Representation theory, randomness, and quantum information science
Abstract/Contents
- Abstract
- Often, understanding physical systems or mathematical structures requires analyzing the generic behaviors instead of specific examples. In such cases, a common approach is identifying the degrees of freedom that are supposed to be generic and replacing them with entirely random values. This line of thinking has been fruitful in many areas of physics, such as nuclear physics, quantum chaos, quantum field theory, and quantum gravity. Within quantum information science, which is the primary focus of this dissertation, multiple areas including quantum entanglement, the quantum capacity of channels and quantum Shannon theory, the construction of quantum codes, and benchmarking quantum systems have heavily benefited from randomization techniques. Most of this manuscript is devoted to random constructions and relevant mathematical formalisms, such as representation theory and group theory, and their applications in quantum information science and quantum gravity. In particular, we will study the following topics: (1) Applications of representation theory and randomization in quantum error correction, including approximate versions of the Eastin-Knill theorem and the reference frame quantum error correction. (2) Schur-Weyl duality for the stabilizer formalism, with applications in quantum property testing and de Finetti theorems (3) Randomized constructions and information theoretic methods for holographic duality, including the holographic entropy cone and random tensor networks.
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource. |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2019; ©2019 |
| Publication date | 2019; 2019 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Ghazi Nezami, Sepehr |
|---|---|
| Degree supervisor | Hayden, Patrick (Patrick M.) |
| Thesis advisor | Hayden, Patrick (Patrick M.) |
| Thesis advisor | Hartnoll, Sean |
| Thesis advisor | Shenker, Stephen Hart, 1953- |
| Degree committee member | Hartnoll, Sean |
| Degree committee member | Shenker, Stephen Hart, 1953- |
| Associated with | Stanford University, Department of Physics. |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Sepehr Ghazi Nezami. |
|---|---|
| Note | Submitted to the Department of Physics. |
| Thesis | Thesis Ph.D. Stanford University 2019. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2019 by Sepehr Ghazi Nezami
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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