  Is is shown here that the "simple test of quantumness for a single system" of
arXiv:0704.1962 (for a recent experimental realization see arXiv:0804.1646) has
exactly the same relation to the discussion of to the problem of describing the
quantum system via a classical probabilistic scheme (that is in terms of hidden
variables, or within a realistic theory) as the von Neumann theorem (1932). The
latter one was shown by Bell (1966) to stem from an assumption that the hidden
variable values for a sum of two non-commuting observables (which is an
observable too) have to be, for each individual system, equal to sums of
eigenvalues of the two operators. One cannot find a physical justification for
such an assumption to hold for non-commeasurable variables. On the positive
side. the criterion may be useful in rejecting models which are based on
stochastic classical fields. Nevertheless the example used by the Authors has a
classical optical realization.
