Genuine Multipartite Nonlocality Is Fermionic Magic

Abstract

Free fermion dynamics is classically simulable, and a single non-Gaussian state makes it universal. We show that the same boundary governs quantum nonlocality. Measured as fermionic qubits, fermionic Gaussian states reach at most the biseparable bound of the Mermin inequality for three parties and, for any number of parties, violate the Mermin family by exactly the factor of a single entangled pair. They are never genuinely multipartite nonlocal. Genuine multipartite nonlocality and computational universality are thus one resource for fermions, the opposite of the stabilizer case. The mechanism is fermion parity. The bound is monogamous and certifies non-Gaussianity from measured correlations alone. On superconducting processors we watch nonlocality beyond free fermions switch on under an interaction between densities, confirm the monogamy law on 96 qubits, and measure the ground state of twelve interacting fermions on a ring cross the bound as the interaction grows, detecting the charge density wave transition.