Non-signaling deterministic models for non-local correlations have to be uncomputable

TL;DR

This paper demonstrates that deterministic, non-signaling models for non-local correlations must be uncomputable, as any computable model would enable hidden signaling and communication, contradicting the non-signaling principle.

Contribution

It proves that deterministic models reproducing non-local correlations cannot be algorithmically computable without enabling hidden signaling.

Findings

Computable deterministic models imply hidden signaling.

Hidden signaling can be exploited for communication.

Non-signaling models must be uncomputable.

Abstract

Quantum mechanics postulates random outcomes. However, a model making the same output predictions but in a deterministic manner would be, in principle, experimentally indistinguishable from quantum theory. In this work we consider such models in the context of non-locality on a device independent scenario. That is, we study pairs of non-local boxes that produce their outputs deterministically. It is known that, for these boxes to be non-local, at least one of the boxes' output has to depend on the other party's input via some kind of hidden signaling. We prove that, if the deterministic mechanism is also algorithmic, there is a protocol which, with the sole knowledge of any upper bound on the time complexity of such algorithm, extracts that hidden signaling and uses it for the communication of information.