Notes on Continuity of Channel Capacities

I spent the summer of 2012 as an undergraduate research assistant working under Debbie Leung at the Institute for Quantum Computing. Since then I have decided to pursue a career in computer graphics, although quantum information remains one of my amateur interests. I have compiled the notes I took during this research semester into one document:

Research notes on continuity of channel capacities

There is little organization within these notes, however they summarize some of the necessary background to start the study of quantum information, and include a few proofs of theorems from various Quantum Information books, as well as a few new ideas aimed at proving the continuity of a particular quantum capacity. These notes aren't complete in any sense, because unfortunately I didn't get a chance to typeset all of my work.