Jianxin Chen: When quantum meets algebraic geometry

Jianxin Chen, Institute for Quantum Computing (IQC)

Abstract

Many intrinsic concepts in quantum information theory have their natural counterpoints in algebraic geometry. For example, the set of entangled states is the complement of Segre variety, the set of pure states with bounded Schmidt rank is isomorphic to some determintant variety, subspaces with fixed dimension are known as Grassmannian which is also Zariski closed. In this talk, I will introduce basic concepts in algebraic geometry and some applications in quantum information theory.