Quantum Information Approaches to Quantum Gravity

In this thesis we apply techniques from quantum information theory to study quantum gravity within the framework of the anti-de Sitter / conformal field theory correspondence (AdS/CFT). We present refinements of a duality between operator product expansion (OPE) blocks in the CFT, and geodesic integrated fields in AdS. Working with excited states within AdS3/CFT2, we show how the OPE block decomposes into more fine-grained CFT observables that are dual to AdS fields integrated over non-minimal geodesics. Additionally, this thesis contains results on the dynamics of entanglement measures for general quantum systems. Results are presented for the family of quantum Renyi entropies and entanglement negativity.