State-Independent Proof of Kochen–Specker Theorem with Thirty Rank-Two Projectors

The Kochen–Specker theorem states that noncontextual hidden variable theories are incompatible with quantum mechanics.We provide a state-independent proof of the Kochen–Specker theorem using the smallest number of projectors,i.e.,thirty rank-2 projectors,associated with the Mermin pentagram for a three-qubit system.