Holography andquantum information

Entanglement is the most counterintuitive feature in quantum mechanics. In recent years, it has been pointed out a deep connection between entanglement and the connectivity of spacetime in the context of AdS/CFT or Holography. The AdS/CFT correspondence states the duality between quantum field theories in d-spacetime dimensions and quantum gravity in at least one extra dimension. This theoretical framework has led to profound consequences and insights for both sides. In this thesis, we study three aspects of entanglement entropy in holography: traversable wormholes, modular Berry phases, and entanglement islands. In Chapter 1, we explain how these concepts are intimately related with entanglement entropy. In Chapter 2, we review the non-local protocol that allows for traversable wormholes using ordinary matter and we implement it to construct an eternal traversable wormhole in asymptotically anti-de Sitter spacetime in four dimensions. We then review the modular Berry transport problem. In the context of three-dimensional gravity, in Chapter 3, we study the parallel transport of modular Hamiltonians governed by a change of global state. We relate the Berry curvature for a fixed interval with the symplectic form for a Euclidean conical singularity geometry obtained from the backreaction of a cosmic brane. Finally, after reviewing the island formula and its use in the resolution of some aspects of the black hole information paradox, we discuss its possible application in cosmology. We study the possible existence of islands in FRW cosmologies supported by thermal radiation, cosmological constant, and non-zero spatial curvature in Chapter 4.