Figure 1: Suppression law for Fock states in a Fourier interferometer.

Conceptual scheme of the protocol: the possible configurations of n photons at the output of an m-mode interferometer can be divided into two categories, unforbidden and forbidden, depending on whether they satisfy or not the suppression condition (2), respectively. The pie charts show the expected output statistics with different classes of particles, where green and red areas represent events with unforbidden and forbidden outputs, respectively. The injection of a cyclic Fock state (beige box) in an m-mode Fourier interferometer results in total suppression of forbidden output states. Cyclic states with distinguishable particles (blue box) show no suppression, so that each output combination is equally likely to occur. A mean field state (purple box), which reproduces some of the features of bosonic statistics, shows suppression with highly reduced contrast. Therefore, with a cyclic input the m-mode Fourier interferometer is able to discriminate, through the measurement of degree of violation , which of these three hypotheses the input state belongs to.