Conditional displacement operator for traveling fields

We show that the conditional displacement operator $\hat{U}_{CD}=\exp [\hat{b}^{\dagger}\hat{b}(\beta \hat{a}^{\dagger}-\beta ^{\ast}\hat{a})]$ acting upon an arbitrary state 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. Applications to the generation of nonclassical states and measurement of Wigner function of arbitrary states are also considered.