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 Rényi 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.

Figure 1

A schematic description of the measurement protocols, given by Eqs. (3) and (32), for either entanglement entropy between $A=A_1\cup A_2$ and $B$, or entanglement negativity between $A_1$ and $A_2$. For discussion, see Sec. 1b.

Figure 2

Simulations of our measurement protocols for the Klich-Levitov quench model; see Sec. 1d. Top: Potential barrier between two spinless leads is eliminated at $t=0$. Bottom: Simulated entanglement measurements at times $t>0$, in units of lattice spacing over Fermi velocity. Dots with error bars display the protocols' outcomes; solid lines depict exact entanglements. Additional parameters are given in Sec. 4.

Figure 3

An example of a manifold with a nontrivial spin structure around a homology cycle; see Coser et al. [96].