Conditional quantum state engineering at beam splitter arrays

The generation of arbitrary single-mode quantum states from the vacuum by a lternate coherent displacement and photon adding as well as the measurement of the overlap of a signal with an arbitrarily chosen quantum state are st udied. With regard to implementations, the transformation of the quantum st ate of a traveling optical field at an array of beam splitters is considere d, using conditional measurement. Allowing for arbitrary quantum states of both the input reference modes and the output reference modes on which the measurements are performed, the setup is described within the concept of tw o-port non-unitary transformation, and the overall non-unitary transformati on operator is derived. It is shown to be a product of operators, where eac h operator is assigned to one of the beam splitters and can be expressed in terms of an s-ordered operator product, with s being determined by the bea m splitter transmittance or reflectance. As an example we discuss the gener ation of and overlap measurement with Schrodinger-cat-like states.