Information, Geometry, and Physics Seminar

Harmonic analysis has long been a powerful tool in theoretical computer science, and we are starting to see applications in the noncommutative world of quantum computing. In this talk we will discuss how to learn quantum operators from very little information, thanks to noncommutative analogues of some classical inequalities in harmonic analysis: Bohnenblust—Hille-type inequalities. To prove these we exploit the geometry of Heisenberg-Weyl eigenspaces to reduce to a commutative question, which in turn is settled by a dimension-free Remez-type inequality, the first of its kind.
We will dive into some proof ideas according to time and interest.
Based on joint works with Lars Becker, Ohad Klein, Alexander Volberg, and Haonan Zhang.