Geometric influences on quantum Boolean cubes

arXiv - MATH - Functional Analysis Pub Date : 2024-08-30 DOI:arxiv-2409.00224

David P. Blecher, Li Gao, Bang Xu

引用次数: 0

Abstract

In this work, we study three problems related to the $L_1$-influence on quantum Boolean cubes. In the first place, we obtain a dimension free bound for $L_1$-influence, which implies the quantum $L^1$-KKL Theorem result obtained by Rouze, Wirth and Zhang. Beyond that, we also obtain a high order quantum Talagrand inequality and quantum $L^1$-KKL theorem. Lastly, we prove a quantitative relation between the noise stability and $L^1$-influence. To this end, our technique involves the random restrictions method as well as semigroup theory.

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量子布尔立方体的几何影响

在这项工作中，我们研究了与量子布尔立方体上的 $L_1$ 影响有关的三个问题。首先，我们得到了$L_1$-影响的无维约束，这意味着鲁兹、维斯和张得到的量子$L^1$-KKL定理结果。除此之外，我们还得到了高阶量子塔拉格兰德不等式和量子 $L^1$-KKL 定理。最后，我们证明了噪声稳定性与 $L^1$ 影响之间的定量关系。为此，我们的技术涉及随机限制方法和半规则理论。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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arXiv - MATH - Functional Analysis

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