In this thesis we investigate multi-photon entanglement in high dimensions, where the high-dimensional Hilbert space is given by the transverse-mode space of photon fields. We first introduce the...Show moreIn this thesis we investigate multi-photon entanglement in high dimensions, where the high-dimensional Hilbert space is given by the transverse-mode space of photon fields. We first introduce the reader to the mathematical framework and the quantization of light fields. Thereafter we discuss the possible partitions of the transverse-mode space, and the generic structure of photons created via type-I collinear degenerate spontaneous parametric down conversion. Finally, we present to the reader strong evidence that such entangled photons can be generated by the experimental setup that we have created.Show less