Graph-theoretic approach to quantum correlations

Adán Cabello, Simone Severini, Andreas Winter

Research output: Contribution to journalArticleResearchpeer-review

187 Citations (Scopus)


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. © 2014 American Physical Society.
Original languageEnglish
Article number040401
JournalPhysical Review Letters
Publication statusPublished - 27 Jan 2014


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