys. Rev. A 83, 033816 (2011).
[CrossRef]

A. M. Yao, “Angular momentum decomposition of entangled photons with an arbitrary pump,” New J. Phys. 13, 053048 (2011).
[CrossRef]

2010

L. Chen, J. Leach, B. Jack, M. J. Padgett, S. Franke-Arnold, W. She, “High-dimensional quantum nature of ghost angular Young’s diffraction,” Phys. Rev. A 82, 033822 (2010).
[CrossRef]

J. T. Barreiro, T.-C. Wei, P. G. Kwiat, “Remote preparation of single-photon “hybrid” entangled and vector-polarization states,” Phys. Rev. Lett. 105, 030407 (2010).
[CrossRef]

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 118–121 (2010).
[CrossRef]

2009

M. R. Dennis, K. O’Holleran, M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293 (2009).
[CrossRef]

2008

J. B. Pors, A. Aiello, S. S. R. Oemrawsingh, M. P. van Exter, E. R. Eliel, J. P. Woerdman, “Angular phase-plate analyzers for measuring the dimensionality of multimode fields,” Phys. Rev. A 77, 033845 (2008).
[CrossRef]

2005

M. D’Angelo, Y. Shih, “Quantum imaging,” Laser Phys. Lett. 2, 567–596 (2005).
[CrossRef]

J. Leach, M. Dennis, J. Courtial, M. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[CrossRef]

Z. Kurucz, P. Adam, Z. Kis, J. Janszky, “Continuous variable remote state preparation,” Phys. Rev. A 72, 052315 (2005).
[CrossRef]

N. A. Peters, J. T. Barreiro, M. E. Goggin, T.-C. Wei, P. G. Kwiat, “Remote state preparation: Arbitrary remote control of photon polarization,” Phys. Rev. Lett. 94, 150502 (2005).
[CrossRef] [PubMed]

2004

S. A. Babichev, B. Brezger, A. I. Lvovsky, “Remote preparation of a single-mode photonic qubit by measuring field quadrature noise,” Phys. Rev. Lett. 92, 047903 (2004).
[CrossRef] [PubMed]

J. Leach, M. R. Dennis, J. Courtial, M. J. Padgett, “Laser beams: knotted threads of darkness,” Nature 432, 165 (2004).
[CrossRef] [PubMed]

C. K. Law, J. H. Eberly, “Analysis and interpretation of high transverse entanglement in optical parametric down conversion,” Phys. Rev. Lett. 92, 127903 (2004).
[CrossRef] [PubMed]

2003

J. P. Torres, Y. Deyanova, L. Torner, G. Molina-Terriza, “Preparation of engineered two-photon entangled states for multidimensional quantum information,” Phys. Rev. A 67, 052313 (2003).
[CrossRef]

D. W. Berry, B. C. Sanders, “Optimal remote state preparation,” Phys. Rev. Lett. 90, 057901 (2003).
[CrossRef] [PubMed]

2002

B. Zeng, P. Zhang, “Remote-state preparation in higher dimension and the parallelizable manifold sn−1,” Phys. Rev. A 65, 022316 (2002).
[CrossRef]

2001

I. Devetak, T. Berger, “Low-entanglement remote state preparation,” Phys. Rev. Lett. 87, 197901 (2001).
[CrossRef] [PubMed]

C. H. Bennett, D. P. DiVincenzo, P. W. Shor, J. A. Smolin, B. M. Terhal, W. K. Wootters, “Remote state preparation,” Phys. Rev. Lett. 87, 077902 (2001).
[CrossRef] [PubMed]

M. Berry, M. Dennis, “Knotted and linked phase singularities in monochromatic waves,” Proc. Roy. Soc. A 457, 2251–2263 (2001).
[CrossRef]

M. Berry, M. Dennis, “Knotting and unknotting of phase singularities: Helmholtz waves, paraxial waves and waves in 2+ 1 spacetime,” J. Phys. A: Math. Gen. 34, 8877 (2001).
[CrossRef]

2000

H.-K. Lo, “Classical-communication cost in distributed quantum-information processing: A generalization of quantum-communication complexity,” Phys. Rev. A 62, 012313 (2000).
[CrossRef]

A. K. Pati, “Minimum classical bit for remote preparation and measurement of a qubit,” Phys. Rev. A 63, 014302 (2000).
[CrossRef]

H. Bechmann-Pasquinucci, W. Tittel, “Quantum cryptography using larger alphabets,” Phys. Rev. A 61, 062308 (2000).
[CrossRef]

1993

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

1992

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, J. P. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Adam, P.

Z. Kurucz, P. Adam, Z. Kis, J. Janszky, “Continuous variable remote state preparation,” Phys. Rev. A 72, 052315 (2005).
[CrossRef]

Aiello, A.

J. B. Pors, A. Aiello, S. S. R. Oemrawsingh, M. P. van Exter, E. R. Eliel, J. P. Woerdman, “Angular phase-plate analyzers for measuring the dimensionality of multimode fields,” Phys. Rev. A 77, 033845 (2008).
[CrossRef]

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, J. P. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Babichev, S. A.

S. A. Babichev, B. Brezger, A. I. Lvovsky, “Remote preparation of a single-mode photonic qubit by measuring field quadrature noise,” Phys. Rev. Lett. 92, 047903 (2004).
[CrossRef] [PubMed]

Barnett, S. M.

J. Romero, J. Leach, B. Jack, M. R. Dennis, S. Franke-Arnold, S. M. Barnett, M. J. Padgett, “Entangled optical vortex links,” Phys. Rev. Lett. 106, 100407 (2011).
[CrossRef] [PubMed]

F. M. Miatto, A. M. Yao, S. M. Barnett, “Full characterization of the quantum spiral bandwidth of entangled biphotons,” Phys. Rev. A 83, 033816 (2011).
[CrossRef]

Barreiro, J. T.

J. T. Barreiro, T.-C. Wei, P. G. Kwiat, “Remote preparation of single-photon “hybrid” entangled and vector-polarization states,” Phys. Rev. Lett. 105, 030407 (2010).
[CrossRef]

N. A. Peters, J. T. Barreiro, M. E. Goggin, T.-C. Wei, P. G. Kwiat, “Remote state preparation: Arbitrary remote control of photon polarization,” Phys. Rev. Lett. 94, 150502 (2005).
[CrossRef] [PubMed]

Bechmann-Pasquinucci, H.

H. Bechmann-Pasquinucci, W. Tittel, “Quantum cryptography using larger alphabets,” Phys. Rev. A 61, 062308 (2000).
[CrossRef]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, J. P. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Bennett, C. H.

C. H. Bennett, D. P. DiVincenzo, P. W. Shor, J. A. Smolin, B. M. Terhal, W. K. Wootters, “Remote state preparation,” Phys. Rev. Lett. 87, 077902 (2001).
[CrossRef] [PubMed]

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

Berger, T.

I. Devetak, T. Berger, “Low-entanglement remote state preparation,” Phys. Rev. Lett. 87, 197901 (2001).
[CrossRef] [PubMed]

Berry, D. W.

D. W. Berry, B. C. Sanders, “Optimal remote state preparation,” Phys. Rev. Lett. 90, 057901 (2003).
[CrossRef] [PubMed]

Berry, M.

M. Berry, M. Dennis, “Knotted and linked phase singularities in monochromatic waves,” Proc. Roy. Soc. A 457, 2251–2263 (2001).
[CrossRef]

M. Berry, M. Dennis, “Knotting and unknotting of phase singularities: Helmholtz waves, paraxial waves and waves in 2+ 1 spacetime,” J. Phys. A: Math. Gen. 34, 8877 (2001).
[CrossRef]

Brassard, G.

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

Brezger, B.

S. A. Babichev, B. Brezger, A. I. Lvovsky, “Remote preparation of a single-mode photonic qubit by measuring field quadrature noise,” Phys. Rev. Lett. 92, 047903 (2004).
[CrossRef] [PubMed]

Chen, L.

L. Chen, J. Lei, J. Romero, “Quantum digital spiral imaging,” Light: Sci. Appl. 3, e153 (2014).
[CrossRef]

L. Chen, J. Leach, B. Jack, M. J. Padgett, S. Franke-Arnold, W. She, “High-dimensional quantum nature of ghost angular Young’s diffraction,” Phys. Rev. A 82, 033822 (2010).
[CrossRef]

Courtial, J.

J. Leach, M. Dennis, J. Courtial, M. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[CrossRef]

J. Leach, M. R. Dennis, J. Courtial, M. J. Padgett, “Laser beams: knotted threads of darkness,” Nature 432, 165 (2004).
[CrossRef] [PubMed]

Crépeau, C.

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

D’Angelo, M.

M. D’Angelo, Y. Shih, “Quantum imaging,” Laser Phys. Lett. 2, 567–596 (2005).
[CrossRef]

Dennis, M.

J. Leach, M. Dennis, J. Courtial, M. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[CrossRef]

M. Berry, M. Dennis, “Knotting and unknotting of phase singularities: Helmholtz waves, paraxial waves and waves in 2+ 1 spacetime,” J. Phys. A: Math. Gen. 34, 8877 (2001).
[CrossRef]

M. Berry, M. Dennis, “Knotted and linked phase singularities in monochromatic waves,” Proc. Roy. Soc. A 457, 2251–2263 (2001).
[CrossRef]

Dennis, M. R.

J. Romero, J. Leach, B. Jack, M. R. Dennis, S. Franke-Arnold, S. M. Barnett, M. J. Padgett, “Entangled optical vortex links,” Phys. Rev. Lett. 106, 100407 (2011).
[CrossRef] [PubMed]

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 118–121 (2010).
[CrossRef]

M. R. Dennis, K. O’Holleran, M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293 (2009).
[CrossRef]

J. Leach, M. R. Dennis, J. Courtial, M. J. Padgett, “Laser beams: knotted threads of darkness,” Nature 432, 165 (2004).
[CrossRef] [PubMed]

Devetak, I.

I. Devetak, T. Berger, “Low-entanglement remote state preparation,” Phys. Rev. Lett. 87, 197901 (2001).
[CrossRef] [PubMed]

Deyanova, Y.

J. P. Torres, Y. Deyanova, L. Torner, G. Molina-Terriza, “Preparation of engineered two-photon entangled states for multidimensional quantum information,” Phys. Rev. A 67, 052313 (2003).
[CrossRef]

DiVincenzo, D. P.

C. H. Bennett, D. P. DiVincenzo, P. W. Shor, J. A. Smolin, B. M. Terhal, W. K. Wootters, “Remote state preparation,” Phys. Rev. Lett. 87, 077902 (2001).
[CrossRef] [PubMed]

Dixon, P. B.

P. B. Dixon, G. A. Howland, J. Schneeloch, J. C. Howell, “Quantum mutual information capacity for high-dimensional entangled states,” Phys. Rev. Lett. 108, 143603 (2012).
[CrossRef] [PubMed]

Eberly, J. H.

C. K. Law, J. H. Eberly, “Analysis and interpretation of high transverse entanglement in optical parametric down conversion,” Phys. Rev. Lett. 92, 127903 (2004).
[CrossRef] [PubMed]

Eliel, E. R.

J. B. Pors, A. Aiello, S. S. R. Oemrawsingh, M. P. van Exter, E. R. Eliel, J. P. Woerdman, “Angular phase-plate analyzers for measuring the dimensionality of multimode fields,” Phys. Rev. A 77, 033845 (2008).
[CrossRef]

Franke-Arnold, S.

J. Romero, J. Leach, B. Jack, M. R. Dennis, S. Franke-Arnold, S. M. Barnett, M. J. Padgett, “Entangled optical vortex links,” Phys. Rev. Lett. 106, 100407 (2011).
[CrossRef] [PubMed]

L. Chen, J. Leach, B. Jack, M. J. Padgett, S. Franke-Arnold, W. She, “High-dimensional quantum nature of ghost angular Young’s diffraction,” Phys. Rev. A 82, 033822 (2010).
[CrossRef]

Goggin, M. E.

N. A. Peters, J. T. Barreiro, M. E. Goggin, T.-C. Wei, P. G. Kwiat, “Remote state preparation: Arbitrary remote control of photon polarization,” Phys. Rev. Lett. 94, 150502 (2005).
[CrossRef] [PubMed]

Howell, J. C.

P. B. Dixon, G. A. Howland, J. Schneeloch, J. C. Howell, “Quantum mutual information capacity for high-dimensional entangled states,” Phys. Rev. Lett. 108, 143603 (2012).
[CrossRef] [PubMed]

Howland, G. A.

P. B. Dixon, G. A. Howland, J. Schneeloch, J. C. Howell, “Quantum mutual information capacity for high-dimensional entangled states,” Phys. Rev. Lett. 108, 143603 (2012).
[CrossRef] [PubMed]

Jack, B.

J. Romero, J. Leach, B. Jack, M. R. Dennis, S. Franke-Arnold, S. M. Barnett, M. J. Padgett, “Entangled optical vortex links,” Phys. Rev. Lett. 106, 100407 (2011).
[CrossRef] [PubMed]

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 118–121 (2010).
[CrossRef]

L. Chen, J. Leach, B. Jack, M. J. Padgett, S. Franke-Arnold, W. She, “High-dimensional quantum nature of ghost angular Young’s diffraction,” Phys. Rev. A 82, 033822 (2010).
[CrossRef]

Janszky, J.

Z. Kurucz, P. Adam, Z. Kis, J. Janszky, “Continuous variable remote state preparation,” Phys. Rev. A 72, 052315 (2005).
[CrossRef]

Jozsa, R.

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

King, R. P.

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 118–121 (2010).
[CrossRef]

Kis, Z.

Z. Kurucz, P. Adam, Z. Kis, J. Janszky, “Continuous variable remote state preparation,” Phys. Rev. A 72, 052315 (2005).
[CrossRef]

Kurucz, Z.

Z. Kurucz, P. Adam, Z. Kis, J. Janszky, “Continuous variable remote state preparation,” Phys. Rev. A 72, 052315 (2005).
[CrossRef]

Kwiat, P. G.

J. T. Barreiro, T.-C. Wei, P. G. Kwiat, “Remote preparation of single-photon “hybrid” entangled and vector-polarization states,” Phys. Rev. Lett. 105, 030407 (2010).
[CrossRef]

N. A. Peters, J. T. Barreiro, M. E. Goggin, T.-C. Wei, P. G. Kwiat, “Remote state preparation: Arbitrary remote control of photon polarization,” Phys. Rev. Lett. 94, 150502 (2005).
[CrossRef] [PubMed]

Law, C. K.

C. K. Law, J. H. Eberly, “Analysis and interpretation of high transverse entanglement in optical parametric down conversion,” Phys. Rev. Lett. 92, 127903 (2004).
[CrossRef] [PubMed]

Leach, J.

J. Romero, J. Leach, B. Jack, M. R. Dennis, S. Franke-Arnold, S. M. Barnett, M. J. Padgett, “Entangled optical vortex links,” Phys. Rev. Lett. 106, 100407 (2011).
[CrossRef] [PubMed]

L. Chen, J. Leach, B. Jack, M. J. Padgett, S. Franke-Arnold, W. She, “High-dimensional quantum nature of ghost angular Young’s diffraction,” Phys. Rev. A 82, 033822 (2010).
[CrossRef]

J. Leach, M. Dennis, J. Courtial, M. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[CrossRef]

J. Leach, M. R. Dennis, J. Courtial, M. J. Padgett, “Laser beams: knotted threads of darkness,” Nature 432, 165 (2004).
[CrossRef] [PubMed]

Lei, J.

L. Chen, J. Lei, J. Romero, “Quantum digital spiral imaging,” Light: Sci. Appl. 3, e153 (2014).
[CrossRef]

Lo, H.-K.

H.-K. Lo, “Classical-communication cost in distributed quantum-information processing: A generalization of quantum-communication complexity,” Phys. Rev. A 62, 012313 (2000).
[CrossRef]

Lvovsky, A. I.

S. A. Babichev, B. Brezger, A. I. Lvovsky, “Remote preparation of a single-mode photonic qubit by measuring field quadrature noise,” Phys. Rev. Lett. 92, 047903 (2004).
[CrossRef] [PubMed]

Miatto, F. M.

F. M. Miatto, A. M. Yao, S. M. Barnett, “Full characterization of the quantum spiral bandwidth of entangled biphotons,” Phys. Rev. A 83, 033816 (2011).
[CrossRef]

Molina-Terriza, G.

J. P. Torres, Y. Deyanova, L. Torner, G. Molina-Terriza, “Preparation of engineered two-photon entangled states for multidimensional quantum information,” Phys. Rev. A 67, 052313 (2003).
[CrossRef]

O’Holleran, K.

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 118–121 (2010).
[CrossRef]

M. R. Dennis, K. O’Holleran, M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293 (2009).
[CrossRef]

Oemrawsingh, S. S. R.

J. B. Pors, A. Aiello, S. S. R. Oemrawsingh, M. P. van Exter, E. R. Eliel, J. P. Woerdman, “Angular phase-plate analyzers for measuring the dimensionality of multimode fields,” Phys. Rev. A 77, 033845 (2008).
[CrossRef]

Padgett, M.

J. Leach, M. Dennis, J. Courtial, M. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[CrossRef]

Padgett, M. J.

J. Romero, J. Leach, B. Jack, M. R. Dennis, S. Franke-Arnold, S. M. Barnett, M. J. Padgett, “Entangled optical vortex links,” Phys. Rev. Lett. 106, 100407 (2011).
[CrossRef] [PubMed]

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 118–121 (2010).
[CrossRef]

L. Chen, J. Leach, B. Jack, M. J. Padgett, S. Franke-Arnold, W. She, “High-dimensional quantum nature of ghost angular Young’s diffraction,” Phys. Rev. A 82, 033822 (2010).
[CrossRef]

M. R. Dennis, K. O’Holleran, M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293 (2009).
[CrossRef]

J. Leach, M. R. Dennis, J. Courtial, M. J. Padgett, “Laser beams: knotted threads of darkness,” Nature 432, 165 (2004).
[CrossRef] [PubMed]

Pati, A. K.

A. K. Pati, “Minimum classical bit for remote preparation and measurement of a qubit,” Phys. Rev. A 63, 014302 (2000).
[CrossRef]

Peres, A.

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

Peters, N. A.

N. A. Peters, J. T. Barreiro, M. E. Goggin, T.-C. Wei, P. G. Kwiat, “Remote state preparation: Arbitrary remote control of photon polarization,” Phys. Rev. Lett. 94, 150502 (2005).
[CrossRef] [PubMed]

Pors, J. B.

J. B. Pors, A. Aiello, S. S. R. Oemrawsingh, M. P. van Exter, E. R. Eliel, J. P. Woerdman, “Angular phase-plate analyzers for measuring the dimensionality of multimode fields,” Phys. Rev. A 77, 033845 (2008).
[CrossRef]

Romero, J.

L. Chen, J. Lei, J. Romero, “Quantum digital spiral imaging,” Light: Sci. Appl. 3, e153 (2014).
[CrossRef]

J. Romero, J. Leach, B. Jack, M. R. Dennis, S. Franke-Arnold, S. M. Barnett, M. J. Padgett, “Entangled optical vortex links,” Phys. Rev. Lett. 106, 100407 (2011).
[CrossRef] [PubMed]

Sanders, B. C.

D. W. Berry, B. C. Sanders, “Optimal remote state preparation,” Phys. Rev. Lett. 90, 057901 (2003).
[CrossRef] [PubMed]

Schneeloch, J.

P. B. Dixon, G. A. Howland, J. Schneeloch, J. C. Howell, “Quantum mutual information capacity for high-dimensional entangled states,” Phys. Rev. Lett. 108, 143603 (2012).
[CrossRef] [PubMed]

She, W.

L. Chen, J. Leach, B. Jack, M. J. Padgett, S. Franke-Arnold, W. She, “High-dimensional quantum nature of ghost angular Young’s diffraction,” Phys. Rev. A 82, 033822 (2010).
[CrossRef]

Shih, Y.

M. D’Angelo, Y. Shih, “Quantum imaging,” Laser Phys. Lett. 2, 567–596 (2005).
[CrossRef]

Shor, P. W.

C. H. Bennett, D. P. DiVincenzo, P. W. Shor, J. A. Smolin, B. M. Terhal, W. K. Wootters, “Remote state preparation,” Phys. Rev. Lett. 87, 077902 (2001).
[CrossRef] [PubMed]

Smolin, J. A.

C. H. Bennett, D. P. DiVincenzo, P. W. Shor, J. A. Smolin, B. M. Terhal, W. K. Wootters, “Remote state preparation,” Phys. Rev. Lett. 87, 077902 (2001).
[CrossRef] [PubMed]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, J. P. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Terhal, B. M.

C. H. Bennett, D. P. DiVincenzo, P. W. Shor, J. A. Smolin, B. M. Terhal, W. K. Wootters, “Remote state preparation,” Phys. Rev. Lett. 87, 077902 (2001).
[CrossRef] [PubMed]

Tittel, W.

H. Bechmann-Pasquinucci, W. Tittel, “Quantum cryptography using larger alphabets,” Phys. Rev. A 61, 062308 (2000).
[CrossRef]

Torner, L.

J. P. Torres, Y. Deyanova, L. Torner, G. Molina-Terriza, “Preparation of engineered two-photon entangled states for multidimensional quantum information,” Phys. Rev. A 67, 052313 (2003).
[CrossRef]

Torres, J. P.

J. P. Torres, Y. Deyanova, L. Torner, G. Molina-Terriza, “Preparation of engineered two-photon entangled states for multidimensional quantum information,” Phys. Rev. A 67, 052313 (2003).
[CrossRef]

van Exter, M. P.

J. B. Pors, A. Aiello, S. S. R. Oemrawsingh, M. P. van Exter, E. R. Eliel, J. P. Woerdman, “Angular phase-plate analyzers for measuring the dimensionality of multimode fields,” Phys. Rev. A 77, 033845 (2008).
[CrossRef]

Wei, T.-C.

J. T. Barreiro, T.-C. Wei, P. G. Kwiat, “Remote preparation of single-photon “hybrid” entangled and vector-polarization states,” Phys. Rev. Lett. 105, 030407 (2010).
[CrossRef]

N. A. Peters, J. T. Barreiro, M. E. Goggin, T.-C. Wei, P. G. Kwiat, “Remote state preparation: Arbitrary remote control of photon polarization,” Phys. Rev. Lett. 94, 150502 (2005).
[CrossRef] [PubMed]

Woerdman, J. P.

J. B. Pors, A. Aiello, S. S. R. Oemrawsingh, M. P. van Exter, E. R. Eliel, J. P. Woerdman, “Angular phase-plate analyzers for measuring the dimensionality of multimode fields,” Phys. Rev. A 77, 033845 (2008).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, J. P. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Wootters, W. K.

C. H. Bennett, D. P. DiVincenzo, P. W. Shor, J. A. Smolin, B. M. Terhal, W. K. Wootters, “Remote state preparation,” Phys. Rev. Lett. 87, 077902 (2001).
[CrossRef] [PubMed]

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

Yao, A. M.

A. M. Yao, “Angular momentum decomposition of entangled photons with an arbitrary pump,” New J. Phys. 13, 053048 (2011).
[CrossRef]

F. M. Miatto, A. M. Yao, S. M. Barnett, “Full characterization of the quantum spiral bandwidth of entangled biphotons,” Phys. Rev. A 83, 033816 (2011).
[CrossRef]

Zeng, B.

B. Zeng, P. Zhang, “Remote-state preparation in higher dimension and the parallelizable manifold sn−1,” Phys. Rev. A 65, 022316 (2002).
[CrossRef]

Zhang, P.

B. Zeng, P. Zhang, “Remote-state preparation in higher dimension and the parallelizable manifold sn−1,” Phys. Rev. A 65, 022316 (2002).
[CrossRef]

J. Phys. A: Math. Gen.

M. Berry, M. Dennis, “Knotting and unknotting of phase singularities: Helmholtz waves, paraxial waves and waves in 2+ 1 spacetime,” J. Phys. A: Math. Gen. 34, 8877 (2001).
[CrossRef]

Laser Phys. Lett.

M. D’Angelo, Y. Shih, “Quantum imaging,” Laser Phys. Lett. 2, 567–596 (2005).
[CrossRef]

Light: Sci. Appl.

L. Chen, J. Lei, J. Romero, “Quantum digital spiral imaging,” Light: Sci. Appl. 3, e153 (2014).
[CrossRef]

Nat. Phys.

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 118–121 (2010).
[CrossRef]

Nature

J. Leach, M. R. Dennis, J. Courtial, M. J. Padgett, “Laser beams: knotted threads of darkness,” Nature 432, 165 (2004).
[CrossRef] [PubMed]

New J. Phys.

A. M. Yao, “Angular momentum decomposition of entangled photons with an arbitrary pump,” New J. Phys. 13, 053048 (2011).
[CrossRef]

J. Leach, M. Dennis, J. Courtial, M. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[CrossRef]

Phys. Rev. A

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, J. P. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

H.-K. Lo, “Classical-communication cost in distributed quantum-information processing: A generalization of quantum-communication complexity,” Phys. Rev. A 62, 012313 (2000).
[CrossRef]

A. K. Pati, “Minimum classical bit for remote preparation and measurement of a qubit,” Phys. Rev. A 63, 014302 (2000).
[CrossRef]

B. Zeng, P. Zhang, “Remote-state preparation in higher dimension and the parallelizable manifold sn−1,” Phys. Rev. A 65, 022316 (2002).
[CrossRef]

Z. Kurucz, P. Adam, Z. Kis, J. Janszky, “Continuous variable remote state preparation,” Phys. Rev. A 72, 052315 (2005).
[CrossRef]

H. Bechmann-Pasquinucci, W. Tittel, “Quantum cryptography using larger alphabets,” Phys. Rev. A 61, 062308 (2000).
[CrossRef]

J. B. Pors, A. Aiello, S. S. R. Oemrawsingh, M. P. van Exter, E. R. Eliel, J. P. Woerdman, “Angular phase-plate analyzers for measuring the dimensionality of multimode fields,” Phys. Rev. A 77, 033845 (2008).
[CrossRef]

J. P. Torres, Y. Deyanova, L. Torner, G. Molina-Terriza, “Preparation of engineered two-photon entangled states for multidimensional quantum information,” Phys. Rev. A 67, 052313 (2003).
[CrossRef]

F. M. Miatto, A. M. Yao, S. M. Barnett, “Full characterization of the quantum spiral bandwidth of entangled biphotons,” Phys. Rev. A 83, 033816 (2011).
[CrossRef]

L. Chen, J. Leach, B. Jack, M. J. Padgett, S. Franke-Arnold, W. She, “High-dimensional quantum nature of ghost angular Young’s diffraction,” Phys. Rev. A 82, 033822 (2010).
[CrossRef]

Phys. Rev. Lett.

P. B. Dixon, G. A. Howland, J. Schneeloch, J. C. Howell, “Quantum mutual information capacity for high-dimensional entangled states,” Phys. Rev. Lett. 108, 143603 (2012).
[CrossRef] [PubMed]

C. K. Law, J. H. Eberly, “Analysis and interpretation of high transverse entanglement in optical parametric down conversion,” Phys. Rev. Lett. 92, 127903 (2004).
[CrossRef] [PubMed]

N. A. Peters, J. T. Barreiro, M. E. Goggin, T.-C. Wei, P. G. Kwiat, “Remote state preparation: Arbitrary remote control of photon polarization,” Phys. Rev. Lett. 94, 150502 (2005).
[CrossRef] [PubMed]

J. T. Barreiro, T.-C. Wei, P. G. Kwiat, “Remote preparation of single-photon “hybrid” entangled and vector-polarization states,” Phys. Rev. Lett. 105, 030407 (2010).
[CrossRef]

S. A. Babichev, B. Brezger, A. I. Lvovsky, “Remote preparation of a single-mode photonic qubit by measuring field quadrature noise,” Phys. Rev. Lett. 92, 047903 (2004).
[CrossRef] [PubMed]

I. Devetak, T. Berger, “Low-entanglement remote state preparation,” Phys. Rev. Lett. 87, 197901 (2001).
[CrossRef] [PubMed]

D. W. Berry, B. C. Sanders, “Optimal remote state preparation,” Phys. Rev. Lett. 90, 057901 (2003).
[CrossRef] [PubMed]

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

C. H. Bennett, D. P. DiVincenzo, P. W. Shor, J. A. Smolin, B. M. Terhal, W. K. Wootters, “Remote state preparation,” Phys. Rev. Lett. 87, 077902 (2001).
[CrossRef] [PubMed]

J. Romero, J. Leach, B. Jack, M. R. Dennis, S. Franke-Arnold, S. M. Barnett, M. J. Padgett, “Entangled optical vortex links,” Phys. Rev. Lett. 106, 100407 (2011).
[CrossRef] [PubMed]

Proc. Roy. Soc. A

M. Berry, M. Dennis, “Knotted and linked phase singularities in monochromatic waves,” Proc. Roy. Soc. A 457, 2251–2263 (2001).
[CrossRef]

Prog. Opt.

M. R. Dennis, K. O’Holleran, M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293 (2009).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

The proposed scheme for RSP of 3D optical vortices (see the text for details).

Fig. 2
Fig. 2

RSP of two- and three-strand vortex lines. (a) and (d) are the desired holograms; (b) and (e) are 3D vortex link and knot [16] at Alice’s side; (c) and (f) are the simulations of desired 3D structures of two- and three-strand vortices at Bob’s side, respectively.

Fig. 3
Fig. 3

The transverse intensity patterns of the target photons. (a), (b) and (c): RSP of two-strand vortices; (d), (e) and (f): RSP of three-strand vortices.

Fig. 4
Fig. 4

The 3D structures of the remotely prepared optical vortices with different pump beam waists wp, where the upper and bottom lows are prepared with = 2 and 3, respectively. (a), (d): Vortex strands (wp = 1 mm); (b), (e): Vortex loops (wp = 1.5 mm); (c), (f): Vortex link and knot (wp = 3 mm).

Fig. 5
Fig. 5

The simplified Klyshko picture for visualization of biphoton channels sustained by the LG modes involved in our RSP scheme.

Tables (1)

Tables Icon

Table 1 The Schmidt numbers for different pump beam waists in our RSP scheme.

Equations (6)

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

LG p ( R , ϕ , z ) = p ! π ( | | + p ) ! R | | exp ( i ϕ ) ( w 2 + i z / k ) | | + 1 exp ( R 2 2 ( w 2 + i z / k ) ) × L p | | ( R 2 w 2 + z 2 / k 2 w 2 ) ( w 2 i z / k w 2 + i z / k ) p ,
| Ψ SPDC = , p s , p i C p s , p i , | , p s | , p i ,
C p s , p i , K p i , p s | | ( 1 γ i 2 + γ s 2 ) p i ( 1 + γ i 2 γ s 2 ) p s ( 2 γ i γ s ) | | ( 1 + γ i 2 + γ s 2 ) p i + p s + | | × F 1 2 [ p i , p s p i p s | | ; 1 ( γ i 2 + γ s 2 ) 2 1 ( γ i 2 γ s 2 ) 2 ] ,
| ψ link , knot = a 0 LG 0 0 ( 8 w ) + a 1 LG 0 ( 2 w ) + a 2 LG 1 ( w ) + a 3 LG 2 ( w ) .
| ψ rp = ψ link , knot | Ψ SPDC = p i ( a 0 * C 0 , p i 0 , 0 LG p i 0 ( 8 w ) + a 1 * C 0 , p i , LG p i ( 2 w ) + a 2 * C 1 , p i , LG p i ( w ) + a 3 * C 2 , p i , LG p i ( w ) ) .
| Ψ ps = p i ( C 0 , p i 0 , 0 | 0 , 0 | 0 , p i + C 0 , p i , | , 0 | , p i + C 1 , p i , | , 1 | , p i + C 2 , p i , | , 2 | , p i ) .

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