  Although it has been known for some time that quantum mechanics can be
formulated in a way that treats prediction and retrodiction on an equal
footing, most attention in engineering quantum states has been devoted to
predictive states, that is, states associated with the a preparation event.
Retrodictive states, which are associated with a measurement event and
propagate backwards in time, are also useful, however. In this paper we show
how any retrodictive state of light that can be written to a good approximation
as a finite superposition of photon number states can be generated by an
optical multiport device. The composition of the state is adjusted by
controlling predictive coherent input states. We show how the probability of
successful state generation can be optimised by adjusting the multiport device
and also examine a versatile configuration that is useful for generating a
range of states.
