Graph approach to quantum systems

Abstract

Using a graph approach to quantum systems, we show that descriptions of 3-dim Kochen-Specker (KS) setups as well as descriptions of 3-dim spin systems by means of Greechie diagrams (a kind of lattice) that we find in the literature are wrong. Correct lattices generated by McKay-Megill-Pavicic (MMP) hypergraphs and Hilbert subspace equations are given. To enable future exhaustive generation of 3-dim KS setups by means of our recently found stripping technique, bipartite graph generation is used to provide us with lattices with equal numbers of elements and blocks (orthogonal triples of elements)-up to 41 of them. We obtain several new results on such lattices and hypergraphs, in particular, on properties such as superposition and orthoraguesian equations. © 2010 American Institute of Physics.