Interplay between quantum information and spacetime

The purpose of this PhD thesis is to study the relation between quantum information and the geometry of spacetime. Even though we would ideally like to be as general as possible, we will most likely use the tools in AdS/CFT to do so. We will start with more established matters involving entanglement entropy. However, we plan to eventually cover some of the latest developments in the so called dictionary between bulk and boundary, including the derivation of the Page curve in black hole physics or the meaning of complexity in holography. The technical methods involved in the thesis will involve both gravitational (differential geometry) and CFT (quantum mechanics) tools