Causality and signalling in non-compact detector-field interactions
In this paper we analyze the problem of "apparent" superluminal signalling and retrocausation that can appear for particle detector models when considering non-compactly supported field-detector interactions in quantum field theory in curved spacetimes and in relativistic quantum information protocols. For this purpose, we define a signalling estimator based on an adapted version of the quantum Fisher information to perturbative regimes. This allows us to study how the internal dynamics of the detectors (for example the gap between the detector energy levels) have an impact on the ability of a particle detectors to communicate with one another. Moreover, we show that, very generally, even for detectors with infinite tails in space and time, if the tails decay exponentially, one can define an effective lightcone, outside of which signalling is negligible. This provides concrete evidence supporting the use of non-compact (but exponentially decaying) detector smearings in protocols of relativistic quantum information.