Bell Correlations and the Common Future

Reichenbach's principle states that in a causal structure, correlations of classical information can stem from a common cause in the common past or a direct influence from one of the events in correlation to the other. The difficulty of explaining Bell correlations through a mechanism in that spirit can be read as questioning either the principle or even its basis: causality. In the former case, the principle can be replaced by its quantum version, accepting as a common cause an entangled state, leaving the phenomenon as mysterious as ever on the classical level (on which, after all, it occurs). If, more radically, the causal structure is questioned in principle, closed space-time curves may become possible that, as is argued in the present note, can give rise to non-local correlations if to-be-correlated pieces of classical information meet in the common future --- which they need to if the correlation is to be detected in the first place. The result is a view resembling Brassard and Raymond-Robichaud's parallel-lives variant of Hermann's and Everett's relative-state formalism, avoiding "multiple realities."Comment: 8 pages, 5 figure

Amortized Communication Complexity of Distributions

Consider the following general communication problem: Alice and Bob have to simulate a probabilistic function p, that with every (x, y) â X à Y associates a probability distribution on A à B. The two parties, upon receiving inputs x and y, need to output a â A, b â B in such a manner that the (a, b) pair is distributed according to p(x, y). They share randomness, and have access to a channel that allows two-way communication. Our main focus is an instance of the above problem coming from the well known EPR experiment in quantum physics. In this paper, we are concerned with the amount of communication required to simulate the EPR experiment when it is repeated in parallel a large number of times, giving rise to a notion of amortized communication complexity. In the 3-dimensional case, Toner and Bacon showed that this problem could be solved using on average 0.85 bits of communication per repetition. We show that their approach cannot go below 0.414 bits, and we give a fundamentally different technique, relying on the reverse Shannon theorem, which allows us to reduce the amortized communication to 0.28 bits for dimension 3, and 0.410 bits for arbitrary dimension. We also give a lower bound of 0.13 bits for this problem (valid for one-way protocols), and conjecture that this could be improved to match the upper bounds. In our investigation we ï¬nd interesting connections to a number of different problems in communication complexity. The results contained herein are entirely classical and no knowledge of the quantum phenomenon is assumed.info:eu-repo/semantics/publishe