Causality and measurement in quantum field theory on fixed backgrounds

One aspect of causality of quantum field theory on fixed backgrounds, such as globally hyperbolic spacetimes, is that no localised intervention (e.g., a non-selective measurement of a local observable) can affect the outcome of a measurement at spacelike separation. In other words, a description of interventions in QFT needs to respect the causal structure of the background. However, despite the fact that the initial focus of algebraic quantum field theory a la Haag and Kastler was exactly on interventions (or "operations"), Sorkin's "Impossible Measurements on Quantum Fields" revealed a major shortcoming of the original description and left QFT without a framework for causal interventions and consequently without a framework capable of describing successive measurements.

In this thesis we address this shortcoming. We motivate that the structure of interventions is that of a convex time-orderable pre-factorisation algebra (ctPFA) and, for a given AQFT, we introduce ctPFAs of causal quantum channels. Using insight gained from thoroughly analysing scattering off spacetime-compact perturbations of AQFTs, we construct for every AQFT (fulfilling additivity and time-slice) a ctPFA of causal quantum channels, which equips AQFT with a framework for causal interventions.

Although we do not claim that our constructed ctPFAs are maximal, we demonstrate that they contain the emergent state-update maps of the AQFT measurement schemes introduced by Fewster and Verch and also generalisations thereof. In particular, for the example of linear real scalar fields, we show that every local observable admits causal state-update maps, which finally settles the quest for a causal measurement theory for AQFT.

Eventually, through the example of entanglement harvesting we show how causal quantum channels may be used for a fully causal implementation of relativistic quantum information protocols.