Contextuality and nonlocality in 'no signaling' theories

TL;DR

This paper introduces a family of 'no signaling' bipartite boxes, called KS-boxes, which exhibit a range of correlations from classical to superquantum, revealing nuanced relationships between contextuality and nonlocality.

Contribution

It defines KS-boxes motivated by the Kochen-Specker theorem, analyzing their classical, quantum, and superquantum correlations within the 'no signaling' framework.

Findings

KS-boxes can be classical in nonlocality measures despite not being classically simulatable.

Certain marginal probabilities lead to classical behavior in nonlocality tests.

KS-boxes include generalized PR-boxes that saturate Bell inequalities.

Abstract

We define a family of 'no signaling' bipartite boxes with arbitrary inputs and binary outputs, and with a range of marginal probabilities. The defining correlations are motivated by the Klyachko version of the Kochen-Specker theorem, so we call these boxes Kochen-Specker-Klyachko boxes or, briefly, KS-boxes. The marginals cover a variety of cases, from those that can be simulated classically to the superquantum correlations that saturate the Clauser-Horne-Shimony-Holt inequality, when the KS-box is a generalized PR-box (hence a vertex of the `no signaling' polytope). We show that for certain marginal probabilities a KS-box is classical with respect to nonlocality as measured by the Clauser-Horne-Shimony-Holt correlation, i.e., no better than shared randomness as a resource in simulating a PR-box, even though such KS-boxes cannot be perfectly simulated by classical or quantum resources for all inputs. We comment on the significance of these results for contextuality and nonlocality in 'no signaling' theories.