Quantum correlations in space-time encapsulate the most defining aspects of quantum physics. The dual of the spatial and temporal perspectives are bind with a one-to-one correspondence between bipartite quantum states and quantum channels. Consequently, causal relations between quantum events can sometimes be inferred solely from correlation statistics, apparently contradicting the classical\textit {credo},correlation does not imply causation'[1-6]. However, since the spatial-temporal duality does not imply a full symmetry of measurement statistics between the two domains [7], the extent to which correlation alone identifies quantum causality ponders inquiry vital for both fundamental and practical interests. Here, demonstrating a unified geometrical representation of spatial-temporal quantum correlation, we show that certain non-unital channels create temporal correlation without spatial analogue and break the spatial-temporal symmetry. By implementing such channels in a photonic architecture, we observe this asymmetry and classify quantum correlations using a distance criterion, thus bringing empirical insight into causal inference in quantum mechanics.