Witnessing entanglement without entanglement witness operators

The experimental detection and theoretical characterization of entanglement in many-body systems is a mostly unsolved problem. Here we relate entanglement to the statistical speed measuring how quickly nearby states become distinguishable under the action of an arbitrary many-body Hamiltonian. The method is remarkably simple: We witness multipartite entanglement, just elaborating on published experimental data with ions and photons. The unveiled connection between the statistical speed and entanglement provides a unifying framework that can shed new light on quantum information science and quantum critical phenomena.