  We study under what circumstances a separable bipartite system A-B can or
cannot become entangled through local interactions with a bi-local entangled
source $\text{S}_1$-$\text{S}_2$. We obtain constraints on the general forms of
the interaction Hamiltonians coupling A with $\text{S}_1$ and B with
$\text{S}_2$ necessary for A and B to become entangled. We are able to
generalize and provide non-perturbative insight on several previous no-go
theorems of entanglement harvesting from quantum fields using these general
results. We also discuss the role of communication in the process of
entanglement extraction, establishing a distinction between genuine
entanglement extraction and communication-assisted entanglement generation.
