Lectures

  1. Introduction, general discussion about course structure, class expectations, assessments, review of basic quantum mechanics (Dirac notation, qubits, Pauli matrices, Stern-Gerlach).
  2. Review of basic quantum mechanics (GHZM experiment), classical and quantum error-correcting codes basic example, no-cloning theorem.
  3. Sphere packing, Shannon entropy, von Neumann entropy.
  4. Entropy basics -ctd-, Holography (partition function, dictionary, general remarks on conformal field theories and gravity).
  5. Invitation to holography -ctd-, CFTs.
  6. Density matrices: definitions, motivation, trace.
  7. Density matrices -ctd-: ensembles, pure vs mixed states, Bloch sphere, reduced density matrices and partial trace, Hilbert-Schmidt inner product.
  8. Schmidt decomposition, purification; Shannon entropy.
  9. Relative entropy, conditional entropy, mutual information, classical entropy inequalities
  10. von Neumann entropy and its properties, inequalities.
  11. von Neumann entropy inequalities (SSA) -ctd-, entropy cone and inequalities.
  12. Holographic entropy cone, entropy in field theories.
  13. Holographic entanglement entropy, Ryu-Takayanagi formula.
  14. Holography, radial locality, bulk reconstruction.
  15. Quantum error-correction and holography: three-qutrit code, structure theorem.
  16. More general holographic codes, proof of structure theorem, quantum singleton bound, RT formula, modular Hamiltonian.
  17. Subsystem quantum encoding, complimentary recovery, subregion duality, Quantum Ryu-Takayangi formula, JLMS.
  18. Finite dimension von Neumann algebras and holography, tensor networks.
  19. Tensor networks -ctd-.
  20. Student presentations.
  21. Student presentations.
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Last updated on May 5, 2019