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