J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010).

[CrossRef]
[PubMed]

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).

[CrossRef]

Z. Wang, Z. Zhang, and Q. Lin, “A novel method to determine the helical phase structure of Laguerre–Gaussian beams,” J. Opt. A, Pure Appl. Opt. 11, 085702 (2009).

[CrossRef]

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional hilbert spaces,” Nat. Phys. 5, 134–140 (2009).

[CrossRef]

J. T. Barreiro, T. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).

[CrossRef]

S. Franke-Arnold, L. Allen, and M. J. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2, 299–313 (2008).

[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).

[CrossRef]

G. Molina-Terriza, A. Vaziri, R. Ursin, and A. Zeilinger, “Experimental quantum coin tossing,” Phys. Rev. Lett. 94, 040501 (2005).

[CrossRef]
[PubMed]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).

[CrossRef]
[PubMed]

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-Level systems,” Phys. Rev. Lett. 88, 127902 (2002).

[CrossRef]
[PubMed]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (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]

D. Kaszlikowski, P. Gnacinacuteski, M. Zdotukowski, W. Miklaszewski, and A. Zeilinger, “Violations of local realism by two entangled N-Dimensional systems are stronger than for two qubits,” Phys. Rev. Lett. 85, 4418–4421 (2000).

[CrossRef]
[PubMed]

P. G. Kwiat, A. G. White, J. R. Mitchell, O. Nairz, G. Weihs, H. Weinfurter, and A. Zeilinger, “High-efficiency quantum interrogation measurements via the quantum Zeno effect,” Phys. Rev. Lett. 83, 4725–4728 (1999).

[CrossRef]

J. Jang, “Optical interaction-free measurement of semitransparent objects,” Phys. Rev. A 59, 2322–2329 (1999).

[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]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).

[CrossRef]

A. C. Elitzur and L. Vaidman, “Quantum mechanical interaction-free measurements,” Found. Phys. 7, 987–997 (1993).

[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).

[CrossRef]
[PubMed]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and 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]

V. Bazhekov, M. Vasnetsov, and M. S. Soskin, “Laser-beams with screw dislocation in their wavefronts,” JETP Lett. 52, 429–431 (1990).

A. Peres, “Zeno paradox in quantum theory,” Am. J. Phys. 48, 931–932 (1980).

[CrossRef]

B. Misra and E. C. G. Sudarshan, “The Zeno’s paradox in quantum theory,” J. Math. Phys. 18, 756–763 (1977).

[CrossRef]

S. Franke-Arnold, L. Allen, and M. J. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2, 299–313 (2008).

[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]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and 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]

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional hilbert spaces,” Nat. Phys. 5, 134–140 (2009).

[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]

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional hilbert spaces,” Nat. Phys. 5, 134–140 (2009).

[CrossRef]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).

[CrossRef]
[PubMed]

J. T. Barreiro, T. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).

[CrossRef]

V. Bazhekov, M. Vasnetsov, and M. S. Soskin, “Laser-beams with screw dislocation in their wavefronts,” JETP Lett. 52, 429–431 (1990).

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).

[CrossRef]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).

[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and 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]

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).

[CrossRef]

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-Level systems,” Phys. Rev. Lett. 88, 127902 (2002).

[CrossRef]
[PubMed]

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-Level systems,” Phys. Rev. Lett. 88, 127902 (2002).

[CrossRef]
[PubMed]

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010).

[CrossRef]
[PubMed]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).

[CrossRef]

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).

[CrossRef]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).

[CrossRef]
[PubMed]

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]

A. C. Elitzur and L. Vaidman, “Quantum mechanical interaction-free measurements,” Found. Phys. 7, 987–997 (1993).

[CrossRef]

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010).

[CrossRef]
[PubMed]

S. Franke-Arnold, L. Allen, and M. J. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2, 299–313 (2008).

[CrossRef]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).

[CrossRef]
[PubMed]

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional hilbert spaces,” Nat. Phys. 5, 134–140 (2009).

[CrossRef]

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-Level systems,” Phys. Rev. Lett. 88, 127902 (2002).

[CrossRef]
[PubMed]

D. Kaszlikowski, P. Gnacinacuteski, M. Zdotukowski, W. Miklaszewski, and A. Zeilinger, “Violations of local realism by two entangled N-Dimensional systems are stronger than for two qubits,” Phys. Rev. Lett. 85, 4418–4421 (2000).

[CrossRef]
[PubMed]

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010).

[CrossRef]
[PubMed]

J. Jang, “Optical interaction-free measurement of semitransparent objects,” Phys. Rev. A 59, 2322–2329 (1999).

[CrossRef]

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional hilbert spaces,” Nat. Phys. 5, 134–140 (2009).

[CrossRef]

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-Level systems,” Phys. Rev. Lett. 88, 127902 (2002).

[CrossRef]
[PubMed]

D. Kaszlikowski, P. Gnacinacuteski, M. Zdotukowski, W. Miklaszewski, and A. Zeilinger, “Violations of local realism by two entangled N-Dimensional systems are stronger than for two qubits,” Phys. Rev. Lett. 85, 4418–4421 (2000).

[CrossRef]
[PubMed]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).

[CrossRef]

J. T. Barreiro, T. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).

[CrossRef]

P. G. Kwiat, A. G. White, J. R. Mitchell, O. Nairz, G. Weihs, H. Weinfurter, and A. Zeilinger, “High-efficiency quantum interrogation measurements via the quantum Zeno effect,” Phys. Rev. Lett. 83, 4725–4728 (1999).

[CrossRef]

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional hilbert spaces,” Nat. Phys. 5, 134–140 (2009).

[CrossRef]

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).

[CrossRef]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).

[CrossRef]
[PubMed]

Z. Wang, Z. Zhang, and Q. Lin, “A novel method to determine the helical phase structure of Laguerre–Gaussian beams,” J. Opt. A, Pure Appl. Opt. 11, 085702 (2009).

[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]

D. Kaszlikowski, P. Gnacinacuteski, M. Zdotukowski, W. Miklaszewski, and A. Zeilinger, “Violations of local realism by two entangled N-Dimensional systems are stronger than for two qubits,” Phys. Rev. Lett. 85, 4418–4421 (2000).

[CrossRef]
[PubMed]

B. Misra and E. C. G. Sudarshan, “The Zeno’s paradox in quantum theory,” J. Math. Phys. 18, 756–763 (1977).

[CrossRef]

P. G. Kwiat, A. G. White, J. R. Mitchell, O. Nairz, G. Weihs, H. Weinfurter, and A. Zeilinger, “High-efficiency quantum interrogation measurements via the quantum Zeno effect,” Phys. Rev. Lett. 83, 4725–4728 (1999).

[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).

[CrossRef]

G. Molina-Terriza, A. Vaziri, R. Ursin, and A. Zeilinger, “Experimental quantum coin tossing,” Phys. Rev. Lett. 94, 040501 (2005).

[CrossRef]
[PubMed]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (2001).

[CrossRef]

P. G. Kwiat, A. G. White, J. R. Mitchell, O. Nairz, G. Weihs, H. Weinfurter, and A. Zeilinger, “High-efficiency quantum interrogation measurements via the quantum Zeno effect,” Phys. Rev. Lett. 83, 4725–4728 (1999).

[CrossRef]

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional hilbert spaces,” Nat. Phys. 5, 134–140 (2009).

[CrossRef]

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).

[CrossRef]

S. Franke-Arnold, L. Allen, and M. J. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2, 299–313 (2008).

[CrossRef]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).

[CrossRef]
[PubMed]

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]

A. Peres, “Zeno paradox in quantum theory,” Am. J. Phys. 48, 931–932 (1980).

[CrossRef]

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional hilbert spaces,” Nat. Phys. 5, 134–140 (2009).

[CrossRef]

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional hilbert spaces,” Nat. Phys. 5, 134–140 (2009).

[CrossRef]

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional hilbert spaces,” Nat. Phys. 5, 134–140 (2009).

[CrossRef]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).

[CrossRef]
[PubMed]

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010).

[CrossRef]
[PubMed]

V. Bazhekov, M. Vasnetsov, and M. S. Soskin, “Laser-beams with screw dislocation in their wavefronts,” JETP Lett. 52, 429–431 (1990).

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and 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]

B. Misra and E. C. G. Sudarshan, “The Zeno’s paradox in quantum theory,” J. Math. Phys. 18, 756–763 (1977).

[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).

[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (2001).

[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).

[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (2001).

[CrossRef]

G. Molina-Terriza, A. Vaziri, R. Ursin, and A. Zeilinger, “Experimental quantum coin tossing,” Phys. Rev. Lett. 94, 040501 (2005).

[CrossRef]
[PubMed]

A. C. Elitzur and L. Vaidman, “Quantum mechanical interaction-free measurements,” Found. Phys. 7, 987–997 (1993).

[CrossRef]

V. Bazhekov, M. Vasnetsov, and M. S. Soskin, “Laser-beams with screw dislocation in their wavefronts,” JETP Lett. 52, 429–431 (1990).

G. Molina-Terriza, A. Vaziri, R. Ursin, and A. Zeilinger, “Experimental quantum coin tossing,” Phys. Rev. Lett. 94, 040501 (2005).

[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]

Z. Wang, Z. Zhang, and Q. Lin, “A novel method to determine the helical phase structure of Laguerre–Gaussian beams,” J. Opt. A, Pure Appl. Opt. 11, 085702 (2009).

[CrossRef]

J. T. Barreiro, T. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).

[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]

P. G. Kwiat, A. G. White, J. R. Mitchell, O. Nairz, G. Weihs, H. Weinfurter, and A. Zeilinger, “High-efficiency quantum interrogation measurements via the quantum Zeno effect,” Phys. Rev. Lett. 83, 4725–4728 (1999).

[CrossRef]

P. G. Kwiat, A. G. White, J. R. Mitchell, O. Nairz, G. Weihs, H. Weinfurter, and A. Zeilinger, “High-efficiency quantum interrogation measurements via the quantum Zeno effect,” Phys. Rev. Lett. 83, 4725–4728 (1999).

[CrossRef]

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional hilbert spaces,” Nat. Phys. 5, 134–140 (2009).

[CrossRef]

P. G. Kwiat, A. G. White, J. R. Mitchell, O. Nairz, G. Weihs, H. Weinfurter, and A. Zeilinger, “High-efficiency quantum interrogation measurements via the quantum Zeno effect,” Phys. Rev. Lett. 83, 4725–4728 (1999).

[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).

[CrossRef]
[PubMed]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).

[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and 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]

D. Kaszlikowski, P. Gnacinacuteski, M. Zdotukowski, W. Miklaszewski, and A. Zeilinger, “Violations of local realism by two entangled N-Dimensional systems are stronger than for two qubits,” Phys. Rev. Lett. 85, 4418–4421 (2000).

[CrossRef]
[PubMed]

G. Molina-Terriza, A. Vaziri, R. Ursin, and A. Zeilinger, “Experimental quantum coin tossing,” Phys. Rev. Lett. 94, 040501 (2005).

[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]

D. Kaszlikowski, P. Gnacinacuteski, M. Zdotukowski, W. Miklaszewski, and A. Zeilinger, “Violations of local realism by two entangled N-Dimensional systems are stronger than for two qubits,” Phys. Rev. Lett. 85, 4418–4421 (2000).

[CrossRef]
[PubMed]

P. G. Kwiat, A. G. White, J. R. Mitchell, O. Nairz, G. Weihs, H. Weinfurter, and A. Zeilinger, “High-efficiency quantum interrogation measurements via the quantum Zeno effect,” Phys. Rev. Lett. 83, 4725–4728 (1999).

[CrossRef]

Z. Wang, Z. Zhang, and Q. Lin, “A novel method to determine the helical phase structure of Laguerre–Gaussian beams,” J. Opt. A, Pure Appl. Opt. 11, 085702 (2009).

[CrossRef]

A. Peres, “Zeno paradox in quantum theory,” Am. J. Phys. 48, 931–932 (1980).

[CrossRef]

A. C. Elitzur and L. Vaidman, “Quantum mechanical interaction-free measurements,” Found. Phys. 7, 987–997 (1993).

[CrossRef]

B. Misra and E. C. G. Sudarshan, “The Zeno’s paradox in quantum theory,” J. Math. Phys. 18, 756–763 (1977).

[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]

Z. Wang, Z. Zhang, and Q. Lin, “A novel method to determine the helical phase structure of Laguerre–Gaussian beams,” J. Opt. A, Pure Appl. Opt. 11, 085702 (2009).

[CrossRef]

V. Bazhekov, M. Vasnetsov, and M. S. Soskin, “Laser-beams with screw dislocation in their wavefronts,” JETP Lett. 52, 429–431 (1990).

S. Franke-Arnold, L. Allen, and M. J. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2, 299–313 (2008).

[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).

[CrossRef]

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S0 and S1 are optical switches that can be switched from been transmittive to reflective. S0 needs to transmit the initial incident light, and be switched to be reflective by the end of the first outer-loop cycle. A high repetition rate is not required and it can be implemeted either mechanically or opto-electrically. Alternatively it could also be a static high-reflectance mirror, if the one-time transmission loss at the very beginning can be tolerated. S1 needs to be switched every QZI loop cycle (ΔT) and need to be polarization insensitive. The fastest switches are Pockels cells, which can operate at 10–100 GHz with 99% transmission. One scheme, similar to the one implemented in Ref. [20], is to an interferometer with Pockels cells in one of the arms. The Pockels cells introduce π phase shift in the arm when activated, and thus switch the beam between two output ports of the interferometer. Using two Pockels cells rotated relative to each other will cancel the birefringent effect.

Technically, each |α|2 is slightly different, but the difference is well within 1%. The |α|2 that matters most is the one corresponding to the QZI loop (including S1), which, without any optimization, consists of 4 beam splitters, 5 mirrors, 1 waveplate and up to three Pockels cells. Assuming all optics are anti-reflection coated so that loss is 1% at each Pockels cell and 0.1% at each other component, we have |α|2 = 0.96.