Abstract
Quantum information theory and the second quantum revolution have brought us within grasping distance of quantum computers, the building block of which is the qubit. Like their classical counter parts---the bit---they are two-dimensional, reaching their power when embedded in an network of many interacting qubits. However, many quantum systems are not two-dimensional in nature, but high dimensional. In this thesis, I explore---both experimentally and theoretically---several applications of encoding and processing information in high dimensional quantum systems. I consider information encoded in the spatial, temporal, and phase space distributions of optical systems. I further analyse the evolution of these systems using the theory of closed and open quantum systems, conditional dynamics and Fock state master equations. These results highlight the unique advantages of high dimensional quantum systems in the sub-disciplines quantum foundations, quantum simulation and quantum sensing. Our results clearly demonstrate that high dimensional quantum information presents many unique applications that could be fostered into new technology.
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