Lectures

Note: Scribe notes for some of the lectures are being edited, and will be posted when ready.

• May 4:    [ pdf ]
  qubit, superposition principle, measurement, 2-into-1 oblivious transfer (or random access code), general state of multiple qubits, quantum fingerprints---definition.

• May 6:    [ ps ]
  quantum fingerprints, simultaneous message complexity of equality, Holevo bound (weak form).

• May 11:    [ ps ]
  Nayak bound, mixed state, Schmidt decomposition, Yao's lemma for quantum communication, protocol for set disjointness.

• May 13:    [ ps ]
  protocol for sampling disjoint subsets, Razborov lower bound for set disjointness (outline).

• May 18:    [ ps ]
  Razborov lower bound for set disjointness (details).

• May 20:    [ ps ]
  Razborov lower bound for set disjointness (conclusion), density matrix, purification, partial trace.

• May 21:    Make-up lecture for May 27.   
  Two relevant extracts from U. Vazirani's lecture notes: [ ps ]     [ ps ]
  Proof of the Schmidt decomposition, impossibility of ideal bit-commitment, trace norm, distinguishability of mixed states.

• May 25:    [ ps ]     (draft)
  Fidelity, Uhlmann theorem, relationship between trace norm and fidelity, (interruption due to fire alarm), a schema for (strong) coin-flipping.

• May 27:    No lecture today.

• June 1:    [ ps ]     (draft)
  A strong coin flipping protocol (cheating strategies and analysis). Information theory basics---Shannon and von Neumann entropy, and their properties.

• June 3:    [ ps ]
  Information theory continued---classical and quantum mutual information and their properties, Holevo's theorem (formal statement). Classical linear error-correcting codes, dual code & the Fourier transform.

• June 8:    [ ps ]
  CSS codes.

• June 10:   
  Shor-Preskill entanglement purification based quantum key agreement.

• June 11:    Make-up lecture for June 15.
  Continuation of the Shor-Preskill proof of security for the Bennett and Brassard quantum key agreement scheme.

• June 15:    No lecture today.

• June 17:   
  Shor-Preskill proof of security of QKD continued.

• June 22:   
  Remnants of the Shor-Preskill proof. Quantum complexity of element distinctness.

• June 24:    Lecture replaced by talk in the quantum information summer school.

• June 29:    [ ps ]
  A classical walk based algorithm for element distinctness. Properties of classical random walks.

• July 6:    [ ps ]
  Analysis of the classical walk for element distinctness, and the algorithm based on it. Szegedy's quantization of classical walks.

• July 8:   
  Szegedy's quantum walk algorithm for search.

• July 9:    Make up lecture for Thursday, July 15.
  Analysis of Szegedy's algorithm.

• July 13:   
  Analysis of Szegedy's algorithm (conclusion). The polynomial method for proving query lower bounds.

• July 15:    No lecture today.

• July 20, 22:    Lectures replaced by talks in the quantum information and control conference at the Fields Institute.

• July 29:   
  Polynomial method for proving query bounds.

• August 3:   
  Ambainis method for query lower bounds. Project presentations.