An operational perspective on holographic entanglement

Abstract

The work presented in this thesis is a contribution towards the understanding of holo- graphic entanglement from an operational perspective. Following the interpretation which is most natural for quantum information theory, entanglement is viewed as a resource that can be produced, stored, transferred and used for practical purposes.
The first chapter introduces the main concepts which are necessary throughout the discussion. Quantum entanglement, as opposed to merely classical correlation, is presented in detail within the framework of quantum mechanics. This is followed by a brief overview on the current state of knowledge about entanglement in quantum field theory and more specifically in gauge/gravity duality.
The second chapter investigates a particular measure of entanglement, known as nega- tivity, in the context of holographic field theories. This is further explored in the following (third) chapter, where an interesting dependence of the entanglement between a region and its complement on the topology of their interface is presented.
The forth chapter investigates qubits systems and compares equivalence classes of entanglement structures to known properties of holographic states.
The fifth chapter focuses on the behaviour of the tripartite information for highly en- tangled states, both in a bipartite and multipartite sense, in relation to the sign definiteness imposed by holography.
A final chapter comments on future directions of investigation within this program.