On the quantum KKL theorem and related inequalities
演讲者
张浩楠
时间
2024年06月20日 14:00 至 15:00
地点
A3-3-301
线上
Zoom 293 812 9202
(BIMSA)
摘要
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).