  Quantum retrodiction involves finding the probabilities for various
preparation events given a measurement event. This theory has been studied for
some time but mainly as an interesting concept associated with time asymmetry
in quantum mechanics. Recent interest in quantum communications and
cryptography, however, has provided retrodiction with a potential practical
application. For this purpose quantum retrodiction in open systems should be
more relevant than in closed systems isolated from the environment. In this
paper we study retrodiction in open systems and develop a general master
equation for the backward time evolution of the measured state, which can be
used for calculating preparation probabilities. We solve the master equation,
by way of example, for the driven two-level atom coupled to the electromagnetic
field.
