  Quantum information, in the form of entanglement with an ancilla, can be
transmitted to a third system through interaction. Here, we investigate this
process of entanglement transmission perturbatively in time. Using the
entanglement monotone negativity, we determine how the proclivity of an
interaction to either generate, transfer or lose entanglement depends on the
choice of Hamiltonians and initial states. These three proclivities are
captured by Hamiltonian- and state-dependent quantities that we call negativity
susceptibility, negativity transmissibility and negativity vulnerability
respectively. These notions could serve, for example, as cost functions in
quantum technologies such as machine-learned quantum error correction.
