Conditional displacement operator for traveling fields

We show that the conditional displacement operator U^CD=exp[bˆ†bˆ(βaˆ†-β∗aˆ)] acting upon arbitrary states of traveling waves can be well approximated by the action of a Kerr-medium placed between two beam splitters whose respective second ports are fed by highly excited coherent states. The scheme is deterministic, since it does not employ any detection event. Applications for generation of nonclassical states and measurement of Wigner function of arbitrary states are also considered.