General no-go theorem for entanglement extraction

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.

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