High-dimensional quantum entanglement realized with orbital-angular-momentum (OAM) modes of photons provides a powerful platform for exploring the topology and geometry of quantum state spaces. Recent experiments using spontaneous parametric down-conversion have demonstrated entangled photon pairs occupying a seven-dimensional OAM Hilbert space whose topology is governed by the Lie group , giving rise to a 48-dimensional manifold of quantum states. In this work, we propose a geometric interpretation of this structure based on octonion algebra. The seven OAM basis modes are mapped onto the seven imaginary units of the octonions, whose multiplication rules are encoded by the Fano plane. Within this framework, nonlinear three-wave interactions that underlie photon-pair generation naturally correspond to cyclic triples in the Fano-plane geometry. This correspondence suggests that the observed topological structure of high-dimensional entangled photon states may admit an octonionic geometric description, providing a potential bridge between structured-light quantum optics and exceptional algebraic structures.
High-dimensional quantum entanglement realized with orbital-angular-momentum (OAM) modes of photons provides a powerful platform for exploring the topology and geometry of quantum state spaces. Recent experiments using spontaneous parametric down-conversion have demonstrated entangled photon pairs occupying a seven-dimensional OAM Hilbert space whose topology is governed by the Lie group , giving rise to a 48-dimensional manifold of quantum states. In this work, we propose a geometric interpretation of this structure based on octonion algebra. The seven OAM basis modes are mapped onto the seven imaginary units of the octonions, whose multiplication rules are encoded by the Fano plane. Within this framework, nonlinear three-wave interactions that underlie photon-pair generation naturally correspond to cyclic triples in the Fano-plane geometry. This correspondence suggests that the observed topological structure of high-dimensional entangled photon states may admit an octonionic geometric description, providing a potential bridge between structured-light quantum optics and exceptional algebraic structures.
The bandwidth of any communication system, classical or quantum, is limited by the number of orthogonal states in which the information can be encoded. Quantum key distribution systems available commercially rely on the two-dimensional polarisation state of photons. Quantum computation has also been largely designed on the basis of qubits. However, a photon is endowed with other degrees of freedom, such as orbital angular momentum (OAM). OAM is an attractive basis to be used for quantum information because it is discrete and theoretically infinite-dimensional. This promises a higher information capacity per photon which can lead to more complex quantum computation protocols and more security and robustness for quantum cryptography. Entanglement of OAM naturally arises from spontaneous parametric down-conversion (SPDC). However, any practical experiment utilising the innately high-dimensional entanglement of the orbital angular momentum (OAM) state space of photons is subject to the modal capacity of the detection system. Only a finite subset of this space is accessible experimentally. Given such a constraint, we show that the number of measured, entangled OAM modes in photon pairs generated by SPDC can be increased by tuning the phase-matching conditions in the SPDC process. We achieve this by tuning the orientation angle of the nonlinear crystal generating the entangled photons.
Entanglement in high-dimensional quantum systems, where one or more degrees of freedom of light are involved, offers increased information capacities and enables new quantum protocols.Here, we demonstrate a functional source of high-dimensional, noise-resilient hyperentangled states encoded in time-frequency and vector vortex structured modes, which in turn carry single-particle entanglement between polarization and orbital angular momentum.Pairing nonlinearity-engineered parametric downconversion in an interferometric scheme with spin-to-orbital-angular-momentum conversion, we generate highly entangled photon pairs at telecom wavelength that we characterize via two-photon interference and quantum state tomography, achieving near-unity visibilities and fidelities.While hyperentanglement has been demonstrated before in photonic qubits, here we present a rich entanglement structure involving spectrally and spatially structured light, where three different forms of entanglement coexist in the same biphoton state.
Orbital angular momentum (OAM) is one of the most recently discovered properties of light, and it is only in the past decade its quantum properties have been the subject of experimental investigations and have found applications. Unlike polarization, which is only bidimensional, orbital angular momentum provides, with relative ease, unprecedented access to a theoretically unbounded discrete state space. The process of spontaneous parametric down-conversion has long been used as a source of two-photon states that can be entangled in several degrees of freedom, including OAM. In this thesis, the properties of the natural OAM spectrum associated with the entangled states produced by parametric down-conversion were investigated. Chapters 2 and 3 describe the production and detection of tunable high-dimensional OAM entanglement in a down-conversion system. By tuning the phase-matching conditions and improving the detection stage, a substantial increase in the half-width of the OAM correlation spectrum was observed. The conjugate variable of OAM, angular position, was also considered when examining high-dimensional states entangled in OAM. In order to efficiently determine their dimension, high-dimensional entangled states were probed by implementing a technique based on phase masks composed of multiple angular sectors, as opposed to narrow single-sector analysers. Presented in chapter 4, this technique allows the measurements of tight angular correlations while maintaining high optical throughput. The states so produced were then used for a number of applications centred around the concept of mutually unbiased bases. One can define sets of mutually unbiased bases for arbitrary subspaces of the OAM state space. Two bases are mutually unbiased if the measurement of a state in one basis provides no information about the state as described in the other basis. Complete measurements in mutually unbiased bases of high-dimensional OAM spaces are presented in chapter 5. Measurements in sets of mutually unbiased bases are integral to quantum science and can be used in a variety of protocols that fully exploit the large size of the OAM state space; we describe their use in efficient quantum state tomography, quantum key distribution and entanglement detection. Caution is however necessary when dealing with state spaces embedded in higher-dimensional spaces, such as that provided by OAM. Experimental tests of Bell-type inequalities allow us to rule out local hidden variable theories in the description of quantum correlations. Correlations inconsistent with the states observed, or even with quantum mechanics, known as super-quantum correlations, have however been recorded previously in experiments that fail to comply with the fair-sampling conditions. Chapter 6 describes an experiment that uses a particular choice of transverse spatial modes for which super-quantum correlations persist even if the detection is made perfectly efficient. The sets of modes carrying OAM allow a complete description of the transverse field. The ability to control and combine additional degrees of freedom provides the possibility for richer varieties of entanglement and can make quantum protocols more powerful and versatile. One such property of light, associated with transverse modes possessing radial nodes in the field distribution, can be accessed within the same type of experimental apparatus used for OAM. In chapter 7, the radial degree of freedom is explored, together with OAM, in the context of Hong-Ou-Mandel interference.
Twisted light, or light with orbital angular momentum (OAM), plays an emerging role in both classical and quantum science, with important applications in areas as diverse as biophotonics, micromachines, spintronics, or quantum information. It offers fascinating opportunities for exploring new fundamental ideas in physics, as well as for being used as a tool for practical applications. One important point is to determine how to generate single photons, and two-photon states, with an appropriate OAM content. Here we describe the paraxial orbital angular momentum of entangled photon pairs generated by spontaneous parametric down-conversion (SPDC) in different non-collinear geometries. These geometries introduce a variety of new features. In particular, we find the OAM of entangled pairs generated in purely transverse-emitting configurations, where the entangled photons counter-propagate perpendicularly to the direction of propagation of the pump beam. The spatial walk-off of all interacting waves in the parametric process also determines the OAM content of the down-converted photons, and here its influence is also revealed.
Photon pairs generated from spontaneous parametric down-conversion are a well-established method to realize entangled bipartite photonic systems. Laguerre-Gaussian modes, which carry orbital angular momentum (OAM), are commonly exploited to engineer high-dimensional entangled quantum states. For Hilbert spaces with dimension d>2, maximally entangled states (MESs) help to improve the capacity and security of quantum communication protocols, among several other promising features. However, the direct generation of MESs in well-defined high-dimensional subspaces of the infinite OAM basis has remained a challenge. Here, we formalize how the spatial distribution of the pump beam and the nonlinear profile of the crystal can be simultaneously utilized to generate MESs without additional spatial filtering of OAM modes within a subspace. We illustrate our approach with maximally entangled qutrits (d=3) and ququints (d=5).
Quantum skyrmions are topological structures that have garnered significant interest due to their demonstrated robustness and versatility across diverse optical platforms. However, existing approaches for their generation are limited to producing pre-determined two dimensional qubit states with a single topology. Here we create multi-dimensional topological states by introducing a non-local interaction between high-dimensional photonic entanglement and a metasurface, where the topological transformation induced by the metasurface is made non-deterministic by the probabilistic nature of the interfacing entangled state. Within this framework, we demonstrate that individual quantum states can host multiple co-existing topologies that are only revealed upon measurement, allowing for their parallel transport within distinct spatial mode channels. We confirm this by revealing the rich topological landscape within our modified Hilbert space while controlling the desired output topology by orbital angular momentum (OAM) projections on one of the entangled photons, producing multiple non-local polarization-OAM entangled states characterized by distinct topological classes, all from a single metasurface device. Our results reveal new capability when structured high-dimensional entanglement is interfaced with structured matter capable of coupling photonic degrees of freedom, establishing a new pathway for the compact generation of complex quantum states.