Quantum KKL-type Inequalities Revisited
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. RWZ2024 and Jiao et al. JLZ2025, which can be viewed as alternative answers to the quantum KKL conjecture proposed by Motanaro and Osborne in MO2010.
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