Geometric influences on quantum Boolean cubes

2024/08/30 by David P. Blecher, Gao Li, Blecher, David P. +3
Computer Science · #Advanced Algebra and Logic #FOS: Mathematics #Functional Analysis (math.FA) #Quantum Computing Algorithms and Architecture

paper · pdf · doi:10.48550/arxiv.2409.00224

openalex publication_date 2024/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work, we study three problems related to the L₁-influence on quantum Boolean cubes. In the first place, we obtain a dimension free bound for L₁-influence, which implies the quantum L¹-KKL Theorem result obtained by Rouze, Wirth and Zhang. Beyond that, we also obtain a high order quantum Talagrand inequality and quantum L¹-KKL theorem. Lastly, we prove a quantitative relation between the noise stability and L¹-influence. To this end, our technique involves the random restrictions method as well as semigroup theory.

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