Quantum error correction and spacetime
Abstract/Contents
- Abstract
- Quantum error correction (QEC) is a branch of quantum information theory, originally invented to protect hypothetical quantum computers against realistic sources of noise. QEC has enjoyed significant success within the paradigm of computation, but the ideas and techniques of quantum error correction have also been effective in tools many fields of physics. In this thesis, we will shed light on the way in which QEC manifests outside of the usual computational paradigm and informs other areas of physics. We'll focus on the role of QEC in quantum gravity, spacetime, and high energy theoretical physics. We start with the general problem of quantum information replication in spacetime, and we show that information replication is possible if and only if transmission of the quantum information does not result in cloning of quantum information or faster-than-light communication. We then study the role of quantum error correction in quantum gravity, specifically within a gauge-gravity duality known as AdS/CFT. We establish a new formula for mapping observables on either side of the duality, showing that the so-called bulk-to-boundary map defines an approximate quantum error correcting code. Motivated by the study of entangled states dual to multi-boundary wormholes in AdS/CFT, we then turn our attention to characterizing the states that can arise from the euclidean path integral in three-dimensional Chern-Simons theories. We study U(1) level k and SO(3) level k Chern-Simons theories on euclidean 3-manifolds with torus boundaries. For the abelian U(1) theory, we find that the set of states that can be prepared exactly coincides with the set of stabilizer states, which are characterized by quantum error correcting codes. For the non-abelian SO(3) theory, we find that any state can be prepared to arbitrary precision, giving rise to a notion of state universality. We conclude with some final observations to support the idea that entanglement gives rise to the connectedness of spacetime. We study the partial transpose of the thermofield double (TFD) state geometrically, and we demonstrate that local time reversal (which is unitarily equivalent to partial transpose) leads to inconsistencies in the connected spacetime dual to the TFD state.
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 | 2018; ©2018 |
| Publication date | 2018; 2018 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Salton, Grant | |
|---|---|---|
| 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 | Grant Salton. |
|---|---|
| Note | Submitted to the Department of Physics. |
| Thesis | Thesis Ph.D. Stanford University 2018. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2018 by Grant Salton
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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