Causality in relativistic quantum interactions without mediators

We analyze the interaction between two quantum systems in spacetime, and we compare two possible models to describe it: (1) a fully quantum field theoretical (QFT) description of the coupling of two quantum systems mediated by a quantum field, and (2) a quantum-controlled model (qc-model), which is an effectively relativistic direct coupling in which the interaction of two quantum systems is not mediated by a field with local quantum degrees of freedom. We show that while there are regimes where the qc-model can approximate QFT arbitrarily well, it can suffer from retrocausal effects. We discuss in what regimes those retrocausal predictions of the qc-model are non-negligible and whether they can be used to argue that gravity induced entanglement experiments can reveal genuinely quantum aspects of the gravitational interaction or not.