  We propose an experimental scheme to implement a second-order nonlocal
superposition operation and its variants by way of Hong-Ou-Mandel interference.
The second-order coherent operations enable us to generate a NOON state with
high particle number in a heralded fashion and also can be used to enhance the
entanglement properties of continuous variable states. We discuss the
feasibility of our proposed scheme considering realistic experimental
conditions such as on-off photodetectors with nonideal efficiency and imperfect
single-photon sources.
