title: Graph-theoretic approach to quantum correlations.
abstract: Correlations in Bell and noncontextuality inequalities can be expressed as a positive linear combination of probabilities of events. Exclusive events can be represented as adjacent vertices of a graph, so correlations can be associated to a subgraph. We show that the maximum value of the correlations for classical, quantum, and more general theories is the independence number, the Lovász number, and the fractional packing number of this subgraph, respectively. We also show that, for any graph, there is always a correlation experiment such that the set of quantum probabilities is exactly the Grötschel-Lovász-Schrijver theta body. This identifies these combinatorial notions as fundamental physical objects and provides a method for singling out experiments with quantum correlations on demand.
authors.affiliation: Departamento de Física Aplicada II, Universidad de Sevilla, E-41012 Sevilla, Spain.
authors.forename: Adán
authors.initials: A
authors.lastname: Cabello
authors.affiliation: Department of Computer Science, and Department of Physics and Astronomy, University College London, WC1E 6BT London, United Kingdom.
authors.forename: Simone
authors.initials: S
authors.lastname: Severini
authors.affiliation: ICREA and Física Teòrica: Informació i Fenomens Quàntics, Universitat Autònoma de Barcelona, E-08193 Bellaterra (Barcelona), Spain.
authors.forename: Andreas
authors.initials: A
authors.lastname: Winter