Title:

Invariant theory and quantum information

Abstract:

Invariant theory is an established branch of mathematics that goes back to the works of Cayley and Hilbert. Quantum information is the resource that powers future quantum computers. Surprisingly, these two subjects are quite intimately related. I will give an overview and explain how this connection comes about. We will see that two fundamental problems are dual to each other: 1. characterizing the null cone in invariant theory and 2. deciding the compatibility of quantum marginals. I will then present an optimization algorithm called tensor scaling that solves both problems exactly. We will end by discussing some interesting open questions.