Maximal Entanglement: Applications in Quantum Information and Particle Physics

TL;DR

This thesis explores maximal entanglement in quantum systems, developing new Bell inequalities, applying multipartite measures to phase transitions, simulating quantum models, and linking entanglement to fundamental particle interactions.

Contribution

It introduces novel Bell inequalities with optimal settings, applies hyperdeterminants to quantum phase transitions, and connects maximal entanglement to fundamental particle physics predictions.

Findings

New Bell inequalities with optimal violation settings

Hyperdeterminant-based detection of quantum phase transitions

Predicted weak mixing angle close to experimental value

Abstract

In this PhD thesis, several aspects regarding maximal entanglement are analyzed. In the first chapter, Bell Inequalities are analyzed from an operational perspective as well as novel Bell inequalities are obtained together with their optimal settings for a maximal violation. Multipartite figures of merit, in particular, the hyperdeterminant, are the subject of the second chapter. They are applied to detect quantum phase transitions in several spin models. The third chapter focuses on the simulation of the XY model in a quantum computer. The quantum circuit obtained is tested in three current quantum devices. Quantum computers must be able to generate and hold highly entangled states in order to show a quantum advantage. This statement is analyzed in chapter four, where quantum circuits for maximally entangled states are presented. Finally, chapter five analyzes how maximal entanglement is generated at its fundamental level. Maximal entanglement constraints the QED vertex interaction and predicts a value for the weak mixing angle close to the experimental value.