Nonlocal magic of fermions is bounded by entanglement fluctuations and is logarithmic for free fermions

arXiv:2611.07003v1 Announce Type: new Abstract: Free-fermion states are classically simulable, yet, written as qubits, they typically carry extensive magic, the quantum resource that stabilizer circuits lack. Part of this magic is nonlocal: local unitaries acting separately on two parts of the system cannot remove it. If these local unitaries are restricted to Gaussian ones, the nonlocal magic grows linearly with the number $m$ of partially entangled fermion pairs. We show that this growth is an artifact of the Gaussian restriction: local Gaussian unitaries minimize the nonlocal stabilizer R\'enyi entropy for up to three pairs, but not from four pairs on.