Causality can be defined in terms of a space-time structure or based on information-theoretic structures, which correspond to very different notions of causation. When analysing physical experiments, these notions must be put together in a compatible manner. The process matrix framework describes quantum indefinite causal structures in the information-theoretic sense, but the physicality of such processes remains an open question. At the same time, there are several experiments in Minkowski spacetime (which implies a definite spacetime notion of causality) that claim to have implemented indefinite information-theoretic causal structures, suggesting an apparent tension between these notions. To address this, we develop a general framework that disentangles these two notions and characterises their compatibility in scenarios where quantum systems may be delocalised over a spacetime. The framework first describes a composition of quantum maps through feedback loops, and then the embedding of the resulting (possibly cyclic) signalling structure in an acyclic spacetime. Relativistic causality then corresponds to the compatibility of the two notions of causation. We reformulate the process matrix framework here and derive a number of no-go results for physical implementations of process matrices in a spacetime. These reveal that it is impossible to physically implement indefinite causal order processes with spacetime localised systems, and also characterise the degree to which they must be delocalised. Further, we show that any physical implementation of an indefinite order process can ultimately be fine-grained to one that admits a fixed acyclic information-theoretic causal order that is compatible with the spacetime causal order, thus resolving the apparent paradox. Our work sheds light on the operational meaning of indefinite causal structures which we discuss in detail.
