Quantum state engineering and tomography of high-dimensional spatial states of photons

We will discuss several experiments studying high-dimensional entanglement in spatial degrees of freedom of photons generated in SPDC. We will see how one can engineer this entanglement using spatially structured pump beams. In particular, we will demonstrate the capabilities to tailor the dimensionality and shape of the generated states without any filtering or post-selection. Then we will discuss the applications of these high-dimensional spatial states in quantum information and show that they are an ideal testbed for quantum tomography. We will overview some experiments in adaptive tomography and application of machine learning techniques to quantum state and process reconstruction.