- Alexander Volberg, MSU
- Noncommutative Bohnenblust--Hille inequalities and application to learning the quantum observables
- 02/08/2023
- 4:10 PM - 5:00 PM
- C304 Wells Hall
(Virtual Meeting Link)
- Willie Wai-Yeung Wong (wongwil2@msu.edu)
Bohnenblust--Hille inequalities for Boolean cubes have been proven with dimension-free constants that grow sub-exponentially in the degree (Defant—Mastylo—Peres). Such inequalities have found great applications in learning low degree Boolean functions (Eskenazis—Ivanisvili). Motivated by learning quantum observables, a quantum counterpart of Bohnenblust--Hille inequality for Boolean cubes was recently conjectured in Cambyse Rouz\’e, Melchior Wirth, and Haonan Zhang: ``Quantum Talagrand, KKL and Friedgut’s theorems and the learnability of quantum Boolean functions.” arXiv preprint, arXiv:2209.07279, 2022.
Haonan Zhang and myself prove such noncommutative Bohnenblust--Hille inequalities with constants that are dimension-free and of exponential growth in the degree. As applications, we study learning problems of quantum observables.
(Speaker will present remotely)