Measuring Fermionic Entanglement: Entropy, Negativity, and Spin Structure

TL;DR

This paper develops methods for experimentally measuring entanglement in fermionic systems, including entropies and negativities, using multi-copy setups and beam splitters, advancing quantum simulation capabilities.

Contribution

It introduces protocols for measuring fermionic entanglement properties with multi-copy experiments, extending entanglement measurement techniques beyond bosonic systems.

Findings

Protocols for measuring fermionic entanglement entropies and negativities.

Simulation of entanglement growth after a local quench.

Potential for quantum simulations on nontrivial spin manifolds.

Abstract

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.