Quantum Information Approaches to Quantum Gravity

Abstract

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). A great deal of interest has arisen around how quantum information ideas in CFT translate to geometric features of the quantum gravitational theory in AdS. Through AdS/CFT, progress has been made in understanding the structure of entanglement in quantum field theories, and in how gravitational physics can emerge from these structures. However, this understanding is far from complete and will require the development of new tools to quantify correlations in CFT.This thesis presents refinements of a duality between operator product expansion (OPE) blocks in the CFT, giving the contribution of a conformal family to the OPE, and geodesic integrated fields in AdS which are diffeomorphism invariant quantities. This duality was originally discovered in the maximally symmetric setting of pure AdS dual to the CFT ground state. In less symmetric states the duality must be modified. Working with excited states within AdS 3 /CFT 2 , this thesis shows how the OPE block decomposes into more fine-grained CFT observables that are dual to AdS fields integrated over non-minimal geodesics. These constructions are presented for several classes of asymptotically AdS spacetimes.Additionally, this thesis contains results on the dynamics of entanglement measures for general quantum systems, not necessarily confined to quantum gravity. The quantification of quantum correlations is the main objective of quantum information theory, and it is crucial to understand how they are generated dynamically. Results are presented for the family of quantum Rényi entropies and entanglement negativity. Rényi entropies are studied for general dynamics by imposing special initial conditions. Around pure, separable initial states, all Rényi entropies grow with the same timescale at leading, and next-to-leading order. For negativity, mathematical tools are developed for the differentiation of non-analytic matrix functions with respect to constrained arguments. These tools are used to construct analytic expressions for derivatives of negativity. We establish bounds on the rate of change of state distinguishability under arbitrary dynamics, and the rate of entanglement growth for closed systems.