Quantum Causal Inference with Extremely Light Touch

We consider the quantum version of inferring the causal relation between events. There has been recent progress towards identifying minimal interventions and observations needed. We here show, by means of constructing an explicit scheme, that quantum observations alone are sufficient for quantum causal inference for the case of a bipartite quantum system with measurements at two times. Our scheme involves the derivation of a closed-form expression for the space-time pseudo-density matrix associated with many times and qubits. This matrix can be determined by coarse-grained quantum observations alone. We show that from this matrix one can infer the causal structure via the sign of a particular function called a causal monotone. Our results show that for quantum processes one can infer the causal structure solely from correlations between observations at different times.