The theme of this semester’s mathematical physics seminar is quantum information theory. To get us started, I’ll introduce density operators, which play a fundamental role in the theory and serve as a tool for understanding subsystems of a composite quantum system. After defining what a density operator is, I’ll cover some of their basic operations and results, including the partial trace, Schmidt decomposition, and purification.
A "Galois Connection" is a formalism that abstracts the relationship between certain algebraic structures I won't mention and automorphism groups studied in classical Galois theory. Galois connections are ubiquitous in Logic, and most notably are used to define the relationship between the "Syntax" and "Semantics" of a system of logic. We will take a look at Galois connections and see several interesting examples of the kind just mentioned (with pictures!)
Introduction to Density Operators