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QIC 890

Topics in Quantum Information

Graduate

Winter 2021 · Functional Analysis Methods for QIT

Topics

  • Metric and topological spaces
  • Banach and Hilbert spaces
  • Operators on Hilbert spaces and spectral theory
  • Compact operators and Schatten classes
  • Unbounded operators and self-adjointness
  • Stone’s theorem
  • Von Neumann algebras and C*-algebras

Readings

  • Instructor lecture notes are provided.
    unspecified
Winter 2020 · Applications of Operator Algebras in QIT

Topics

  • C*-algebras, operator systems and operator spaces in quantum information
  • Completely positive and completely bounded maps
  • Compact operators and Schatten classes
  • von Neumann algebras and GNS theory
  • Stinespring dilation
  • Knill–Laflamme theory, private channels and quantum marginals
  • Capacity theory and Bell-inequality violations
Sources