Measuring fermionic entanglement: Entropy, negativity, and spin structure

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 to measure 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.