Experimental causal inference from measurements alone in the presence of spatial and temporal quantum correlations

The causal structure of a set of events specifies which events influence which others. Determining this structure, known as causal inference, is a fundamental task in science. Reset-style intervention is commonly used to determine causal structure in classical scenarios. However, in the more fundamental quantum theory, there is evidence that projective measurements alone can suffice in some cases. We here extend those cases to two systems at two times, more general channels, and from fine-grained to less invasive coarse-grained projective measurements. The measurements are implemented by scattering circuits in a nuclear magnetic resonance platform. The measurement data are analysed via the pseudo-density matrix (PDM) formalism for measurements on systems at several times, in order to determine compatibility with given causal structures. We thereby successfully demonstrate causal inference from coarse-grained measurements alone, in a scenario with several qubits and two times.