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Quantum mass functions (QMFs), which are tightly related to decoherencefunctionals, were introduced by Loeliger and Vontobel [IEEE Trans. Inf. Theory,2017, 2020] as a generalization of probability mass functions toward modelingquantum information processing setups in terms of factor graphs.  Simple quantum mass functions (SQMFs) are a special class of QMFs that do notexplicitly model classical random variables. Nevertheless, classical randomvariables appear implicitly in an SQMF if some marginals of the SQMF satisfysome conditions; variables of the SQMF corresponding to these "emerging" randomvariables are called classicable variables. Of particular interest are jointlyclassicable variables.  In this paper we initiate the characterization of the set of marginals givenby the collection of jointly classicable variables of a graphical model andcompare them with other concepts associated with graphical models like the setsof realizable marginals and the local marginal polytope.  In order to further characterize this set of marginals given by thecollection of jointly classicable variables, we generalize the CHSH inequalitybased on the Pearson correlation coefficients, and thereby prove a conjectureproposed by Pozsgay et al. A crucial feature of this inequality is itsnonlinearity, which poses difficulties in the proof.

Sets of Marginals and Pearson-Correlation-based CHSH Inequalities for a Two-Qubit System