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arXiv · 2411.12399

Quantum KKL-type Inequalities Revisited

Yong Jiao·Wenlong Lin·Sijie Luo·Dejian Zhou
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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}.

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Yong Jiao, Wenlong Lin, Sijie Luo, Dejian Zhou. 2024-11-19. Quantum KKL-type Inequalities Revisited. https://arxiv.org/abs/2411.12399

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