Impossible measurements require impossible apparatus

Abstract

A well-recognized open conceptual problem in relativistic quantum field theory concerns the relation between measurement and causality. Naive generalizations of quantum measurement rules can allow for superluminal signaling (``impossible measurements''). This raises the problem of delineating physically allowed quantum measurements and operations. We analyze 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 (nonlocal) apparatus.