Interplay between quantum information and spacetime

本博士论文的目的是研究量子信息与时空几何的关系。即使我们理想地希望尽可能通用，我们也很可能使用AdS/CFT中的工具来做到这一点。我们将从涉及纠缠熵的更成熟的问题开始。然而，我们计划最终涵盖一些所谓的体积和边界之间字典的最新发展，包括黑洞物理学中Page曲线的推导或全息学中复杂性的含义。论文中涉及的技术方法将涉及重力（微分几何）和CFT（量子力学）工具

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