The PIQUaNT project has made significant progress in its first half. We have developed methods to manipulate the spatial structure of quantum light using a technology known as multi-plane light-conversion (MPLC). This technique uses multiple reflections on a programmable spatial light modulator to implement complex operations on a structured photon. We have used the MPLC platform to design a mode sorter for overlapping quantum states of light as well as implement high-dimensional transformations that simulate the exchange statistics of quasiparticles known as Anyons. In parallel, we have developed a powerful technique that harnesses complex mode-mixing inside a commercial optical fibre to programme quantum circuits for light using methods of inverse design. Using this technique, we have demonstrated the transport, measurement, and control of high-dimensional entanglement within the transmission channel itself! During the course of this experiment, we also developed a new reference-less technique for characterising complex scattering media using physics-based multi-plane neural networks, and applied it for measuring the transmission matrix of a commercial multi-mode fibre. On the theoretical front, we have developed a complete model for high-dimensional entanglement in the spatial and spectral degrees-of-freedom and developed an experimental technique to rapidly characterise it in the lab. This has allowed us to optimise how we generate and measure entanglement in the lab, enabling us to produce quantum states of two photons with a record entanglement dimensionality. Finally, we have developed a powerful one-sided device-independent entanglement (steering) witness that utilises the above methodology to achieve noise and loss-tolerant entanglement distribution. We have implemented this witness in the lab to steer entanglement through conditions of loss equivalent to 79km of telecom fibre in the presence of noise.
