Quantum Information meets K-theory


In ongoing (unpublished) work with Matt Hastings, we explore some questions in multipartite entanglement in the context of parameter families of quantum systems.  Vector bundles are parameterized vector spaces, and bundle theory is parameterized linear algebra.  In the quantum world our vector spaces usually have fixed tensor product structures (corresponding to parts of the system held by Alice, Bob, Claire, etc… ) and questions about entanglement are generally studied one at a time.  But in the spirit of bundle theory, we can study such questions in X-parameter families, for a space X. (X might be the momentum torus or “Brillion zone” in some  condensed matter applications.) I will give a glimpse of what I hope will become a theory of quantum characteristic classes.