This page contains lecture notes for a couple of courses I've taught. They can be used freely, but please understand that they are just lecture notes and undoubtedly contain errors.

Theory of Quantum Information (notes from Fall 2011)

All 22 lectures in one file
[pdf]

Lecture 1 Mathematical preliminaries (part 1)
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Lecture 2 Mathematical preliminaries (part 2)
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Lecture 3 States, measurements, and channels
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Lecture 4 Purifications and fidelity
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Lecture 5 Naimark's theorem; characterizations of channels
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Lecture 6 Further remarks on measurements and channels
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Lecture 7 Semidefinite programming
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Lecture 8 Semidefinite programs for fidelity and optimal measurements
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Lecture 9 Entropy and compression
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Lecture 10 Continuity of von Neumann entropy; quantum relative entropy
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Lecture 11 Strong subadditivity of von Neumann entropy
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Lecture 12 Holevo's theorem and Nayak's bound
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Lecture 13 Majorization for real vectors and Hermitian operators
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Lecture 14 Separable operators
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Lecture 15 Separable mappings and the LOCC paradigm
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Lecture 16 Nielsen's theorem on pure state entanglement transformation
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Lecture 17 Measures of entanglement
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Lecture 18 The partial transpose and its relationship to entanglement and distillation
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Lecture 19 LOCC and separable measurements
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Lecture 20 Channel distinguishability and the completely bounded trace norm
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Lecture 21 Alternate characterizations of the completely bounded trace norm
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Lecture 22 The finite quantum de Finetti theorem
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Introduction to Quantum Computing (notes from Winter 2006)

All 22 lectures in one file
[pdf]

Lecture 1 Overview of quantum information
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Lecture 2 Overview of quantum information (continued)
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Lecture 3 Superdense coding; quantum circuits, and partial measurements
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Lecture 4 Quantum teleportation; Deutsch's algorithm
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Lecture 5 A simple searching algorithm; the Deutsch-Jozsa algorithm
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Lecture 6 Simon's algorithm
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Lecture 7 Arithmetic/number-theoretic problems; reversible computation
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Lecture 8 Phase estimation
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Lecture 9 Phase estimation (continued); the quantum Fourier transform
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Lecture 10 Order finding
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Lecture 11 Order finding (continued); reducing factoring to order finding
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Lecture 12 Grover's algorithm
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Lecture 13 Grover’s Algorithm (continued)
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Lecture 14 Quantum information revisited
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Lecture 15 Quantum information revisited (continued)
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Lecture 16 Quantum error correction
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Lecture 17 General quantum errors; CSS codes
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Lecture 18 Quantum key distribution
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Lecture 19 Impossibility of quantum bit commitment
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Lecture 20 Bell inequalities and nonlocality
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Lecture 21 Quantum communication complexity
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Lecture 22 Quantum computational complexity
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