Representation theory, randomness, and quantum information science

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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.


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


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.


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

© 2019 by Sepehr Ghazi Nezami
This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).

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