# Tensor diagrams for Haar integrals

**August 30, 2018.** *Sufficiently complex quantum mechanical systems
look random, in the sense that we can model their evolution as an
operator chosen uniformly at random. Here, I’ll explain what
“uniformly at random” means, and discuss a simple graphical method
for calculating average properties of these random systems. I’ll finish with a
proof of Page’s theorem, a beautiful result connecting random
evolution to entanglement, and discuss its application to black holes.*

Written on August 20, 2018