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Geometrical and Topological Aspects of Quantum Information Systems

In this Thesis we examine the interplay between the encoding of information in quantum systems and their geometrical and topological properties. We first study photonic qubit probes of space-time curvature, showing how gauge-independent trajectories of photons can help to perform quantum information tasks in space. Then we introduce the first example of topologically ordered systems constructed using interacting light modes on a two-dimensional lattice, which paves the way for feasible observations of topological order in bosonic systems. To conclude, motivated by a theory of quantum gravity we analyze the convergence of entropy in unitarily inequivalent quantization schemes.