All noncontextuality inequalities for the n-cycle scenario

By Mateus Araújo, Marco T'ulio Quintino, Costantino Budroni, M. T. Cunha, Adán Cabello. 2012

150 citations recorded by the source corpus.

The problem of separating classical from quantum correlations is in general intractable and has been solved explicitly only in few cases. In particular, known methods cannot provide general solutions for an arbitrary number of settings. We provide the complete characterization of the classical correlations and the corresponding maximal quantum violations for the case of n >= 4 observables X_0, ...,X_{n-1}, where each consecutive pair {X_i,X_{i+1}}, sum modulo n, is jointly measurable. This generalizes both the Clauser-Horne-Shimony-Holt and the Klyachko-Can-Binicioglu-Shumovsky scenarios, which are the simplest ones for, respectively, locality and noncontextuality. In addition, we provide explicit quantum states and settings with maximal quantum violation and minimal quantum dimension.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/a468ab98a9017ce2fa75abb95ea9cb5f00518eed

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

A Combinatorial Approach to Nonlocality and Contextuality (2012, background): “Compare [8] for the characterization of classical models in a related scenario.”
Theory-independent limits on correlations from generalized Bayesian networks (2014, background): “For a given P, the existence of ′ P is then a linear feasibility problem (studied in [2, 15]), and hence an efficiently checkable necessary condition for ∈  P (and thus also for  and ).”