Nonsignaling Deterministic Models for Nonlocal Correlations have to 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 nonlocality on a device-independent scenario. That is, we study pairs of nonlocal boxes that produce their outputs deterministically. It is known that, for these boxes to be nonlocal, at least one of the boxes' outputs 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 that, with the sole knowledge of any upper bound on the time complexity of such an algorithm, extracts that hidden signaling and uses it for the communication of information.