Understanding and characterising causal structures which posses provably non-classical features is of direct relevance for the research on quantum theory with indefinite causal order as well as for quantum gravity. Due to diffeomorphism invariance of general relativity (GR), causal structure of spacetime in GR requires an operational description â in terms of physical systems and their ability to exchange information. In quantum theory such systems can be taken as composite quantum particles, modelling ideal clocks as well as particle detectors. I will discuss how such particles allow insights into quantum causal structures by allowing us to construct quantum spacetimes and quantify non-classical features of their causal structures. Surprisingly, this approach also shows that operational means may fail to distinguish a genuine superposition of different (non-diffeomorphic) spacetimes from a single classical spacetime. This opens a question: under what conditions non-classical spacetimes can be operationally distinguished from the classical ones. |