Non-signaling deterministic models for non-local 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 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.

5 pages, 2 figures

References in corpus (4)

• Significant-loophole-free test of Bell's theorem with entangled photons
• A strong loophole-free test of local realism
• The Communication Cost of Simulating Bell Correlations
• Strong Kochen-Specker theorem and incomputability of quantum randomness

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• Epistemic Horizons and the Foundations of Quantum Mechanics
• Undecidability in Physics: a Review
• Epistemic Horizons From Deterministic Laws: Lessons From a Nomic Toy Theory
• Randomness of imperfectly entangled states
• Undecidability of the spectral gap in rotationally symmetric Hamiltonians
• Impossibility of memory in hidden-signaling models for quantum correlations