The U(1,1) and U(2) transformations realized by three-mode interaction in t
he respective parametric approximations are studied in conditional measurem
ent, and the corresponding non-unitary transformation operators are derived
. As an application, the preparation of single-mode quantum states using an
optical feedback loop is discussed, with special emphasis on Fock-state pr
eparation. For that example, the influence of non-perfect detection and fee
dback is also considered.