Entanglement is central to the modern understanding of quantum systems and the primary resource for upcoming quantum technologies. However, a potential bottleneck for future advances is the need for scalable protocols to detect and characterize entanglement. In particular, there is an increasing demand for procedures that can certify the presence of entanglement in quantum many-body systems.
The quantum Fisher information(QFI) is a witness for multipartite entanglement of great relevance to quantum metrology. Unfortunately, it is hard to estimate the QFI so its use as a tool for entanglement certification is limited, for now. In this talk, we discuss recent works that address this issue and demonstrate that the QFI can be extracted with experimentally friendly protocols based on engineered dynamics. We show results from numerical simulations for the one dimensional Fermi-Hubard model and certify the presence of multipartite mode entanglement across the phase diagram.