Conditional quantum-state transformation at a beam splitter

Using conditional measurement on a beam splitter, we study the transformati on of the quantum state of the signal mode within the concept of two-port n on-unitary transformation. Allowing for arbitrary quantum states of both th e input reference mode and the output reference mode on which the measureme nt is performed, we show that the non-unitary transformation operator can b e given in a closed form by an s-ordered operator product, where the value of s is entirely determined by the absolute value of the beam splitter refl ectance (or transmittance). The formalism generalizes previously obtained r esults which can be recovered by simple specification of the non-unitary tr ansformation operator. As an application, we consider the generation of Sch rodinger-cat-like states. An extension to mixed states and imperfect detect ion is outlined.