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Quantum Machine Learning

The Grothendieck Constant is Strictly Larger than Davie-Reeds' Bound

arXiv
Authors: Chris Jones, Giulio Malavolta

Year

2026

Paper ID

38919

Status

Preprint

Abstract Read

~2 min

Abstract Words

125

Citations

N/A

Abstract

The Grothendieck constant KG is a fundamental quantity in functional analysis, with important connections to quantum information, combinatorial optimization, and the geometry of Banach spaces. Despite decades of study, the value of KG is unknown. The best known lower bound on KG was obtained independently by Davie and Reeds in the 1980s. In this paper we show that their bound is not optimal. We prove that KG ge KDR + 10-12, where KDR denotes the Davie-Reeds lower bound. Our argument is based on a perturbative analysis of the Davie-Reeds operator. We show that every near-extremizer for the Davie-Reeds problem has Ω(1) weight on its degree-3 Hermite coefficients, and therefore introducing a small cubic perturbation increases the integrality gap of the operator.

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  • The Grothendieck constant KG is a fundamental quantity in functional analysis, with important connections to quantum information, combinatorial optimization, and the geometry...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2603.30039 [2] arXiv https://arxiv.org/abs/2603.30039 [3] Publisher https://arxiv.org/abs/2603.30039

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