Quantum KKL-type Inequalities Revisited
Functional Analysis
2024-11-20 v1
Abstract
In the present paper, we develop the random restriction method in the quantum framework. By applying this method, we establish the quantum Eldan-Gross inequality, the quantum Talagrand isoperimetric inequality, and related quantum KKL-type inequalities. Our results recover some recent results of Rouz\'e et al. \cite{RWZ2024} and Jiao et al. \cite{JLZ2025}, which can be viewed as alternative answers to the quantum KKL conjecture proposed by Motanaro and Osborne in \cite{MO2010}.
Cite
@article{arxiv.2411.12399,
title = {Quantum KKL-type Inequalities Revisited},
author = {Yong Jiao and Wenlong Lin and Sijie Luo and Dejian Zhou},
journal= {arXiv preprint arXiv:2411.12399},
year = {2024}
}