  We consider how to tell the time-ordering associated with measurement data
from quantum experiments at two times and any number of qubits. We define an
arrow of time inference problem. We consider conditions on the initial and
final states that are symmetric or asymmetric under time reversal. We represent
the spatiotemporal measurement data via the pseudo density matrix space-time
state. There is a forward process which is CPTP and a reverse process which is
obtained via a novel recovery map based on inverting unitary dilations. For
asymmetric conditions, the protocol determines whether the data is consistent
with the unitary dilation recovery map or the CPTP map. For symmetric
conditions, the recovery map yields a valid CPTP map and the experiment may
have taken place in either direction. We also discuss adapting the approach to
the Leifer-Spekkens or Process matrix space-time states.
