Abstract

Quantum key distribution (QKD) promises information-theoretically secure communication and is already on the verge of commercialization. The next step will be to implement high-dimensional protocols in order to improve noise resistance and increase the data rate. Hitherto, no experimental verification of high-dimensional QKD in the single-photon regime has been conducted outside of the laboratory. Here, we report the realization of such a single-photon QKD system in a turbulent free-space link of 0.3 km over the city of Ottawa, taking advantage of both the spin and orbital angular momentum photonic degrees of freedom. This combination of optical angular momenta allows us to create a 4-dimensional quantum state; wherein, using a high-dimensional BB84 protocol, a quantum bit error rate of 11% was attained with a corresponding secret key rate of 0.65 bits per sifted photon. In comparison, an error rate of 5% with a secret key rate of 0.43 bits per sifted photon is achieved for the case of 2-dimensional structured photons. We thus demonstrate that, even through moderate turbulence without active wavefront correction, high-dimensional photon states are advantageous for securely transmitting more information. This opens the way for intracity high-dimensional quantum communications under realistic conditions.

© 2017 Optical Society of America

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    [Crossref]
  20. F. Tamburini, E. Mari, A. Sponselli, B. Thidé, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: first experimental test,” New J. Phys. 14, 033001 (2012).
    [Crossref]
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  22. M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16, 113028 (2014).
    [Crossref]
  23. M. Krenn, J. Handsteiner, M. Fink, R. Fickler, R. Ursin, M. Malik, and A. Zeilinger, “Twisted light transmission over 143 km,” Proc. Natl. Acad. Sci. USA 113, 13648–13653 (2016).
    [Crossref]
  24. G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2014).
    [Crossref]
  25. M. Krenn, J. Handsteiner, M. Fink, R. Fickler, and A. Zeilinger, “Twisted photon entanglement through turbulent air across Vienna,” Proc. Natl. Acad. Sci. USA 112, 14197–14201 (2015).
    [Crossref]
  26. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1, 1–57 (2009).
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    [Crossref]
  28. H. Larocque, J. Gagnon-Bischoff, F. Bouchard, R. Fickler, J. Upham, R. W. Boyd, and E. Karimi, “Arbitrary optical wavefront shaping via spin-to-orbit coupling,” J. Opt. 18, 124002 (2016).
    [Crossref]
  29. E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103, 013601 (2009).
    [Crossref]
  30. N. Ageorges and C. Dainty, Laser Guide Star Adaptive Optics for Astronomy (Springer, 2013), Vol. 551.
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    [Crossref]

2016 (3)

S. K. Goyal, A. H. Ibrahim, F. S. Roux, T. Konrad, and A. Forbes, “The effect of turbulence on entanglement-based free-space quantum key distribution with photonic orbital angular momentum,” J. Opt. 18, 064002 (2016).
[Crossref]

M. Krenn, J. Handsteiner, M. Fink, R. Fickler, R. Ursin, M. Malik, and A. Zeilinger, “Twisted light transmission over 143 km,” Proc. Natl. Acad. Sci. USA 113, 13648–13653 (2016).
[Crossref]

H. Larocque, J. Gagnon-Bischoff, F. Bouchard, R. Fickler, J. Upham, R. W. Boyd, and E. Karimi, “Arbitrary optical wavefront shaping via spin-to-orbit coupling,” J. Opt. 18, 124002 (2016).
[Crossref]

2015 (5)

M. Krenn, J. Handsteiner, M. Fink, R. Fickler, and A. Zeilinger, “Twisted photon entanglement through turbulent air across Vienna,” Proc. Natl. Acad. Sci. USA 112, 14197–14201 (2015).
[Crossref]

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photon. 7, 66–106 (2015).
[Crossref]

F. Cardano, F. Massa, H. Qassim, E. Karimi, S. Slussarenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, R. W. Boyd, and L. Marrucci, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
[Crossref]

O. J. Faras, V. D’Ambrosio, C. Taballione, F. Bisesto, S. Slussarenko, L. Aolita, L. Marrucci, S. P. Walborn, and F. Sciarrino, “Resilience of hybrid optical angular momentum qubits to turbulence,” Sci. Rep. 5, 8424 (2015).
[Crossref]

M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’sullivan, B. Rodenburg, M. Malik, M. P. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
[Crossref]

2014 (3)

H.-K. Lo, M. Curty, and K. Tamaki, “Secure quantum key distribution,” Nat. Photonics 8, 595–604 (2014).
[Crossref]

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16, 113028 (2014).
[Crossref]

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2014).
[Crossref]

2013 (1)

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

2012 (3)

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

F. Tamburini, E. Mari, A. Sponselli, B. Thidé, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: first experimental test,” New J. Phys. 14, 033001 (2012).
[Crossref]

M. Malik, M. O’Sullivan, B. Rodenburg, M. Mirhosseini, J. Leach, M. P. Lavery, M. J. Padgett, and R. W. Boyd, “Influence of atmospheric turbulence on optical communications using orbital angular momentum for encoding,” Opt. Express 20, 13195–13200 (2012).
[Crossref]

2010 (1)

E. Nagali, L. Sansoni, L. Marrucci, E. Santamato, and F. Sciarrino, “Experimental generation and characterization of single-photon hybrid ququarts based on polarization and orbital angular momentum encoding,” Phys. Rev. A 81, 052317 (2010).
[Crossref]

2009 (3)

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).
[Crossref]

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1, 1–57 (2009).
[Crossref]

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103, 013601 (2009).
[Crossref]

2007 (1)

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

2006 (3)

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8(5), 75 (2006).
[Crossref]

G. M. Nikolopoulos, K. S. Ranade, and G. Alber, “Error tolerance of two-basis quantum-key-distribution protocols using qudits and two-way classical communication,” Phys. Rev. A 73, 032325 (2006).
[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]

2005 (1)

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94, 153901 (2005).
[Crossref]

2002 (1)

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]

2001 (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref]

2000 (1)

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

1992 (1)

L. Allen, M. W. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

1966 (1)

1941 (1)

A. N. Kolmogorov, “The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers,” Dokl. Akad. Nauk SSSR 30, 301–3051941.

Ageorges, N.

N. Ageorges and C. Dainty, Laser Guide Star Adaptive Optics for Astronomy (Springer, 2013), Vol. 551.

Ahmed, N.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photon. 7, 66–106 (2015).
[Crossref]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Alber, G.

G. M. Nikolopoulos, K. S. Ranade, and G. Alber, “Error tolerance of two-basis quantum-key-distribution protocols using qudits and two-way classical communication,” Phys. Rev. A 73, 032325 (2006).
[Crossref]

Allen, L.

L. Allen, M. W. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

Aolita, L.

O. J. Faras, V. D’Ambrosio, C. Taballione, F. Bisesto, S. Slussarenko, L. Aolita, L. Marrucci, S. P. Walborn, and F. Sciarrino, “Resilience of hybrid optical angular momentum qubits to turbulence,” Sci. Rep. 5, 8424 (2015).
[Crossref]

Ashrafi, N.

Ashrafi, S.

Bao, C.

Bauer, T.

M. P. Lavery, B. Heim, C. Peuntinger, E. Karimi, O. S. Magaña-Loaiza, T. Bauer, C. Marquardt, R. W. Boyd, M. Padgett, and G. Leuchs, “Study of turbulence induced orbital angular momentum channel crosstalk in a 1.6 km free-space optical link,” in CLEO: Science and Innovations (Optical Society of America, 2015), paper STu1L–4.

Bechmann-Pasquinucci, H.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).
[Crossref]

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

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

Bennett, C. H.

C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in International Conference on Computer System and Signal Processing (IEEE, 1984), pp. 175–179.

Bianchini, A.

F. Tamburini, E. Mari, A. Sponselli, B. Thidé, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: first experimental test,” New J. Phys. 14, 033001 (2012).
[Crossref]

Bisesto, F.

O. J. Faras, V. D’Ambrosio, C. Taballione, F. Bisesto, S. Slussarenko, L. Aolita, L. Marrucci, S. P. Walborn, and F. Sciarrino, “Resilience of hybrid optical angular momentum qubits to turbulence,” Sci. Rep. 5, 8424 (2015).
[Crossref]

Bouchard, F.

H. Larocque, J. Gagnon-Bischoff, F. Bouchard, R. Fickler, J. Upham, R. W. Boyd, and E. Karimi, “Arbitrary optical wavefront shaping via spin-to-orbit coupling,” J. Opt. 18, 124002 (2016).
[Crossref]

Bourennane, M.

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]

Boyd, R. W.

H. Larocque, J. Gagnon-Bischoff, F. Bouchard, R. Fickler, J. Upham, R. W. Boyd, and E. Karimi, “Arbitrary optical wavefront shaping via spin-to-orbit coupling,” J. Opt. 18, 124002 (2016).
[Crossref]

F. Cardano, F. Massa, H. Qassim, E. Karimi, S. Slussarenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, R. W. Boyd, and L. Marrucci, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
[Crossref]

M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’sullivan, B. Rodenburg, M. Malik, M. P. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
[Crossref]

M. Malik, M. O’Sullivan, B. Rodenburg, M. Mirhosseini, J. Leach, M. P. Lavery, M. J. Padgett, and R. W. Boyd, “Influence of atmospheric turbulence on optical communications using orbital angular momentum for encoding,” Opt. Express 20, 13195–13200 (2012).
[Crossref]

M. P. Lavery, B. Heim, C. Peuntinger, E. Karimi, O. S. Magaña-Loaiza, T. Bauer, C. Marquardt, R. W. Boyd, M. Padgett, and G. Leuchs, “Study of turbulence induced orbital angular momentum channel crosstalk in a 1.6 km free-space optical link,” in CLEO: Science and Innovations (Optical Society of America, 2015), paper STu1L–4.

Brassard, G.

C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in International Conference on Computer System and Signal Processing (IEEE, 1984), pp. 175–179.

Cao, Y.

Cardano, F.

F. Cardano, F. Massa, H. Qassim, E. Karimi, S. Slussarenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, R. W. Boyd, and L. Marrucci, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
[Crossref]

Cerf, N. J.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (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]

Curty, M.

H.-K. Lo, M. Curty, and K. Tamaki, “Secure quantum key distribution,” Nat. Photonics 8, 595–604 (2014).
[Crossref]

D’Ambrosio, V.

O. J. Faras, V. D’Ambrosio, C. Taballione, F. Bisesto, S. Slussarenko, L. Aolita, L. Marrucci, S. P. Walborn, and F. Sciarrino, “Resilience of hybrid optical angular momentum qubits to turbulence,” Sci. Rep. 5, 8424 (2015).
[Crossref]

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2014).
[Crossref]

Dainty, C.

N. Ageorges and C. Dainty, Laser Guide Star Adaptive Optics for Astronomy (Springer, 2013), Vol. 551.

de Lisio, C.

F. Cardano, F. Massa, H. Qassim, E. Karimi, S. Slussarenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, R. W. Boyd, and L. Marrucci, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
[Crossref]

De Martini, F.

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103, 013601 (2009).
[Crossref]

Dolinar, S.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Dudley, A.

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

Dušek, M.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).
[Crossref]

Faras, O. J.

O. J. Faras, V. D’Ambrosio, C. Taballione, F. Bisesto, S. Slussarenko, L. Aolita, L. Marrucci, S. P. Walborn, and F. Sciarrino, “Resilience of hybrid optical angular momentum qubits to turbulence,” Sci. Rep. 5, 8424 (2015).
[Crossref]

Fazal, I. M.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Fickler, R.

M. Krenn, J. Handsteiner, M. Fink, R. Fickler, R. Ursin, M. Malik, and A. Zeilinger, “Twisted light transmission over 143 km,” Proc. Natl. Acad. Sci. USA 113, 13648–13653 (2016).
[Crossref]

H. Larocque, J. Gagnon-Bischoff, F. Bouchard, R. Fickler, J. Upham, R. W. Boyd, and E. Karimi, “Arbitrary optical wavefront shaping via spin-to-orbit coupling,” J. Opt. 18, 124002 (2016).
[Crossref]

M. Krenn, J. Handsteiner, M. Fink, R. Fickler, and A. Zeilinger, “Twisted photon entanglement through turbulent air across Vienna,” Proc. Natl. Acad. Sci. USA 112, 14197–14201 (2015).
[Crossref]

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M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16, 113028 (2014).
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E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103, 013601 (2009).
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Slussarenko, S.

F. Cardano, F. Massa, H. Qassim, E. Karimi, S. Slussarenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, R. W. Boyd, and L. Marrucci, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
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O. J. Faras, V. D’Ambrosio, C. Taballione, F. Bisesto, S. Slussarenko, L. Aolita, L. Marrucci, S. P. Walborn, and F. Sciarrino, “Resilience of hybrid optical angular momentum qubits to turbulence,” Sci. Rep. 5, 8424 (2015).
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G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2014).
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G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2014).
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F. Tamburini, E. Mari, A. Sponselli, B. Thidé, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: first experimental test,” New J. Phys. 14, 033001 (2012).
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Thidé, B.

F. Tamburini, E. Mari, A. Sponselli, B. Thidé, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: first experimental test,” New J. Phys. 14, 033001 (2012).
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H. Larocque, J. Gagnon-Bischoff, F. Bouchard, R. Fickler, J. Upham, R. W. Boyd, and E. Karimi, “Arbitrary optical wavefront shaping via spin-to-orbit coupling,” J. Opt. 18, 124002 (2016).
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M. Krenn, J. Handsteiner, M. Fink, R. Fickler, R. Ursin, M. Malik, and A. Zeilinger, “Twisted light transmission over 143 km,” Proc. Natl. Acad. Sci. USA 113, 13648–13653 (2016).
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G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2014).
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G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2014).
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O. J. Faras, V. D’Ambrosio, C. Taballione, F. Bisesto, S. Slussarenko, L. Aolita, L. Marrucci, S. P. Walborn, and F. Sciarrino, “Resilience of hybrid optical angular momentum qubits to turbulence,” Sci. Rep. 5, 8424 (2015).
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A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photon. 7, 66–106 (2015).
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J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Weihs, G.

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8(5), 75 (2006).
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A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref]

Willner, A. E.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photon. 7, 66–106 (2015).
[Crossref]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

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L. Allen, M. W. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

Xie, G.

Yan, Y.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photon. 7, 66–106 (2015).
[Crossref]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Yang, J.-Y.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Yue, Y.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Zeilinger, A.

M. Krenn, J. Handsteiner, M. Fink, R. Fickler, R. Ursin, M. Malik, and A. Zeilinger, “Twisted light transmission over 143 km,” Proc. Natl. Acad. Sci. USA 113, 13648–13653 (2016).
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M. Krenn, J. Handsteiner, M. Fink, R. Fickler, and A. Zeilinger, “Twisted photon entanglement through turbulent air across Vienna,” Proc. Natl. Acad. Sci. USA 112, 14197–14201 (2015).
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Zhao, Z.

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H. Larocque, J. Gagnon-Bischoff, F. Bouchard, R. Fickler, J. Upham, R. W. Boyd, and E. Karimi, “Arbitrary optical wavefront shaping via spin-to-orbit coupling,” J. Opt. 18, 124002 (2016).
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J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
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H.-K. Lo, M. Curty, and K. Tamaki, “Secure quantum key distribution,” Nat. Photonics 8, 595–604 (2014).
[Crossref]

Nat. Phys. (1)

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

Nature (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref]

New J. Phys. (4)

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8(5), 75 (2006).
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F. Tamburini, E. Mari, A. Sponselli, B. Thidé, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: first experimental test,” New J. Phys. 14, 033001 (2012).
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E. Nagali, L. Sansoni, L. Marrucci, E. Santamato, and F. Sciarrino, “Experimental generation and characterization of single-photon hybrid ququarts based on polarization and orbital angular momentum encoding,” Phys. Rev. A 81, 052317 (2010).
[Crossref]

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M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
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M. Krenn, J. Handsteiner, M. Fink, R. Fickler, R. Ursin, M. Malik, and A. Zeilinger, “Twisted light transmission over 143 km,” Proc. Natl. Acad. Sci. USA 113, 13648–13653 (2016).
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Supplementary Material (1)

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Figures (3)

Fig. 1.
Fig. 1.

Mode structure of mutually unbiased bases for =2. (a) {|ψi} and (b) {|ϕj} are examples of two bases of structured states of light, encoding in both polarization and OAM of =2. Each basis is orthonormal, and the two bases are mutually unbiased with respect to each other such that |ψ|ϕij|2=1/4. These MUBs have the advantage of possessing identical intensity profiles—“doughnut” shaped—and are shape-invariant upon free-space propagation. The information, therefore, is encoded in the transverse polarization and phase distributions, denoted by the white lines and the hue, respectively.

Fig. 2.
Fig. 2.

Ottawa intracity quantum communication link. Schematic of the sender (left) with a heralded single-photon source (signal, s, and idler, i) and Alice’s state preparation setup. Alice prepares a state from {|ψi} or {|ϕj} using a polarizing beam splitter (PBS), wave plates (WP), and a q-plate (QP). The signal and idler photons are recombined on a dichroic mirror (DM) before being sent to Bob. Two telescopes comprised of lenses with focal lengths of f1=75  mm, f2=f3=400  mm (diameter of 75 mm), and f4=50  mm are used to enlarge and collect the beam, minimizing its divergence through the 0.3 km link. Bob, receiver (right), can then perform measurements on the sent states and record the coincidences between the signal and idler photons with detectors D1 and D2 at a coincidence logic box. Enclosures are built around the sender and receiver to shelter them from the wind and weather, as well as to shield them from background light. Examples of experimentally reconstructed polarization distributions for a structured mode from {|ϕj} using a continuous wave laser that Alice prepared (top left) and Bob measured (bottom right) are shown in the insets. ppKTP, periodically poled KTP crystal; LP, long-pass filter; BP, bandpass filter. Map data: Google Maps, 2016.

Fig. 3.
Fig. 3.

Simulated encryption of an image with structured photons. (a) Experimentally measured probability-of-detection matrices, Pi,j=|α|βij|2, where α,β={ψ,ϕ}, for 2D (top row) and 4D (bottom row) structured photons with turbulence. These matrices have the corresponding bit error rates of Q2D=5% and Q4D=11%, respectively. (b) Image of the Parliament of Canada that Alice encrypts and sends to Bob through a classical channel using their shared secret key. (c) Alice discretizes her intended image (left column) with d levels, where d is the encryption dimension, such that each pixel corresponds to three single photons (RGB values, leading to d3 colors per pixel) that she sends to Bob. Using the experimentally measured probability-of-detection matrices (a), Alice then adds the shared secret key, generated from a BB84 protocol, on top of her discretized image to encrypt it (middle column). Bob decrypts Alice’s sent image with his shared key to recover the image (right column). Implementing a 4-dimensional state clearly allows the ability to send more information per photon, where, in the ideal case, Alice can send twice the amount of information with respect to 2-dimensional states. However, due to noise present in the channel, we experimentally obtain an increase of 1.51 in the amount of information sent by Alice with respect to the case of 2-dimensional states. Image credit: Norman Bouchard.