Entanglement preparation using symmetric multiports

We investigate the entanglement produced by a multi-path interferometer that is composed of two symmetric multiports, with phase shifts applied to the output of the first multiport. Particular attention is paid to the case when we have a single photon entering the interferometer. For this situation we derive a simple condition that characterizes the types of entanglement that one can generate. We then show how one can use the results from the single-photon case to determine what kinds of multi-photon entangled states one can prepare using the interferometer.