Robust generation of N-partite N-level singlet states by identical particle interferometry

We propose an interferometric scheme for generating the totally antisymmetric state of N identical bosons with N internal levels (generalized singlet). This state is a resource for various problems with dramatic quantum advantage. The procedure uses a sequence of Fourier multi-ports, combined with coincidence measurements filtering the results. Successful preparation of the generalized singlet is confirmed when the N particles of the input state stay separate (anti-bunch) on each multiport. The scheme is robust to local lossless noise and works even with a totally mixed input state.