University of Illinois Urbana-Champaign

Dynamical approach in quantum information theory

Wu, Peixue

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

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
Copyright and License Information
Copyright 2023 Peixue Wu

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