  Nonclassicality cannot be a single-observable property since the statistics
of any quantum observable is compatible with classical physics. We develop a
general procedure to reveal nonclassical behavior from the joint measurement of
multiple observables. This requires enlarged spaces and couplings with
auxiliary degrees of freedom so it must be followed by an inversion procedure
to infer system properties from the observed statistics. In particular this
discloses nonclassical properties of standard examples of classical-like
behavior, such as SU(2) and Glauber coherent states. Moreover, when combined
with other criteria it would imply that every quantum state would be
nonclassical.
