Structured light refers to the generation and application of custom light fields. As the tools and technology to create and detect structured light have evolved, steadily the applications have begun to emerge. This roadmap touches on the key fields within structured light from the perspective of experts in those areas, providing insight into the current state and the challenges their respective fields face. Collectively the roadmap outlines the venerable nature of structured light research and the exciting prospects for the future that are yet to be realized.

Single photons with helical phase structures may carry a quantized amount of orbital angular momentum (OAM), and their entanglement is important for quantum information science and fundamental tests of quantum theory. Because there is no theoretical upper limit on how many quanta of OAM a single photon can carry, it is possible to create entanglement between two particles with an arbitrarily high difference in quantum number. By transferring polarization entanglement to OAM with an interferometric scheme, we generate and verify entanglement between two photons differing by 600 in quantum number. The only restrictive factors toward higher numbers are current technical limitations. We also experimentally demonstrate that the entanglement of very high OAM can improve the sensitivity of angular resolution in remote sensing.

Twisted photons can be used as alphabets to encode information beyond one bit per single photon. This ability offers great potential for quantum information tasks, as well as for the investigation of fundamental questions. In this review article, we give a brief overview of the theoretical differences between qubits and higher dimensional systems, qudits, in different quantum information scenarios. We then describe recent experimental developments in this field over the past three years. Finally, we summarize some important experimental and theoretical questions that might be beneficial to understand better in the near future.

Quantum key distribution (QKD) promises informationtheoretically secure communication, and is already on the verge of commercialization. Thus far, different QKD protocols have been proposed theoretically and implemented experimentally [1, 2]. The next step will be to implement high-dimensional protocols in order to improve noise resistance and increase the data rate [3][4][5][6][7]. 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 state [8]; wherein, using a high-dimensional BB84 protocol [3, 4], a quantum bit error rate of 11% was attained with a corresponding secret key rate of 0.65 bits per sifted photon. While 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. Even through moderate turbulence without active wavefront correction, it is possible to securely transmit information carried by structured photons, opening the way for intra-city high-dimensional quantum communications under realistic conditions.In addition to wavelength and polarization, a light wave is characterized by its orbital angular momentum (OAM) [9], which corresponds to its helical wavefronts. Polarization is naturally bi-dimensional, i.e. {|L , |R }, and the associated angular momentum can take the values of ± per photon, where is the reduced Planck constant, and |L and |R are left-and right-handed circular polarizations, respectively. In contrast, OAM is inherently unbounded, such that a photon with intertwined helical wavefronts, | , carries units of OAM, where is an integer [10]. Quantum states of light resulting from an arbitrary coherent superposition of different polarizations and spatial modes, e.g. OAM, are referred to as structured photons; these photons can be used to realize higher-dimensional states of light [8]. Aside from their fundamental significance in quantum physics [11,12], single photons encoded in higher dimensions provide an advantage in terms of security tolerance and encrypting alphabets for quantum cryptography [3, 4,7] and classical communications [13]. The behaviour of light carrying OAM through turbulent conditions has been studied theoretically and simulated in the laboratory scale [14][15][16][17]. Experimentally, OAM states have been tested in classical communications across intra-city links in Los Angeles (120 m) [18], Venice (420 m) [19], Erlangen (1.6 km) [20], Vienna (3 km) [21], and between two Canary Islands (143 km) [22] which is the longest link thus far. With attenuated lasers, OAM states and vector vortex beams have been respectively implemented in high-dimensional and 2-dimensional BB84 protocols, where the former was performed ...