Retractive Groups

Abstract: One goal of our current research is to define a new area called algebraic information theory. It began with the realization that many important classes of channels, both quantum and classical, possess the structure of a compact affine monoid. The idea is then to use this structure as the basis for new techniques in information theory.
In practice, many classes of channels arise as the convex closure of a certain underlying group, and among these, certain groups distinguish themselves in that they generate very restricted classes, which are remarkable in that they always contain the solution to optimization problems posed over the set of all channels. These groups, which we call retractive, can also be used to derive useful inequalities, devise methods for tomography of quantum channels and appear to always generate channels whose capacities can be expressed in closed form.

Speaker's Bio: Keye Martin is a senior research mathematician at the Naval Research Laboratory. He is the founder of the informatic phenomena group and the director of its quantum optics lab.