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Maximal Non-Kochen-Specker Sets and a Lower Bound on the Size of Kochen-Specker Sets (2403.05230v2)

Published 8 Mar 2024 in quant-ph, cs.DM, and math.MG

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.

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