Contextuality and nonlocality in 'no signaling' theories

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.

22 pages. Changes to Introduction and final Commentary section. Added two tables, one to Section 5, and some new references

References in corpus (2)

• A simple test for hidden variables in spin-1 system
• Emergence of Quantum Correlations from Non-Locality Swapping

Cited by in corpus (9)

• Pentagrams and paradoxes
• What makes quantum clicks special?
• New forms of quantum value indefiniteness suggest that incompatible views on contexts are epistemic
• Faithful orthogonal representations of graphs from partition logics
• Roots and (re)sources of value (in)definiteness versus contextuality. A contribution to the Pitowsky Volume in memory of Itamar Pitowsky (1950--2010)
• A State-Dependent Noncontextuality Inequality in Algebraic Quantum Theory
• Varieties of contextuality based on probability and structural nonembeddability
• Non-classical Correlations in n-Cycle Setting
• Chromatic Quantum Contextuality