Dynamical approach in quantum information theory

Wu, Peixue

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

Description

Title

Dynamical approach in quantum information theory

Author(s)

Wu, Peixue

Issue Date

2023-07-10

Director of Research (if dissertation) or Advisor (if thesis)

• Junge, Marius
• Song, Renming

Doctoral Committee Chair(s)

Leditzky, Felix

Committee Member(s)

• Dey, Partha
• Araiza, Roy

Department of Study

Mathematics

Discipline

Mathematics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• open quantum system
• quantum information theory
• large deviation
• stability properties.

Abstract

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.

Graduation Semester

2023-08

Type of Resource

Thesis

Handle URL

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

Copyright and License Information

Copyright 2023 Peixue Wu

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