Macroscopic distinguishability and scalability of N-mode field states

We compare the global properties of different types of N-mode states and discuss their distinguishability in the macroscopic limit N >> 1 by using the collective Wigner function, which is obtained by averaging over all the individual modes. It is shown that factorized N-mode states with a concentration of photons in a few modes are asymptotically indistinguishable from their symmetrized (i.e., highly correlated) counterparts in the case of collective measurements. In contrast, the collective properties of states with intermode distributed excitations are very different when compared to their symmetrized versions. We also discuss a class of scalable states for which the functional form of the collective Wigner function does not depend on the number of field modes, and we present results for the negativity of the collective Wigner function, for which in the macroscopic limit some states lose negativity and some do not.