Linear optics and projective measurements alone suffice to create large-photon-number path entanglement

We propose a method for preparing maximal path entanglement with a definite photon-number N, larger than two, using projective measurements. In contrast with the previously known schemes, our method uses only linear optics. Specifically, we exhibit a way of generating four-photon, path-entangled states of the form $|4,0〉+|0,4〉,$ using only four beam splitters and two detectors. These states are of major interest as a resource for quantum interferometric sensors as well as for optical quantum lithography and quantum holography.