Probing quantum causality with geometric asymmetry in spatial-temporal correlations

Causation promotes the understanding of correlation to an advanced stage by elucidating its underlying mechanism. Although statisticians have specified the possible causal relations among correlations, inferring causal structures is impossible from only the observed correlations in the classical world. Quantum correlations encapsulating the most defining aspects of quantum physics have taken a new turn for the causal inference problem — the two-point spatial and temporal quantum correlations with observationally discernible characteristics correspond exactly to the two most basic causal structures. However, a direct causal interpretation for quantum correlations has only been established in very limited cases. Here, we explore to what extent quantum correlations promote causal inference. Theoretically, we have found that the distinguishable causal regime of two-point Pauli correlations can be expanded from a single value to an asymmetric interval, and the causal structures determining the quantum correlations can be interpreted by a simple distance criterion. Experimentally, we have devised and implemented a versatile non-unital quantum channel in an optical architecture to directly observe such an asymmetric interval. The setup enabled quantum causal inference without any requirement of active intervention, which is impossible in the classical realm. Our work facilitates the identification of causal links among quantum variables and provides insight into characterizing causation and spatial-temporal correlation in quantum mechanics.