Geometrical and Topological Aspects of Quantum Information Systems

TL;DR

This thesis explores the relationship between quantum information encoding and geometrical/topological properties, including photon-based space-time probes, topologically ordered light systems, and entropy convergence in quantum gravity contexts.

Contribution

It introduces novel methods for probing space-time with photons, constructs the first topologically ordered bosonic systems, and analyzes entropy convergence in quantum gravity models.

Findings

Photon trajectories can be used for quantum information tasks in curved space

Topologically ordered systems can be realized with interacting light modes

Entropy convergence varies across different quantization schemes

Abstract

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.