Quantum state-independent contextuality requires 13 rays

Abstract

We show that, regardless of the dimension of the Hilbert space, there exists\nno set of rays revealing state-independent contextuality with less than 13\nrays. This implies that the set proposed by Yu and Oh in dimension three [Phys.\nRev. Lett. 108, 030402 (2012)] is actually the minimal set in quantum theory.\nThis contrasts with the case of Kochen-Specker sets, where the smallest set\noccurs in dimension four.\n