  The symmetrization postulate in quantum mechanics is formally reflected in
the appearance of an exchange phase ruling the symmetry of identical particle
global states under particle swapping. Many indirect measurements of this
fundamental phase have been reported so far, while a direct observation has
been only recently achieved for photons. Here we propose a general scheme
capable to directly measure the exchange phase of any type of particles
(bosons, fermions, anyons), exploiting the operational framework of spatially
localized operations and classical communication. We experimentally implement
it in an all-optical platform providing proof-of-principle for different
simulated exchange phases. As a byproduct, we supply a direct measurement of
the real bosonic exchange phase of photons. Also, we analyze the performance of
the proposed scheme when mixtures of particles of different nature are
injected. Our results confirm the symmetrization tenet and provide a tool to
explore it in various scenarios.
