Measuring entanglement in many-body systems

This talk will be concerned with how entanglement may be quantified without any assumptions using simple measurements. I will show how bipartite entanglement may be followed across quantum phase transitions in recent experimental quantum simulations of spin chains. Further, a scheme will be presented that allows to directly read of lower bounds to multi-partite entanglement from the scattering cross section of Neutrons deflected from solid state samples and the time-of-flight distribution of bosons in optical lattices.