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The Quantum KKL Inequality — E8 Intelligence Research

Year: 2026

Type: preprint

Abstract: In this paper, we resolve the quantum KKL conjecture of Montanaro and Osborne \cite{MO2010} for quantum Boolean functions on the $n$-qubit hypercube. More precisely, for every self-adjoint unitary $T$, we bound the largest $L_2$-influence from below by a constant multiple of $\mathrm{Var}(T)\log(n)/n$. The proof heavily depends on upper and lower commutator estimates on the Hilbert space. Source: http://arxiv.org/abs/2609.21900v1 (arXiv:2609.21900v1) Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.24075471

Author: Caldin, Andrew Stewart

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7225616435

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