# Quantum information measures and their applications in quantum field theory

## TL;DR

This paper explores how quantum information measures like entanglement and relative entropy can be applied to analyze various phenomena in quantum field theory, including the Aharonov-Bohm effect and holographic entanglement.

## Contribution

It demonstrates novel applications of quantum information tools to quantum field theory, including new insights into energy inequalities and the validation of the Ryu-Takayanagi formula.

## Key findings

- Entanglement entropy used to study the Aharonov-Bohm effect in QFT.
- Relative entropy employed to test the Ryu-Takayanagi formula in holography.
- Quantum energy inequalities derived from relative entropy constrain negative energy densities.

## Abstract

In the last decades, it has been understood that a wide variety of phenomena in quantum field theory (QFT) can be characterised using quantum information measures, such as the entanglement entropy of a state and the relative entropy between quantum states in the same Hilbert space. In this thesis, we use these and other tools from quantum information theory to study several interesting problems in quantum field theory. The topics analysed range from the study of the Aharonov-Bohm effect in QFT using entanglement entropy, to the consistence of the Ryu-Takayanagi formula (proposed in the context of the AdS/CFT duality) using properties of relative entropy. We show that relative entropy can also be used to obtain new interesting quantum energy inequalities, that constrain the spatial distribution of negative energy density.