UC San Diego

Quantum entanglement is a bizarre phenomena and one of the characteristic features of quantum mechanics. It has wide applications ranging from quantum computation, quantum communication to understanding properties of quantum many-body systems and black holes. This dissertation aims to provide a systematic framework to extract physical properties of topologically ordered quantum many-body systems from their entanglement structures. This framework, called entanglement bootstrap, only assumes two axioms about the entanglement structure, and can be used to derive a plethora of physical properties using various quantum information tools. In Chapter 2 we derive knotted excitation types and fusion data associated with (3+1)-dimensional topologically ordered quantum states using entanglement bootstrap. In Chapter 3 we discuss how to derive remote detectability using this framework, where remote detectability means the ability to detect the existence of topological excitations using distant topological excitations.