  Quantum mass functions (QMFs), which are tightly related to decoherence
functionals, were introduced by Loeliger and Vontobel [IEEE Trans. Inf. Theory,
2017, 2020] as a generalization of probability mass functions toward modeling
quantum information processing setups in terms of factor graphs.
  Simple quantum mass functions (SQMFs) are a special class of QMFs that do not
explicitly model classical random variables. Nevertheless, classical random
variables appear implicitly in an SQMF if some marginals of the SQMF satisfy
some conditions; variables of the SQMF corresponding to these "emerging" random
variables are called classicable variables. Of particular interest are jointly
classicable variables.
  In this paper we initiate the characterization of the set of marginals given
by the collection of jointly classicable variables of a graphical model and
compare them with other concepts associated with graphical models like the sets
of realizable marginals and the local marginal polytope.
  In order to further characterize this set of marginals given by the
collection of jointly classicable variables, we generalize the CHSH inequality
based on the Pearson correlation coefficients, and thereby prove a conjecture
proposed by Pozsgay et al. A crucial feature of this inequality is its
nonlinearity, which poses difficulties in the proof.
