Circuit locality from relativistic locality in scalar field mediated entanglement

Locality is a central notion in modern physics, but different disciplines understand it in different ways. Quantum field theory focuses on relativistic locality, based on spacetime regions, while quantum information theory focuses circuit locality, based on the notion of subsystems. Here, we investigate how spacetime and subsystem locality are related in the context of systems getting entangled while interacting via a scalar field. We show how, when the systems are put in a quantum-controlled superposition of localised states, relativistic locality (in the form of microcausality) gives rise to a specific kind of circuit. The relation between these forms of locality is relevant for understanding whether it is possible to formulate quantum field theory in quantum circuit language, and has bearing on the recent discussions on low-energy tests of quantum gravity.