Maximal Non-Kochen-Specker Sets and a Lower Bound on the Size of Kochen-Specker Sets
Abstract
The challenge of determining bounds for the minimal number of vectors in a three-dimensional Kochen-Specker (KS) set has captivated the quantum foundations community for decades. This paper establishes a weak lower bound of 10 vectors, which does not surpass the current best-known bound of 24 vectors. By exploring the complementary concept of large non-KS sets and employing a probability argument independent of the graph structure of KS sets, we introduce a novel technique that could be applied in the future to derive tighter bounds. Additionally, we highlight an intriguing connection to a generalisation of the moving sofa problem in navigating a right-angled hallway on the surface of a two-dimensional sphere.
Keywords
Cite
@article{arxiv.2403.05230,
title = {Maximal Non-Kochen-Specker Sets and a Lower Bound on the Size of Kochen-Specker Sets},
author = {Tom Williams and Andrei Constantin},
journal= {arXiv preprint arXiv:2403.05230},
year = {2025}
}
Comments
8 pages, 7 figures; v2: published version