We review recent progress on the information paradox. We explain why exponentially small
correlations in the radiation emitted by a black hole are sufficient to resolve the original …

These are notes on some entanglement properties of quantum field theory, aiming to make
accessible a variety of ideas that are known in the literature. The main goal is to explain how …

In holographic duality an eternal Anti-de Sitter black hole is described by two copies of the
boundary Conformal Field Theory in the thermal field double state. In this paper we provide …

A bstract We propose a family of exactly solvable toy models for the AdS/CFT
correspondence based on a novel construction of quantum error-correcting codes with a …

A bstract We point out a connection between the emergence of bulk locality in AdS/CFT and
the theory of quantum error correction. Bulk notions such as Bogoliubov transformations …

In this Letter we prove a simple theorem in quantum information theory, which implies that
bulk operators in the anti–de Sitter/conformal field theory (AdS/CFT) correspondence can be …

A bstract We consider the gravity dual of the modular Hamiltonian associated to a general
subregion of a boundary theory. We use it to argue that the relative entropy of nearby states …

In holographic duality an eternal anti–de Sitter black hole is described by two copies of the
boundary conformal field theory in the thermal field double state. This identification has …

I argue that a version of the quantum-corrected Ryu–Takayanagi formula holds in any
quantum error-correcting code. I present this result as a series of theorems of increasing …

These lectures give an introduction to the quantum physics of black holes, including recent
developments based on quantum information theory such as the firewall paradox and its …