Generalized measurements by linear elements

I give a first characterization of the class of generalized measurements that can be exactly realized on a pair of qudits encoded in indistinguishable particles, by using only linear elements and particle detectors. Two immediate results follow from this characterization. (i) The Schmidt number of each element in the positive operator valued measure cannot exceed the number of initial particles. This rules out any possibility of performing perfect Bell measurements for qudits. (ii) The maximum probability of performing a generalized incomplete Bell measurement is one-half.