Quantum KKL-type Inequalities Revisited

• DOI: 10.48550/arxiv.2411.12399
• Publication Date: 2024-01-01
• Authors: Jiao, Yong; Lin, Wenlong; Luo, Sijie; Zhou, Dejian
• Keywords: Mathematics - Functional Analysis; Primary 46L53, Secondary 94D10, 47D07; FOS: Mathematics; Functional Analysis (math.FA)

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 Rouzé 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}.