All noncontextuality inequalities for the n-cycle scenario

TL;DR

This paper fully characterizes classical correlations and quantum violations in the n-cycle scenario, generalizing key nonlocality and noncontextuality cases, and provides explicit states and settings for maximal violations.

Contribution

It offers the complete set of noncontextuality inequalities for the n-cycle scenario, extending previous cases and providing explicit quantum states and measurements for maximal violations.

Findings

Complete characterization of classical correlations for n >= 4

Explicit quantum states and settings for maximal violations

Generalization of CHSH and KCBS scenarios

Abstract

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.