  The measurement statistics for spatial and temporal quantum processes are
produced through distinct mechanisms. Measurements that are space-like
separated exhibit non-signaling behavior. However, time-like separated
measurements can only result in one-way non-signaling, as the past is
independent of the future, but the opposite is not true. This work presents the
doubled density operator as a comprehensive framework for studying quantum
processes in space-time. It effectively captures all the physical information
of the process, with the measurement and Born rule showing uniformity for both
spatial and temporal cases. We demonstrate that the equal-time density operator
can be derived by performing a partial trace operation on the doubled density
operator. Furthermore, the temporality of the quantum process can be detected
by conducting a partial trace operation on either the left or right half of the
doubled density operator.
