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Conditional Independence in Quantum Many-Body Systems

Citation

Kim, Isaac Hyun (2013) Conditional Independence in Quantum Many-Body Systems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/PZJN-A841. http://resolver.caltech.edu/CaltechTHESIS:05102013-172241867

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Abstract

In this thesis, I will discuss how information-theoretic arguments can be used to produce sharp bounds in the studies of quantum many-body systems. The main advantage of this approach, as opposed to the conventional field-theoretic argument, is that it depends very little on the precise form of the Hamiltonian. The main idea behind this thesis lies on a number of results concerning the structure of quantum states that are conditionally independent. Depending on the application, some of these statements are generalized to quantum states that are approximately conditionally independent. These structures can be readily used in the studies of gapped quantum many-body systems, especially for the ones in two spatial dimensions. A number of rigorous results are derived, including (i) a universal upper bound for a maximal number of topologically protected states that is expressed in terms of the topological entanglement entropy, (ii) a first-order perturbation bound for the topological entanglement entropy that decays superpolynomially with the size of the subsystem, and (iii) a correlation bound between an arbitrary local operator and a topological operator constructed from a set of local reduced density matrices. I also introduce exactly solvable models supported on a three-dimensional lattice that can be used as a reliable quantum memory.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:conditional mutual information, conditional independence, entanglement, topological entanglement entropy, strong subadditivity, entanglement spectrum
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Preskill, John P.
Group:Institute for Quantum Information and Matter, IQIM
Thesis Committee:
  • Preskill, John P. (chair)
  • Kitaev, Alexei
  • Refael, Gil
  • Motrunich, Olexei I.
Defense Date:8 May 2013
Record Number:CaltechTHESIS:05102013-172241867
Persistent URL:http://resolver.caltech.edu/CaltechTHESIS:05102013-172241867
DOI:10.7907/PZJN-A841
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7697
Collection:CaltechTHESIS
Deposited By: Isaac Kim
Deposited On:17 May 2013 22:43
Last Modified:26 Apr 2019 18:21

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