Quantum state-independent contextuality requires 13 rays

TL;DR

This paper proves that at least 13 rays are necessary to demonstrate state-independent contextuality in quantum systems, establishing the minimal set size and contrasting it with Kochen-Specker sets.

Contribution

It establishes the minimal number of rays needed for state-independent contextuality in any dimension as 13, confirming the Yu-Oh set as minimal in three dimensions.

Findings

No smaller set than 13 rays can reveal state-independent contextuality.

The Yu-Oh set in dimension three is minimal for this purpose.

Minimal sets for Kochen-Specker contextuality occur in dimension four.

Abstract

We show that, regardless of the dimension of the Hilbert space, there exists no set of rays revealing state-independent contextuality with less than 13 rays. This implies that the set proposed by Yu and Oh in dimension three [Phys. Rev. Lett. 108, 030402 (2012)] is actually the minimal set in quantum theory. This contrasts with the case of Kochen-Specker sets, where the smallest set occurs in dimension four.