Contextuality and nonlocality in 'no signaling' theories

TitleContextuality and nonlocality in 'no signaling' theories
Publication TypeJournal Article
Year of Publication2009
AuthorsBub, J, Stairs, A
JournalFoundations of Physics
Pages690 - 711
Date Published2009/4/21

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.

Short TitleFound Phys