The paper presents a method to measure entanglement in a system of interacting delocalized particles using quantum interference of many-body twins. The authors leverage their control over ultra-cold bosonic atoms in optical lattices to prepare and interfere two identical copies of a many-body state, enabling the direct measurement of quantum purity, Rényi entanglement entropy, and mutual information. This approach provides a way to characterize quantum phases and dynamics of strongly correlated many-body systems. The experiments demonstrate the measurement of entanglement in a Bose-Hubbard model, showing the emergence of spatial entanglement as the system transitions from a Mott insulator to a superfluid. The results highlight the potential of this method for studying non-equilibrium entanglement dynamics andmultipartite entanglement in larger systems.The paper presents a method to measure entanglement in a system of interacting delocalized particles using quantum interference of many-body twins. The authors leverage their control over ultra-cold bosonic atoms in optical lattices to prepare and interfere two identical copies of a many-body state, enabling the direct measurement of quantum purity, Rényi entanglement entropy, and mutual information. This approach provides a way to characterize quantum phases and dynamics of strongly correlated many-body systems. The experiments demonstrate the measurement of entanglement in a Bose-Hubbard model, showing the emergence of spatial entanglement as the system transitions from a Mott insulator to a superfluid. The results highlight the potential of this method for studying non-equilibrium entanglement dynamics andmultipartite entanglement in larger systems.