Allen Stairs

In a recent paper, Michael Friedman and Hilary Putnam argued that the Luders rule is ad hoc from the point of view of the Copenhagen interpretation but that it receives a natural explanation within realist quantum logic as a probability conditionalization rule. Geoffrey Hellman maintains that quantum logic cannot give a non-circular explanation of the rule, while Jeffrey Bub argues that the rule is not ad hoc within the Copenhagen interpretation. As I see it, all four are wrong. Given that there is to be a projection postulate, there are at least two natural arguments which the Copenhagen advocate can offer on behalf of the Luders rule, contrary to Friedman and Putnam. However, the argument which Bub offers is not a good one. At the same time, contrary to Hellman, quantum logic really does provide an explanation of the Luders rule, and one which is superior to that of the Copenhagen account, since it provides an understanding of why there should be a projection postulate at all

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