  Recently, Vedral and one of us proposed an entanglement-based witness of
non-classicality in systems that need not obey quantum theory, based on
constructor-information-theoretic ideas, which offers a robust foundation for
recently proposed table-top tests of non-classicality in gravity. The witness
asserts that if a mediator can entangle locally two quantum systems, then it
has to be non-classical. Hall and Reginatto claimed that there are classical
systems that can entangle two quantum systems, thus violating our proposed
witness. Here we refute that claim, explaining that the counterexample proposed
by Hall and Reginatto in fact validates the witness, vindicating the witness of
non-classicality in its full generality.
