On the quantum KKL theorem and related inequalities
Organizers
Speaker
Haonan Zhang
Time
Thursday, June 20, 2024 2:00 PM - 3:00 PM
Venue
A3-3-301
Online
Zoom 293 812 9202
(BIMSA)
Abstract
The KKL theorem is a fundamental result in Boolean analysis, stating that any Boolean function has an influential variable. Montanaro and Osborne proposed a quantum extension of Boolean functions. In this context, some classical results have been extended to the quantum setting, such as Talagrand's $L^1$-$L^2$ inequality. However, a quantum version of the KKL theorem seems to be missing, as conjectured by Montanaro and Osborne. In this talk, I will present an alternative answer to this question, saying that every balanced quantum Boolean function has a geometrically influential variable. This is based on joint work with Cambyse Rouzé (Inria) and Melchior Wirth (IST Austria).