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Multipartite entanglement, such as witnessed through the quantum Fisherinformation (QFI), is a crucial resource for quantum technologies, but itsexperimental certification is highly challenging. Here, we propose anexperimentally friendly protocol to measure the QFI. It relies on recording theshort-time dynamics of simple observables after a quench from a thermal state,works for spins, bosons, and fermions, and can be implemented in standardcold-atom experiments and other platforms with temporal control over the systemHamiltonian. To showcase the protocol, we simulate it for the one-dimensionalFermi--Hubbard model. Further, we establish a family of bounds connecting theQFI to multipartite mode entanglement for fermionic systems, which enable thedetection of multipartite entanglement at sizable temperatures. Our work pavesa way to experimentally accessing entanglement for quantum enhanced metrology.

From entanglement certification with quench dynamics to multipartite entanglement of interacting fermions