rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Quantum Coloring of Quantum Graphs
  name:
    name part: Ganesan, Priyanga
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: ROWELL, ERIC
    role:
      role term: thesis advisor.
  name:
    name part: Texas A&M University
    role:
      role term: degree granting institution.
  type of resource: text
  genre: bibliography
  origin info:
    place:
      place term: txu
    date issued: 2023
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource.
  abstract: Quantum graphs are an operator space generalization of classical graphs that have appeared in different branches of mathematics including operator systems theory, non-commutative topology and quantum information theory. In this work, we develop a notion of quantum coloring for quantum graphs using a non-local game with quantum inputs & classical outputs that generalizes the coloring game for classical graphs. Using this game, we define chromatic numbers for quantum graphs in the various (quantum) models and show that they are a analogue of D.Stahlke⁰́₉s [53] entanglement assisted chromatic numbers and that the classical model is equivalent to Kim & Mehta⁰́₉s [37] strong chromatic numbers for non-commutative graphs. We demonstrate explicit quantum colorings of all quantum complete graphs and prove that every quantum graph has a finite quantum chromatic number (but not necessarily classical chromatic number). We also show that every quantum graph is 4-colorable in the algebraic model. Further, we obtain five lower bounds for the classical and quantum chromatic number of quantum graphs using the spectrum of the quantum adjacency operator. These bounds are achieved by applying a combinatorial characterization of quantum graph coloring obtained from the winning strategies of the quantum-to-classical nonlocal coloring game. We generalize all the spectral estimates of Elphick & Wocjan [19] to the quantum graph setting and in particular, prove a quantum generalization of the Hoffman⁰́₉s bound. We also demonstrate the tightness of our bounds in the case of quantum complete graphs. The electronic version of this dissertation is accessible from https://hdl.handle.net/1969.1/197273
  note: by Priyanga Ganesan.
  note: "Major Subject: Mathematics"
  note: Includes vita.
  note: Doctor of Philosophy Texas A&M University 2022 https://hdl.handle.net/1969.1/197273
  note: Includes bibliographical references.
  note: Text (Dissertation)
  subject:
    topic: Major Mathematics
  subject:
    topic: Quantum graphs
  subject:
    topic: Non-local games
  subject:
    topic: Operator system
  subject:
    topic: Quantum adjacency operator
  subject:
    topic: Graph coloring
  subject:
    topic: Chromatic number
  subject:
    topic: Spectral bounds
  identifier: https://hdl.handle.net/1969.1/197273
  record info:
    record content source: TXA
    record creation date: 240819
    record change date: 20240820145859.6
    record identifier: in00005463645
    language of cataloging:
      language term: eng