  A well-recognised open conceptual problem in relativistic quantum field
theory concerns the relation between measurement and causality. Naive
generalisations of quantum measurement rules can allow for superluminal
signalling ('impossible measurements'). This raises the problem of delineating
physically allowed quantum measurements and operations. We analyse this issue
in a recently proposed framework in which local measurements (in possibly
curved spacetime) are described physically by coupling the system to a probe.
We show that the state-update rule in this setting is consistent with causality
provided that the coupling between the system and probe is local. Thus, by
establishing a well-defined framework for successive measurements, we also
provide a class of physically allowed operations. Conversely, impossible
measurements can only be performed using impossible (non-local) apparatus.
