The Quantum KKL Inequality — E8 Intelligence Research

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

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-09
DOI
https://doi.org/10.5281/zenodo.24075471
Primary Topic
Quantum Computing Algorithms and Architecture
Type
preprint
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preprint

The Quantum KKL Inequality — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Quantum Computing Algorithms and Architecture
preprint

The Quantum KKL Inequality — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

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

Zenodo (CERN European Organization for Nuclear Research)
Quantum Computing Algorithms and Architecture
DOIOpen Access PDFOpenAlex
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The Quantum KKL Inequality — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS