Abstract

Orbital angular momentum (OAM) entanglement is investigated in the Bessel-Gaussian (BG) basis. Having a readily adjustable radial scale, BG modes provide an alternative basis for OAM entanglement over Laguerre-Gaussian modes. We show that the OAM bandwidth in terms of BG modes can be increased by selection of particular radial wavevectors and leads to a flattening of the spectrum, which allows for higher dimensionality in the entangled state. We demonstrate entanglement in terms of BG modes by performing a Bell-type experiment and showing a violation of the Clauser-Horne-Shimony-Holt inequality for the = ±1 subspace. In addition, we use quantum state tomography to indicate higher-dimensional entanglement in terms of BG modes.

© 2012 OSA

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  1. H. Arnaut and G. Barbosa, “Orbital and intrinsic angular momentum of single photons and entangled pairs of photons generated by parametric down-conversion,” Phys. Rev. Lett.85, 286–289 (2000).
    [CrossRef] [PubMed]
  2. Franke-Arnold, S. S. Barnett, M. Padgett, and L. Allen, “Two-photon entanglement of orbital angular momentum states,” Phys. Rev. A65(3), 033823 (2002).
    [CrossRef]
  3. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature412, 313–316 (2001).
    [CrossRef] [PubMed]
  4. T. Pittman, Y. Shih, D. Strekalov, and A. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A52, R3429–R3432 (1995).
    [CrossRef] [PubMed]
  5. A. Ekert, “Quantum cryptography based on Bells theorem,” Phys. Rev. Lett.67, 661–663 (1991).
    [CrossRef] [PubMed]
  6. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptograpy,” Rev. Mod. Phys.74, 145–195 (2002).
    [CrossRef]
  7. M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2000).
  8. V. Salakhutdinov, E. Eliel, and W. Löffler, “Full-field quantum correlations of spatially entangled photons,” Phys. Rev. Lett.108, 173604 (2012).
    [CrossRef] [PubMed]
  9. L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45, 8185–8189 (1992).
    [CrossRef] [PubMed]
  10. J. Durnin, “Exact solutions for nondiffracting beams. i. the scalar theory,” J. Opt. Soc. Am. A4, 651–654 (1987).
    [CrossRef]
  11. J. Durnin, J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58, 1499–1501 (1987).
    [CrossRef] [PubMed]
  12. F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun.64, 491–495 (1987).
    [CrossRef]
  13. M. Agnew, J. Leach, M. McLaren, F. Roux, and R. Boyd, “Tomography of the quantum state of photons entangled in high dimensions,” Phys. Rev. A84, 062101 (2011).
    [CrossRef]
  14. D. James, P. Kwiat, W. Munro, and A. White, “Measurement of qubits,” Phys. Rev. A64, 052312 (2001).
    [CrossRef]
  15. R.T. Thew, K. Nemoto, A.G. White, and W.J. Munro, “Qudit quantum-state tomography,” Phys. Rev. A66, 012303 (2002).
    [CrossRef]
  16. V. Arrizon, “Optimum on-axis computer-generated hologram encoded into low-resolution phase- modulation devices,” Opt. Lett.28, 2521–2523 (2003).
    [CrossRef] [PubMed]
  17. J. Leach, B. Jack, M. Ritsch-Marte, R. Boyd, A. Jha, S. Barnett, S. Franke-Arnold, and M. Padgett, “Violation of a Bell inequality in two-dimensional orbital angular momentum state-spaces,” Opt. Express17, 8287–8293 (2009).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  20. A. Vaziri, J.W Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher-dimensional entanglement: Qutrits of photon orbital angular momentum,” Phys. Rev. Lett.91, 227902 (2003).
    [CrossRef] [PubMed]
  21. J. Clauser, M. Horne, A. Shimony, and R. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett.23, 880–884 (1969).
    [CrossRef]
  22. B. Jack, J. Leach, H. Ritsch, S. Barnett, and M. Padgett, “Precise quantum tomography of photon pairs with entangled orbital angular momentum,” New J. of Phys.811, 103024 (2009).
    [CrossRef]
  23. S. Bose and V. Vedral, “Mixedness and teleportation,” Phys. Rev. A61, 040101(R) (2000).
    [CrossRef]
  24. D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, “Bell inequalities for arbitrarily high-dimensional systems,” Phys. Rev. Lett.88, 040404 (2002).
    [CrossRef] [PubMed]

2012 (1)

V. Salakhutdinov, E. Eliel, and W. Löffler, “Full-field quantum correlations of spatially entangled photons,” Phys. Rev. Lett.108, 173604 (2012).
[CrossRef] [PubMed]

2011 (2)

M. Agnew, J. Leach, M. McLaren, F. Roux, and R. Boyd, “Tomography of the quantum state of photons entangled in high dimensions,” Phys. Rev. A84, 062101 (2011).
[CrossRef]

A. Dada, J. Leach, G. Buller, M. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of the generalized Bell inequalities,” Nat. Phys.7, 677–680 (2011).
[CrossRef]

2009 (2)

B. Jack, J. Leach, H. Ritsch, S. Barnett, and M. Padgett, “Precise quantum tomography of photon pairs with entangled orbital angular momentum,” New J. of Phys.811, 103024 (2009).
[CrossRef]

J. Leach, B. Jack, M. Ritsch-Marte, R. Boyd, A. Jha, S. Barnett, S. Franke-Arnold, and M. Padgett, “Violation of a Bell inequality in two-dimensional orbital angular momentum state-spaces,” Opt. Express17, 8287–8293 (2009).
[CrossRef] [PubMed]

2003 (2)

V. Arrizon, “Optimum on-axis computer-generated hologram encoded into low-resolution phase- modulation devices,” Opt. Lett.28, 2521–2523 (2003).
[CrossRef] [PubMed]

A. Vaziri, J.W Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher-dimensional entanglement: Qutrits of photon orbital angular momentum,” Phys. Rev. Lett.91, 227902 (2003).
[CrossRef] [PubMed]

2002 (4)

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, “Bell inequalities for arbitrarily high-dimensional systems,” Phys. Rev. Lett.88, 040404 (2002).
[CrossRef] [PubMed]

R.T. Thew, K. Nemoto, A.G. White, and W.J. Munro, “Qudit quantum-state tomography,” Phys. Rev. A66, 012303 (2002).
[CrossRef]

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptograpy,” Rev. Mod. Phys.74, 145–195 (2002).
[CrossRef]

Franke-Arnold, S. S. Barnett, M. Padgett, and L. Allen, “Two-photon entanglement of orbital angular momentum states,” Phys. Rev. A65(3), 033823 (2002).
[CrossRef]

2001 (2)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature412, 313–316 (2001).
[CrossRef] [PubMed]

D. James, P. Kwiat, W. Munro, and A. White, “Measurement of qubits,” Phys. Rev. A64, 052312 (2001).
[CrossRef]

2000 (2)

H. Arnaut and G. Barbosa, “Orbital and intrinsic angular momentum of single photons and entangled pairs of photons generated by parametric down-conversion,” Phys. Rev. Lett.85, 286–289 (2000).
[CrossRef] [PubMed]

S. Bose and V. Vedral, “Mixedness and teleportation,” Phys. Rev. A61, 040101(R) (2000).
[CrossRef]

1995 (1)

T. Pittman, Y. Shih, D. Strekalov, and A. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A52, R3429–R3432 (1995).
[CrossRef] [PubMed]

1994 (1)

R. Grobe, K. Rzazewski, and J. Eberly, “Measure of electron-electron correlation in atomic physics,” J. Phys. B-At. Mol. Opt.27, L503–L508 (1994).
[CrossRef]

1992 (1)

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45, 8185–8189 (1992).
[CrossRef] [PubMed]

1991 (1)

A. Ekert, “Quantum cryptography based on Bells theorem,” Phys. Rev. Lett.67, 661–663 (1991).
[CrossRef] [PubMed]

1987 (3)

J. Durnin, “Exact solutions for nondiffracting beams. i. the scalar theory,” J. Opt. Soc. Am. A4, 651–654 (1987).
[CrossRef]

J. Durnin, J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58, 1499–1501 (1987).
[CrossRef] [PubMed]

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun.64, 491–495 (1987).
[CrossRef]

1969 (1)

J. Clauser, M. Horne, A. Shimony, and R. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett.23, 880–884 (1969).
[CrossRef]

Agnew, M.

M. Agnew, J. Leach, M. McLaren, F. Roux, and R. Boyd, “Tomography of the quantum state of photons entangled in high dimensions,” Phys. Rev. A84, 062101 (2011).
[CrossRef]

Allen, L.

Franke-Arnold, S. S. Barnett, M. Padgett, and L. Allen, “Two-photon entanglement of orbital angular momentum states,” Phys. Rev. A65(3), 033823 (2002).
[CrossRef]

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45, 8185–8189 (1992).
[CrossRef] [PubMed]

Andersson, E.

A. Dada, J. Leach, G. Buller, M. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of the generalized Bell inequalities,” Nat. Phys.7, 677–680 (2011).
[CrossRef]

Arnaut, H.

H. Arnaut and G. Barbosa, “Orbital and intrinsic angular momentum of single photons and entangled pairs of photons generated by parametric down-conversion,” Phys. Rev. Lett.85, 286–289 (2000).
[CrossRef] [PubMed]

Arrizon, V.

Barbosa, G.

H. Arnaut and G. Barbosa, “Orbital and intrinsic angular momentum of single photons and entangled pairs of photons generated by parametric down-conversion,” Phys. Rev. Lett.85, 286–289 (2000).
[CrossRef] [PubMed]

Barnett, S.

B. Jack, J. Leach, H. Ritsch, S. Barnett, and M. Padgett, “Precise quantum tomography of photon pairs with entangled orbital angular momentum,” New J. of Phys.811, 103024 (2009).
[CrossRef]

J. Leach, B. Jack, M. Ritsch-Marte, R. Boyd, A. Jha, S. Barnett, S. Franke-Arnold, and M. Padgett, “Violation of a Bell inequality in two-dimensional orbital angular momentum state-spaces,” Opt. Express17, 8287–8293 (2009).
[CrossRef] [PubMed]

Barnett, S. S.

Franke-Arnold, S. S. Barnett, M. Padgett, and L. Allen, “Two-photon entanglement of orbital angular momentum states,” Phys. Rev. A65(3), 033823 (2002).
[CrossRef]

Beijersbergen, M.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45, 8185–8189 (1992).
[CrossRef] [PubMed]

Bose, S.

S. Bose and V. Vedral, “Mixedness and teleportation,” Phys. Rev. A61, 040101(R) (2000).
[CrossRef]

Boyd, R.

Buller, G.

A. Dada, J. Leach, G. Buller, M. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of the generalized Bell inequalities,” Nat. Phys.7, 677–680 (2011).
[CrossRef]

Chuang, I.

M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2000).

Clauser, J.

J. Clauser, M. Horne, A. Shimony, and R. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett.23, 880–884 (1969).
[CrossRef]

Collins, D.

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, “Bell inequalities for arbitrarily high-dimensional systems,” Phys. Rev. Lett.88, 040404 (2002).
[CrossRef] [PubMed]

Dada, A.

A. Dada, J. Leach, G. Buller, M. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of the generalized Bell inequalities,” Nat. Phys.7, 677–680 (2011).
[CrossRef]

Durnin, J.

J. Durnin, J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58, 1499–1501 (1987).
[CrossRef] [PubMed]

J. Durnin, “Exact solutions for nondiffracting beams. i. the scalar theory,” J. Opt. Soc. Am. A4, 651–654 (1987).
[CrossRef]

Eberly, J.

R. Grobe, K. Rzazewski, and J. Eberly, “Measure of electron-electron correlation in atomic physics,” J. Phys. B-At. Mol. Opt.27, L503–L508 (1994).
[CrossRef]

J. Durnin, J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58, 1499–1501 (1987).
[CrossRef] [PubMed]

Ekert, A.

A. Ekert, “Quantum cryptography based on Bells theorem,” Phys. Rev. Lett.67, 661–663 (1991).
[CrossRef] [PubMed]

Eliel, E.

V. Salakhutdinov, E. Eliel, and W. Löffler, “Full-field quantum correlations of spatially entangled photons,” Phys. Rev. Lett.108, 173604 (2012).
[CrossRef] [PubMed]

Franke-Arnold,

Franke-Arnold, S. S. Barnett, M. Padgett, and L. Allen, “Two-photon entanglement of orbital angular momentum states,” Phys. Rev. A65(3), 033823 (2002).
[CrossRef]

Franke-Arnold, S.

Gisin, N.

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, “Bell inequalities for arbitrarily high-dimensional systems,” Phys. Rev. Lett.88, 040404 (2002).
[CrossRef] [PubMed]

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptograpy,” Rev. Mod. Phys.74, 145–195 (2002).
[CrossRef]

Gori, F.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun.64, 491–495 (1987).
[CrossRef]

Grobe, R.

R. Grobe, K. Rzazewski, and J. Eberly, “Measure of electron-electron correlation in atomic physics,” J. Phys. B-At. Mol. Opt.27, L503–L508 (1994).
[CrossRef]

Guattari, G.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun.64, 491–495 (1987).
[CrossRef]

Holt, R.

J. Clauser, M. Horne, A. Shimony, and R. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett.23, 880–884 (1969).
[CrossRef]

Horne, M.

J. Clauser, M. Horne, A. Shimony, and R. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett.23, 880–884 (1969).
[CrossRef]

Jack, B.

B. Jack, J. Leach, H. Ritsch, S. Barnett, and M. Padgett, “Precise quantum tomography of photon pairs with entangled orbital angular momentum,” New J. of Phys.811, 103024 (2009).
[CrossRef]

J. Leach, B. Jack, M. Ritsch-Marte, R. Boyd, A. Jha, S. Barnett, S. Franke-Arnold, and M. Padgett, “Violation of a Bell inequality in two-dimensional orbital angular momentum state-spaces,” Opt. Express17, 8287–8293 (2009).
[CrossRef] [PubMed]

James, D.

D. James, P. Kwiat, W. Munro, and A. White, “Measurement of qubits,” Phys. Rev. A64, 052312 (2001).
[CrossRef]

Jennewein, T.

A. Vaziri, J.W Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher-dimensional entanglement: Qutrits of photon orbital angular momentum,” Phys. Rev. Lett.91, 227902 (2003).
[CrossRef] [PubMed]

Jha, A.

Kwiat, P.

D. James, P. Kwiat, W. Munro, and A. White, “Measurement of qubits,” Phys. Rev. A64, 052312 (2001).
[CrossRef]

Leach, J.

A. Dada, J. Leach, G. Buller, M. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of the generalized Bell inequalities,” Nat. Phys.7, 677–680 (2011).
[CrossRef]

M. Agnew, J. Leach, M. McLaren, F. Roux, and R. Boyd, “Tomography of the quantum state of photons entangled in high dimensions,” Phys. Rev. A84, 062101 (2011).
[CrossRef]

B. Jack, J. Leach, H. Ritsch, S. Barnett, and M. Padgett, “Precise quantum tomography of photon pairs with entangled orbital angular momentum,” New J. of Phys.811, 103024 (2009).
[CrossRef]

J. Leach, B. Jack, M. Ritsch-Marte, R. Boyd, A. Jha, S. Barnett, S. Franke-Arnold, and M. Padgett, “Violation of a Bell inequality in two-dimensional orbital angular momentum state-spaces,” Opt. Express17, 8287–8293 (2009).
[CrossRef] [PubMed]

Linden, N.

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, “Bell inequalities for arbitrarily high-dimensional systems,” Phys. Rev. Lett.88, 040404 (2002).
[CrossRef] [PubMed]

Löffler, W.

V. Salakhutdinov, E. Eliel, and W. Löffler, “Full-field quantum correlations of spatially entangled photons,” Phys. Rev. Lett.108, 173604 (2012).
[CrossRef] [PubMed]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature412, 313–316 (2001).
[CrossRef] [PubMed]

Massar, S.

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, “Bell inequalities for arbitrarily high-dimensional systems,” Phys. Rev. Lett.88, 040404 (2002).
[CrossRef] [PubMed]

McLaren, M.

M. Agnew, J. Leach, M. McLaren, F. Roux, and R. Boyd, “Tomography of the quantum state of photons entangled in high dimensions,” Phys. Rev. A84, 062101 (2011).
[CrossRef]

Miceli, J.

J. Durnin, J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58, 1499–1501 (1987).
[CrossRef] [PubMed]

Munro, W.

D. James, P. Kwiat, W. Munro, and A. White, “Measurement of qubits,” Phys. Rev. A64, 052312 (2001).
[CrossRef]

Munro, W.J.

R.T. Thew, K. Nemoto, A.G. White, and W.J. Munro, “Qudit quantum-state tomography,” Phys. Rev. A66, 012303 (2002).
[CrossRef]

Nemoto, K.

R.T. Thew, K. Nemoto, A.G. White, and W.J. Munro, “Qudit quantum-state tomography,” Phys. Rev. A66, 012303 (2002).
[CrossRef]

Nielsen, M.

M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2000).

Padgett, M.

A. Dada, J. Leach, G. Buller, M. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of the generalized Bell inequalities,” Nat. Phys.7, 677–680 (2011).
[CrossRef]

B. Jack, J. Leach, H. Ritsch, S. Barnett, and M. Padgett, “Precise quantum tomography of photon pairs with entangled orbital angular momentum,” New J. of Phys.811, 103024 (2009).
[CrossRef]

J. Leach, B. Jack, M. Ritsch-Marte, R. Boyd, A. Jha, S. Barnett, S. Franke-Arnold, and M. Padgett, “Violation of a Bell inequality in two-dimensional orbital angular momentum state-spaces,” Opt. Express17, 8287–8293 (2009).
[CrossRef] [PubMed]

Franke-Arnold, S. S. Barnett, M. Padgett, and L. Allen, “Two-photon entanglement of orbital angular momentum states,” Phys. Rev. A65(3), 033823 (2002).
[CrossRef]

Padovani, C.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun.64, 491–495 (1987).
[CrossRef]

Pan, J.W

A. Vaziri, J.W Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher-dimensional entanglement: Qutrits of photon orbital angular momentum,” Phys. Rev. Lett.91, 227902 (2003).
[CrossRef] [PubMed]

Pittman, T.

T. Pittman, Y. Shih, D. Strekalov, and A. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A52, R3429–R3432 (1995).
[CrossRef] [PubMed]

Popescu, S.

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, “Bell inequalities for arbitrarily high-dimensional systems,” Phys. Rev. Lett.88, 040404 (2002).
[CrossRef] [PubMed]

Ribordy, G.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptograpy,” Rev. Mod. Phys.74, 145–195 (2002).
[CrossRef]

Ritsch, H.

B. Jack, J. Leach, H. Ritsch, S. Barnett, and M. Padgett, “Precise quantum tomography of photon pairs with entangled orbital angular momentum,” New J. of Phys.811, 103024 (2009).
[CrossRef]

Ritsch-Marte, M.

Roux, F.

M. Agnew, J. Leach, M. McLaren, F. Roux, and R. Boyd, “Tomography of the quantum state of photons entangled in high dimensions,” Phys. Rev. A84, 062101 (2011).
[CrossRef]

Rzazewski, K.

R. Grobe, K. Rzazewski, and J. Eberly, “Measure of electron-electron correlation in atomic physics,” J. Phys. B-At. Mol. Opt.27, L503–L508 (1994).
[CrossRef]

Salakhutdinov, V.

V. Salakhutdinov, E. Eliel, and W. Löffler, “Full-field quantum correlations of spatially entangled photons,” Phys. Rev. Lett.108, 173604 (2012).
[CrossRef] [PubMed]

Sergienko, A.

T. Pittman, Y. Shih, D. Strekalov, and A. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A52, R3429–R3432 (1995).
[CrossRef] [PubMed]

Shih, Y.

T. Pittman, Y. Shih, D. Strekalov, and A. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A52, R3429–R3432 (1995).
[CrossRef] [PubMed]

Shimony, A.

J. Clauser, M. Horne, A. Shimony, and R. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett.23, 880–884 (1969).
[CrossRef]

Spreeuw, R.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45, 8185–8189 (1992).
[CrossRef] [PubMed]

Strekalov, D.

T. Pittman, Y. Shih, D. Strekalov, and A. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A52, R3429–R3432 (1995).
[CrossRef] [PubMed]

Thew, R.T.

R.T. Thew, K. Nemoto, A.G. White, and W.J. Munro, “Qudit quantum-state tomography,” Phys. Rev. A66, 012303 (2002).
[CrossRef]

Tittel, W.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptograpy,” Rev. Mod. Phys.74, 145–195 (2002).
[CrossRef]

Vaziri, A.

A. Vaziri, J.W Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher-dimensional entanglement: Qutrits of photon orbital angular momentum,” Phys. Rev. Lett.91, 227902 (2003).
[CrossRef] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature412, 313–316 (2001).
[CrossRef] [PubMed]

Vedral, V.

S. Bose and V. Vedral, “Mixedness and teleportation,” Phys. Rev. A61, 040101(R) (2000).
[CrossRef]

Weihs, G.

A. Vaziri, J.W Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher-dimensional entanglement: Qutrits of photon orbital angular momentum,” Phys. Rev. Lett.91, 227902 (2003).
[CrossRef] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature412, 313–316 (2001).
[CrossRef] [PubMed]

White, A.

D. James, P. Kwiat, W. Munro, and A. White, “Measurement of qubits,” Phys. Rev. A64, 052312 (2001).
[CrossRef]

White, A.G.

R.T. Thew, K. Nemoto, A.G. White, and W.J. Munro, “Qudit quantum-state tomography,” Phys. Rev. A66, 012303 (2002).
[CrossRef]

Woerdman, J.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45, 8185–8189 (1992).
[CrossRef] [PubMed]

Zbinden, H.

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Figures (4)

Fig. 1
Fig. 1

(a) Experimental setup used to detect the OAM eigenstate after SPDC. The plane of the crystal was relayed imaged onto two separate SLMs using lenses, f1 = 400 mm and f2 = 750 mm, where the BG modes were selected. Lenses f3 = 300 mm and f4 = 1.5 mm were used to relay image the SLM planes through 10 nm bandwidth interference filters (IF) to the inputs of the single-mode fibres (SMF). Examples of a phase-only binary Bessel hologram with a helical phase of = 2 for different values of kr are shown in (b) kr = 0 rad/mm, (c) kr = 21 rad/mm and (d) kr = 35 rad/mm. The inset (at BBO crystal) shows a back-projected CCD image of a binary Bessel mode with helical phase = 2 and radial wavevector kr = 21 rad/mm measured at the plane of the crystal.

Fig. 2
Fig. 2

(a) OAM bandwidth (blue) and Schmidt number (red) are shown as a function of kr. As the radial wavevector increases from kr = 0 rad/mm (azimuthal modes), the OAM bandwidth increases. (b) OAM spectrum for azimuthal modes (red) and BG modes for kr = 21 rad/mm (purple) and kr = 35 rad/mm (green), in terms of the modal weightings. The maximum coincidence count rate is lower for both BG modes; however a broader spectrum is observed with increasing kr.

Fig. 3
Fig. 3

Sinusoidal behaviour of the normalised coincidence counts as a function of the angular position of the holograms, for = ±1 subspace at positions αA = 0° (blue), 45° (pink), 90° (green) and 135° (yellow). The insets show the holograms used for αA = 0° and αA = 45°, where the phase varies from 0 (black) to π (white).

Fig. 4
Fig. 4

Results from a full quantum state tomography of a BG mode with kr = 21 rad/mm. (a) & (b) Graphical representation of the real part of the density matrix for dimension d = 2 and d = 5, respectively. (c) Linear entropy and (d) fidelity as a function of dimension. The red triangles represent the measured data for the azimuthal modes, the green squares represent the measured data for the BG modes and the blue circles represent the threshold states in Eq. (13).

Equations (13)

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E BG ( r , ϕ , z ) = 2 π J ( z R k r r z R i z ) exp ( i ϕ i k z z ) × exp ( i k r 2 z w 0 2 2 k r 2 4 ( z R i z ) )
| Ψ = a ( k r 1 , k r 2 ) | , k r 1 s | , k r 2 i d k r 1 d k r 2 ,
| Ψ ( k r 1 , k r 2 ) = c | s | i ,
ρ = m , n = 0 d 2 1 b m , n τ m τ n ,
| α = 1 2 [ | , k r + exp ( i α ) | 2 , k r ] .
T ( r ) = sign { J ( k r r ) } exp ( i ϕ ) ,
χ 2 = i = 1 N 2 [ p i ( M ) p i ( P ) ] 2 p i ( P ) ,
B = [ 2 C ( k r ) C ( k r ) ] 1 / 2
K = [ C ( k r ) ] 2 C 2 ( k r ) .
S = E ( α A , α B ) E ( α A , α B ' ) + E ( α A ' , α B ) E ( α A ' , α B ' ) ,
E ( α A , α B ) = C ( α A , α B ) + C ( α A + π 2 , α B + π 2 ) C ( α A + π 2 , α B ) C ( α A , α B + π 2 ) C ( α A , α B ) + C ( α A + π 2 , α B + π 2 ) + C ( α A + π 2 , α B ) + C ( α A , α B + π 2 ) ,
F = [ Tr { ( ρ T ρ d ρ R ) 1 / 2 } ] 2 ,
ρ B = p d min | ψ ψ | + ( 1 p d min ) I d 2 ,

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