Five-qubit contextuality, noise-like distribution of distances between maximal bases and finite geometry

Employing five commuting sets of five-qubit observables, we propose specific 160–661 and 160–21 state proofs of the Bell–Kochen–Specker theorem that are also proofs of Bellʼs theorem. A histogram of the ‘Hilbert–Schmidt’ distances between the corresponding maximal bases shows in both cases a noise-like behavior. The five commuting sets are also ascribed a finite-geometrical meaning in terms of the structure of symplectic polar space W(9,2)W(9,2).

► We provide a five-qubit ray proof of the Bell–Kochen–Specker theorem with 21 maximal bases.
► The five-qubit contextuality crucially depends on the noise-like distances among the bases.
► The finite geometry of the operator diagrams is revealed.