Universal Generation of Maximal Entanglement from Bell Measurements of Fermionic Gaussian States

Exploring universal entanglement structure in many-body systems is both fundamental and challenging, especially for system subjected to non-unitary operations. In this work, we investigate the entanglement structure of fermonic Gaussian states subjected to Bell measurements. In particular, by choosing a specific measurement protocol that performed onto two initially decoupled copies of a half-filled fermionic Gaussian state, the post-measurement state becomes a product of Bell pairs across the two copies, and thereby generating maximal inter-layer entanglement. Crucially, this behavior is independent of the initial state and is therefore universal. We prove this by showing that, given the measurement protocol,only the specific Bell-pair product state can host a non-vanishing post-measurement wavefunction. Our analytic derivation traces this phenomenon to its fermionic origin, arising from the combination of anti-symmetric statistics and the Gaussianity of the states.