We consider the problem of implementing a given conditional distribution relating the states of a physical system at two separate times using a physical process with (potentially time-inhomogeneous) master equation dynamics .
<clarity> We consider the problem of implementing a given conditional distribution relating the states of a physical system at two separate times using a physical process with (potentially time-inhomogeneous) master equation dynamics .
We consider the problem of how to construct a physical process over a state space X that applies some desired conditional distribution P to initial states to produce final states .