We reappraise some of the hybrid classical-quantum models proposed in the
literature with the goal of retrieving some of their common characteristics. In
particular, first, we analyze in detail the Peres-Terno argument regarding the
inconsistency of hybrid quantizations of the Sudarshan type. We show that to
accept such hybrid formalism entails the necessity of dealing with additional
degrees of freedom beyond those in the straight complete quantization of the
system. Second, we recover a similar enlargement of degrees of freedom in the
so-called statistical hybrid models. Finally, we use Wigner's quantization of a
simple model to illustrate how in hybrid systems the subsystems are never
purely classical or quantum. A certain degree of quantumness (classicality) is
being exchanged between the different sectors of the theory, which in this
particular unphysical toy model makes them undistinguishable.Comment: 13 pages, 3 figures (minor changes to match the published version
