Allen Stairs

Jarrett (1984) and Ballentine and Jarrett (1987) have argued that violations of Jarrett's locality condition are strictly forbidden by the theory of relativity. In Ballentine and Jarrett, this claim is supported by an appeal to the fact that superluminal signalling gives rise to causal paradoxes. In this paper, it is argued that if violations of locality are permitted, certain puzzles indeed arise. The result takes the form of a set of apparent "no go" theorems. However, it is argued that the results may not really show what they seem to, and that contrary to Ballentine and Jarrett, it is by no means clear that relativity forbids violations of Jarrett's locality condition.

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.

Quantum theory is a probabilistic theory that embodies notoriously striking correlations, stronger than any that classical theories allow but not as strong as those of hypothetical ‘super-quantum’ theories. This raises the question ‘Why the quantum?’—whether there is a handful of principles that account for the character of quantum probability. We ask what quantum-logical notions correspond to this investigation. This project isn’t meant to compete with the many beautiful results that information-theoretic approaches have yielded but rather aims to complement that work

I begin with an appeal to the GHZ/Mermin state to illustrate the allure of contextualism and value-definiteness. I then point out that standard contextualism, with its special status for non-degenerate operators, faces some embarrassing questions. Further, there is an alternative that apparently does not have the same problems. A modest re-pasting of Hilbert space makes the honors almost even between these two varieties. The paper closes with some reflections on the peculiarities of contextualism.