Department of Mathematics

Analysis and PDE

  •  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 (

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)



Department of Mathematics
Michigan State University
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C212 Wells Hall
East Lansing, MI 48824

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