Bell's theorem in an indeterministic universe

Menas C. Kafatos

Michaël Esfeld

K Sujan, Ravi Kunjwal

The study of quantum correlations is central to quantum information and foundations. The paradigmatic case of Bell scenarios considers product measurements implemented on a multipartite state. The more general case of contextuality scenarios--where the measurements do not have to be of product form or even on a composite system--has been studied for the case of projective measurements. While it is known that in any Bell scenario extremal indeterministic correlations (e.g., Popescu-Rohrlich or PR boxes) are unachievable quantumly, the case of general contextuality scenarios has remained open. Here we study quantum realizations of extremal correlations in arbitrary contextuality scenarios and prove that, for all such scenarios, no extremal indeterministic correlation can be achieved using projective quantum measurements, i.e., there exists no quantum state and no set of projective measurements, for any contextuality scenario, that can achieve such correlations. This no-go result follows as a corollary of a more general no-go theorem that holds when the most general set of quantum measurements (i.e., positive operator-valued measures, or POVMs) is taken into account. This general no-go theorem entails that no non-trivial quantum realization of an extremal indeterministic correlation exists, i.e., any "quantum" realization must be simulable by classical randomness. We discuss implications of this no-go theorem and the open questions it raises.

Reinhold A. Bertlmann

Eric G. Cavalcanti

In the early stages of the famous debates between Einstein and Bohr on the foundations of quantum mechanics, Einstein attempted to devise thought experiments aiming at showing that arbitrarily accurate predictions of incompatible physical quantities was possible, in violation of Heisenberg's uncertainty principle. Bohr was able to defend quantum mechanics from those attacks by showing that a careful application of the uncertainty principle to the experimental apparata as well as the measured system lead to consistent results. Could Bohr have given an independent argument for the irreducible unpredictability implied by the uncertainty principle? The celebrated 1964 theorem of John Bell shows that no model that reproduces the predictions of quantum mechanics can simultaneously satisfy the ontological concepts of locality and determinism. However, nothing can be concluded from Bell's theorem alone about locality by itself or determinism by itself--it is possible to reproduce quantum-mechanical predictions with deterministic models which violate locality as well as indeterministic models which satisfy locality. On the other hand, there's almost universal agreement that the epistemic form of locality--signal locality, or the impossibility of faster-than-light communication--must hold in a relativistic universe. By making a similar distinction between determinism and the epistemic concept of predictability, I show that signal locality plus the bare observed phenomena of Bell inequality violations lead to the remarkable conclusion that Nature is fundamentally unpredictable. This result grounds the quantum-mechanical prohibition of arbitrarily accurate predictions on the principle of relativity, regardless of any postulates of quantum mechanics.