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- 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).

Speaker Biography：Haonan Zhang is an assistant professor at the University of South Carolina. He mainly works on harmonic analysis, functional analysis, functional inequalities and quantum information.