Dynamical approach in quantum information theory

We study how we can design a dissipative open quantum system such that the system will be driven to a subspace. We study its stability properties and propose a random model for a class of dynamics.Moreover, we establish large deviation inequalities via different approaches. The dissertation consists of six chapters. In Chapter 1, we briefly review the background and state our main result. Chapter 2 is devoted to some preliminaries. In Chapter 3, we study the stability properties via completely dissipative generators, also known as gradient forms. Our perturbation is not limited to local perturbations. Chapter 4 is devoted to a discrete random model. We establish a general deviation inequalities. The model we consider is given by random unitary channel but we do not assume any symmetry. Chapter 5 is devoted to a continuous random model. We establish large deviation principle via potential theory. Finally in Chapter 6, we discuss how we can derive large deviation principles from group transference technique.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2023

Author dc:creator

• Wu, Peixue

Contributors dc:contributor

• Junge, Marius
• Song, Renming
• Leditzky, Felix
• Dey, Partha
• Araiza, Roy

• Open Quantum System
• Quantum Information Theory
• Large Deviation
• Stability Properties.

Statement dc:rights

• Copyright 2023 Peixue Wu

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/121293

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F121293