  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 give an explicit quantum causal
inference scheme using quantum observations alone for the case of a bipartite
quantum system with measurements at two times. In this scenario there may be
combinations of temporal and spatial correlations. We derive 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 and the protocol is in that sense extremely light touch. We
prove that if there is no signalling between two subsystems, the associated
reduced state of the pseudo-density matrix cannot have negativity, regardless
of the possible presence of initial spatial correlations. We further exploit
the time asymmetry of the pseudo-density matrix to determine the temporal order
of events. The negativity and time asymmetry are used to determine
compatibility with 5 causal structures distinguished by the direction of causal
influence and whether there are initial correlations or not. The protocol
succeeds for a state with coherence undergoing a fully decohering channel,
showing that coherence in the channel is not necessary for the quantum
advantage of causal inference from observations alone.
