Structure of Quantum Theory

In quantum field theory (QFT) there are currently two proposals to model local operations. One of them relies on an explicit characterization of all "causal" QFT instruments that do not allow superluminal communication. The other one is the Fewster-Verch framework, which implicitly defines a set of QFT instruments by analogy with non-relativistic measurement theory. FV instruments were quickly shown to be causal, and most people (me included) believed that both sets of instruments were actually the same.
But we were wrong. Using ideas from quantum nonlocality, in this paper (https://arxiv.org/abs/2607.12976) we find that the causal set is actually larger than the FV set; in fact, it contains quantum channels that would allow two space-like separated parties to violate basic physical principles, like information causality. Exploiting the connection with non-locality a bit more, we show that approximately characterizing the set of FV-realizable instruments is impossible: otherwise, one could solve the problem of approximately computing the quantum value of a non-local game, which we now know it's undecidable. This is an unexpected application of tools from quantum nonlocality in algebraic QFT.