Generability of most causal channels via realistic QFT interactions

Determine whether most causal quantum channels on local algebras in algebraic quantum field theory cannot be implemented by interactions between realistic quantum fields—namely, unitary evolutions generated by self-adjoint interaction operators arising from standard coupling constructions—or whether existing and yet-to-be-developed explicit coupling models can realize a substantially larger subset of causal channels than currently demonstrated.

Background

The paper proves that causal channels are topologically rare: the set of causal normal local channels is nowhere dense in the set of all normal local channels, and the set of causal unitaries is meagre in the set of local unitaries. It also shows that unbounded self-adjoint operators generating causal unitaries form a nowhere dense subset among self-adjoint generators, which is significant because many concrete QFT measurement models rely on unbounded interaction generators.

These findings raise a practical question about realizability: most explicit measurement and coupling models in QFT (e.g., in the Fewster–Verch framework or detector-based approaches) use unbounded interactions such as field couplings. If causal-unitary generators arising from such interactions form only a nowhere dense set, either most causal channels cannot be implemented via realistic QFT interactions, or new coupling/measurement constructions are needed to realize a larger class of causal channels.