2010/10/11 by Adan Cabello, Adán Cabello, Cabello, Adan +4 · 10 citations
Computer Science · Physics and Astronomy · #Computability, Logic, AI Algorithms #Computational Drug Discovery Methods #FOS: Physical sciences #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.1010.2163
REVTeX4-1, 8 pages
arxiv created 2010/10/11 · openalex publication_date 2010/10/11 · arxiv updated 2010/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the noncontextual inequality proposed by Klyachko et al. [Phys. Rev. Lett. 101, 020403 (2008)] belongs to a broader family of inequalities, one associated to each compatibility structure of a set of events (a graph), and its independence number. These have the surprising property that the maximum quantum violation is given by the Lovasz theta-function of the graph, which was originally proposed as an upper bound on its Shannon capacity. Furthermore, probabilistic theories beyond quantum mechanics may have an even larger violation, which is given by the so-called fractional packing number. We discuss in detail, and compare, the sets of probability distributions attainable by noncontextual, quantum, and generalized models; the latter two are shown to have semidefinite and linear characterizations, respectively. The implications for Bell inequalities, which are examples of noncontextual inequalities, are discussed. In particular, we show that every Bell inequality can be recast as a noncontextual inequality a la Klyachko et al.