Quantum Contextuality

Physics: Kochen-Specker (1967): no non-contextual hidden variable model can reproduce QM. Measurement outcome depends on which compatible observables are measured simultaneously — the "context." KCBS inequality: Σᵢ⟨AᵢAᵢ₊₁⟩ ≥ −3 (classical, i cyclic mod 5) but quantum minimum is −√5 ≈ −2.236 — a violation. Unlike Bell: involves a single system, not pairs. Mermin's magic square: 3×3 grid of Pauli products provides simpler proof. Howard et al. (2014): contextuality is a computational resource — necessary for quantum speedup via magic state injection. Contextuality → Bell nonlocality for distributed measurements.