CO 781
Topics in Quantum Information
Fall 2006
Lectures
Scribe notes will be posted as they are received and edited.
-
Sep. 11--15: (Ashwin Nayak)
Quantum state, density matrix, purification, impossibility of
superluminal communication, Schmidt decomposition, local transitions,
impossibility of bit commitment.
-
Sep. 18--22: (Debbie Leung) [ notes1,
notes2,
notes3
]
Generalized measurement--unitary picture and POVM formalism. Quantum operations--the
unitary picture, Kraus representation, and Jamiolkowski-Choi representation.
Error-correction--classical repetition code, Shor 9-qubit
code, classical linear codes. CSS codes.
-
Sep. 25--28: (Debbie Leung) [ notes
]
Quantum error-correction criterion. Stabilizer formalism, stabilizer codes.
-
Sep. 29: (Guest Lecturer: Graeme Smith) [ notes
above ];
Degenerate quantum error correcting codes.
-
Oct. 11--16: (Debbie Leung) [ notes1,
notes2 ]
Encoded operations and measurements, transversality,
fault tolerant computation, threshold theorem.
-
Oct. 18--20: (Ashwin Nayak)
Distinguishability of quantum states, trace distance, fidelity,
their properties.
-
Oct. 23--Oct. 25: (Debbie Leung) [ notes
]
Von Neumann Entropy, and its properties. Compression.
-
Oct. 27: (Ashwin Nayak)
Quantum coin flipping, analysis and cheating strategies for a strong
coin-flipping protocol with bias 1/4.
-
Oct. 30--Nov. 8: (Ashwin Nayak)
[ notes2
]
Quantum key distribution, assumptions, security guarantee. Shor-Preskill
proof of security for BB'84. Key rate. (3 lectures on Lo-Chau type
protocol and its security, 1 lecture on CSS code protocol, and
1 on BB'84 and wrap-up.)
-
Nov. 10--Nov. 20: (Debbie Leung)
Quantum channels, resources and capacities.
-
Nov. 22--Nov. 24:
Term paper presentations.
-
Nov. 27--Dec. 4: (Ashwin Nayak)
Holevo theorem, in-probability bound. Random access codes.
Lower bound for the length of smooth codes.
Average encoding theorem. Local transitions revisited.
Communication complexity of Set Disjointness.