| Summary: | In this thesis we explore several questions at the intersection of quantum information theory and quantum many-body physics. We study properties like entanglement and chaos, and we use intuition from discrete, few-body systems to learn about continuum systems. First we study quantum scars, a phenomenon previously studied in chaotic, few-body quantum systems, and we extend the analysis from the case of few-body quantum mechanics to the case of quantum field theory. Next we turn to the study of multipartite entanglement. Inspired by the operational interpretation of bipartite entanglement, we propose a new information-theoretic measure for tripartite entanglement based on subsystem recoverability, and we study this quantity in the vacuum state of (1+1)-D conformal field theory. Then we consider toy models of quantum gravity, where the objective is to construct qubit models that reproduce aspects of holography. We study toy models that consist of putting a lattice gauge theory on a tensor network, and we show how such toy models can be made background-independent. Finally we propose a new tensor network toy model for 3D gravity that features a topologically defined area operator, such that the areas on crossing cuts do not commute.
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