  The recent direct experimental measurement of quantum entanglement paves the
way towards a better understanding of many-body quantum systems and their
correlations. Nevertheless, the experimental and theoretical advances had so
far been predominantly limited to bosonic systems. Here, we study fermionic
systems. Using experimental setups where multiple copies of the same state are
prepared, arbitrary order Renyi entanglement entropies and entanglement
negativities can be extracted by utilizing spatially-uniform beam splitters and
on-site occupation measurement. As an example, we simulate the use of our
protocols for measuring the entanglement growth following a local quench. We
also illustrate how our paradigm could be used for experimental quantum
simulations of fermions on manifolds with nontrivial spin structures.
