Hypergraph Theory Applied to Quantum Structures

We study the maximum possible number of edges in certain classes of hypergraphs with a given number of vertices. Our approach uses a generalized notion of a path, which need not consist solely of a sequence of vertices and may terminate in an edge. Certain hypergraphs, known as Greechie diagrams, are used to model events in quantum experiments described by orthoalgebras, orthomodular posets, and orthomodular lattices. Previous work has investigated Greechie diagrams with “many” edges. We apply our method to estimate the minimum possible size of such examples.