Vector vortex beams are structured states of light that are non-separable in their polarisation and spatial mode, they are eigenmodes of free-space and many fibre systems, and have the capacity to be used as a modal basis for both classical and quantum communication. Here we outline recent progress in our understanding of these modes, from their creation to their characterization and detection. We then use these tools to study the propagation behaviour of such modes in free-space and optical fibre and show that modal cross-talk results in a decay of vector states into separable scalar modes, with a concomitant loss of information. We present a comparison between probabilistic and deterministic detection schemes showing that the former, while ubiquitous, negates the very benefit of increased dimensionality in quantum communication while reducing signal in classical communication links. This work provides a useful introduction to the field as well as presenting new findings and perspectives to advance it further.

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Quantum mechanics is now a mature topic dating back more than a century. During its scientific development, it fostered many technological advances that now are integrated into our everyday lives. More recently, over the past few decades, the authors have seen the emergence of a second quantum revolution, ushering in control of quantum states. Here, the spatial modes of light, “patterns of light,” hold tremendous potential: light is weakly interacting and so an attractive avenue for exploring entanglement preservation in open systems, while spatial modes of light offer a route to high dimensional Hilbert spaces for larger encoding alphabets, promising higher information capacity per photon, better security, and enhanced robustness to noise. Yet, progress in harnessing high dimensional spatial mode entanglement remains in its infancy. Here, the authors review the recent progress in this regard, outlining the core concepts in a tutorial manner before delving into the advances made in creation, manipulation, and detection of such quantum states. The authors cover advances in using orbital angular momentum as well as vectorial states that are hybrid entangled, combining spatial modes with polarization to form an infinite set of two-dimensional spaces: multidimensional entanglement. The authors highlight the exciting work in pushing the boundaries in both the dimension and the photon number, before finally summarizing the open challenges, and the questions that remain unanswered.

A quantitative analysis of optical fields is essential, particularly when the light is structured in some desired manner, or when there is perhaps an undesired structure that must be corrected for. A ubiquitous procedure in the optical community is that of optical mode projections—a modal analysis of light—for the unveiling of amplitude and phase information of a light field. When correctly performed, all the salient features of the field can be deduced with high fidelity, including its orbital angular momentum, vectorial properties, wavefront, and Poynting vector. Here, we present a practical tutorial on how to perform an efficient and effective optical modal decomposition, with emphasis on holographic approaches using spatial light modulators, highlighting the care required at each step of the process.

Vector beams, non-separable in spatial mode and polarisation, have emerged as enabling tools in many diverse applications, from communication to imaging. This applicability has been achieved by sophisticated laser designs controlling the spin and orbital angular momentum, but so far is restricted to only two-dimensional states. Here we demonstrate the first vectorially structured light created and fully controlled in eight dimensions, a new state-of-the-art. We externally modulate our beam to control, for the first time, the complete set of classical Greenberger–Horne–Zeilinger (GHZ) states in paraxial structured light beams, in analogy with high-dimensional multi-partite quantum entangled states, and introduce a new tomography method to verify their fidelity. Our complete theoretical framework reveals a rich parameter space for further extending the dimensionality and degrees of freedom, opening new pathways for vectorially structured light in the classical and quantum regimes.

The global quantum network requires the distribution of entangled states over long distances, with significant advances already demonstrated using entangled polarisation states, reaching approximately 1200 km in free space and 100 km in optical fibre. Packing more information into each photon requires Hilbert spaces with higher dimensionality, for example, that of spatial modes of light. However spatial mode entanglement transport requires custom multimode fibre and is limited by decoherence induced mode coupling. Here we transport multi-dimensional entangled states down conventional single-mode fibre (SMF). We achieve this by entangling the spin-orbit degrees of freedom of a bi-photon pair, passing the polarisation (spin) photon down the SMF while accessing multi-dimensional orbital angular momentum (orbital) subspaces with the other. We show high fidelity hybrid entanglement preservation down 250 m of SMF across multiple 2 × 2 dimensions, demonstrating quantum key distribution protocols, quantum state tomographies and quantum erasers. This work offers an alternative approach to spatial mode entanglement transport that facilitates deployment in legacy networks across conventional fibre.

One of the most captivating properties of diffraction-free optical fields is their ability to reconstruct upon propagation in the presence of an obstacle both, classically and in the quantum regime. Here we demonstrate that the local entanglement, or non-separability, between the spatial and polarisation degrees of freedom also experience self-healing. We measured and quantified the degree of nonseparability between the two degrees of freedom when propagating behind various obstructions, which were generated digitally. Experimental results show that even though the degree of nonseparability reduces after the obstruction, it recovers to its maximum value within the classical selfhealing distance. To confirm our findings, we performed a Clauser-Horne-Shimony-Holt Bell-like inequality measurement, proving the self-reconstruction of non-separability. These results indicate that local entanglement between internal degrees of freedom of a photon, can be recovered by suitable choice of the enveloping wave function. I. INTRODUCTIONSelf-healing is one of the most fascinating properties of diffraction-free optical fields [1]. These fields have the ability to reconstruct if they are partially disturbed by an obstruction placed in their propagation path. Diffraction-free beams have found applications in fields such as imaging [2][3][4], optical trapping [5][6][7][8], laser material processing [9], amongst many others. Arguably, the most well-known propagation invariant (self-healing) fields are Bessel modes of light, first introduced in 1987 by J. Durin [1,10]. However, the self-healing property is not limited to so called non-diffracting beams, but also appears in helico-conical [11], caustic, or self-similar fields, namely Airy [12], Pearcey [13], Laguerre-Gaussian [14,15] and even standard Gaussian beams [16]. Furthermore, within the last years, it has been shown that self-healing can also be observed at the quantum level, for example, McLaren et al. demonstrated experimentally the self-reconstruction of quantum entanglement [17]. Importantly, self-healing is not only an attribute of scalar fields but it can also apply to beams with spatially variant polarization [18][19][20]. Bessel beams also appear as complex vector light fields, where polarisation and spatial shape can be coupled in a non-separable way [21][22][23]. This property has fueled a wide variety of applications, from industrial processes, such as, drilling or cutting [9,24,25], to optical trapping [26][27][28][29][30][31], high resolution microscopy [32], quantum and classical communication [33][34][35], amongst many others. Controversially, such non-separable states of classical light are sometimes referred to as classically or nonquantum entangled [36]. This stems from the fact that the quintessential property of quantum entanglement is non-separability, which is not limited to quantum systems. Indeed, the equivalence has been shown to be more than just a mathematical construct [34]. While such classical non-separable fields do not exhibit non-locality, they

Encoding information in high-dimensional degrees of freedom of photons has led to new avenues in various quantum protocols such as communication and information processing. Yet to fully benefit from the increase in dimension requires a deterministic detection system, e.g., to reduce dimension dependent photon loss in quantum key distribution. Recently, there has been a growing interest in using vector vortex modes, spatial modes of light with entangled degrees of freedom, as a basis for encoding information. However, there is at present no method to detect these non-separable states in a deterministic manner, negating the benefit of the larger state space. Here we present a method to deterministically detect single photon states in a four dimensional space spanned by vector vortex modes with entangled polarisation and orbital angular momentum degrees of freedom. We demonstrate our detection system with vector vortex modes from the || = 1 and || = 10 subspaces using classical and weak coherent states and find excellent detection fidelities for both pure and superposition vector states. This work opens the possibility to increase the dimensionality of the state-space used for encoding information while maintaining deterministic detection and will be invaluable for long distance classical and quantum communication.