When studying entropy functions of multivariate probability distributions,
polymatroids and matroids emerge. Entropy functions of pure multiparty quantum
states give rise to analogous notions, called here polyquantoids and quantoids.
Polymatroids and polyquantoids are related via linear mappings and duality.
Quantum secret sharing schemes that are ideal are described by selfdual
matroids. Expansions of integer polyquantoids to quantoids are studied and
linked to that of polymatroids
