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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
- Handle URL
- https://hdl.handle.net/2142/121293
- Copyright and License Information
- Copyright 2023 Peixue Wu
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Graduate Dissertations and Theses at Illinois PRIMARY
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