Quantum Information & Semidefinite Programming
Polished slides and a unified set of lecture notes will both be posted at the end of the summer. Probably.
Part 1: Semidefinite programming
Mathematical background [Slides] [Slides (annotated)] [Scribe notes]
Positive semidefinite matrices [Slides] [Slides (annotated)][Scribe notes]
Real Analysis [Slides] [Slides (annotated)][Scribe notes]
Convex analysis [Slides] [Slides (annotated)][Scribe notes]
Semidefinite programming introduction [Slides] [Slides (annotated)][Scribe notes]
Standard form reductions and real vs. complex data [Slides] [Slides annotated] [Scribe notes]
Duality theory [Slides] [Slides annotated] [Scribe notes]
The dual of the dual [Slides] [Slides annotated] [Scribe notes]
Lifehack: How to really take the dual [Slides annotated] [Scribe notes]
Slater's theorem and optimality conditions [Slides] [Slides annotated] [Scribe notes]
Clark's theorem and ascent directions [Slides] [Slides annotated] [Scribe notes]
Part 2: Quantum applications
Quantum states and measurements [Slides][Slides annotated] [Scribe notes]
Distinguishing between two states and the trace norm [Slides][Slides annotated] [Part 1, Part 2]
Optimal measurements [Slides][Slides annotated] [Scribe notes]
Uhlmann's Theorem and Alberti's Theorem are dual [Slides][Slides annotated] [Notes part 1, Part 2]
The completely bounded trace norm and properties of the fidelity function [Slides][Slides annotated] [Scribe notes]
Operator geometric means [Slides] [Notes part 1, Part 2]
Quantum entropy functions [Slides] [Notes part 1, Part 2]
Quantum nonlocal games [Slides]
Quantum money [Slides annotated]