UC Berkeley

This dissertation explores numerous applications of concepts from quantum information theory to quantum gravity, the AdS/CFT correspondence, as well as holographic dualities more generally. A recurring theme will be the notion that geometric quantities in the bulk are dual to information-theoretic quantities in the boundary.

The Ryu-Takayanagi formula and related results tell us that entanglement entropies in the CFT are given in terms of the areas of minimal surface in the bulk. This geometric formula for entanglement entropy imposes inequalities on the entanglement entropies of various CFT regions for static spacetimes, known as the holographic entropy cone. We will numerically investigate the validity of the five-region inequalities for a specific dynamical spacetime, a collapsing black hole spacetime. We find that, for all cases considered, all of the inequalities are satisfied when the null energy condition is satisfied in the bulk, while all of the inequalities are violated if the null energy condition is not satisfied in the bulk. This provides some evidence for the validity of the five-region inequalities in general settings in AdS/CFT with a dynamical bulk. We then discuss the complexity-action and complexity-volume conjectures in the setting of holographic Friedmann–Robertson–Walker universes, which are more realistic cosmological models than AdS space. These conjectures pass some non-trivial consistency checks in these settings. Following this, operator complexity is studied numerically for one- and two-qubit systems using Nielsen complexity geometry. Even though these are relatively simple systems, some interesting similarities are found with the behavior of complexity for more interesting, larger systems. Finally, we explore the use of sandwiched Renyi relative entropy in holography, and in finite-dimensional models of quantum error correction.