PreprintCC BY 4.0arXiv
The Quantum KKL Inequality
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 L2-influence from below by a constant multiple of Var(T)log(n)/n. The proof heavily depends on upper and lower commutator estimates on the Hilbert space.
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BibTeX
@misc{jiao2026quantum,
title = {{The Quantum KKL Inequality}},
author = {Yong Jiao and Wenlong Lin and Sijie Luo and Dejian Zhou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21900},
eprint = {2609.21900},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21900},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Quantum KKL Inequality
AU - Yong Jiao
AU - Wenlong Lin
AU - Sijie Luo
AU - Dejian Zhou
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21900
UR - https://arxiv.org/abs/2609.21900
AB - 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 Var(T)log(n)/n. The proof heavily depends on upper and lower commutator estimates on the Hilbert space.
ER -