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Strong Constraints on Models that Explain the Violation of Bell Inequalities with Hidden Superluminal Influences

Valerio Scarani, Jean-Daniel Bancal, Antoine Suárez, Nicolas Gisin

Published Jan 1, 2014• 33 citations
OpenAlex

Abstract

We discuss models that attempt to provide an explanation for the violation of Bell inequalities at a distance in terms of hidden influences.These models reproduce the quantum correlations in most situations, but are restricted to produce local correlations in some configurations.The argument presented in (Bancal et al.Nat Phys 8:867, 2012) applies to all of these models, which can thus be proved to allow for faster-than-light communication.In other words, the signalling character of these models cannot remain hidden.

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Strong Constraints on Models that Explain the Violation of Bell Inequalities with Hidden Superluminal Influences

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It is one of the most remarkable features of quantum physics that measurements on spatially separated systems cannot always be described by a locally causal theory. In such a theory, the outcomes of local measurements are determined in advance solely by some unknown (or hidden) variables and the choice of local measurements. Correlations that are allowed within the framework of a locally causal theory are termed classical. Typically, the fact that quantum mechanics does not always result in classical correlations is revealed by the violation of Bell inequalities, which are constraints that have to be satisfied by any classical correlations. It has been known for a long time that entanglement is necessary to demonstrate nonclassical correlations, and hence a Bell inequality violation. However, since some entangled quantum states are known to admit explicit locally causal models, the exact role of entanglement in Bell inequality violation has remained obscure. This thesis provides both a comprehensive review on these issues as well as a report on new discoveries made to clarify the relationship between entanglement and Bell inequality violation.

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Since Bell's theorem, it is known that quantum correlations cannot be described by local variables (LV) alone: if one does not want to abandon classical mechanisms for correlations, a superluminal form of communication among the particles must be postulated. A natural question is whether such a postulate would imply the possibility of superluminal signaling. Here we show that the assumption of finite-speed superluminal communication indeed leads to signaling when no LV are present, and more generally when only LV derivable from quantum statistics are allowed. When the most general LV are allowed, we prove in a specific case that the model can be made again consistent with relativity, but the question remains open in general.

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We discuss models that attempt to provide an explanation for the violation of Bell inequalities at a distance in terms of hidden influences.These models reproduce the quantum correlations in most situations, but are restricted to produce local correlations in some configurations.The argument presented in (Bancal et al.Nat Phys 8:867, 2012) applies to all of these models, which can thus be proved to allow for faster-than-light communication.In other words, the signalling character of these models cannot remain hidden.
Abstract Relativistic invariance is a physical law verified in several domains of physics. The impossibility of faster than light influences is not questioned by quantum theory. In quantum electrodynamics, in quantum field theory and in the standard model relativistic invariance is incorporated by construction. Quantum mechanics predicts strong long range correlations between outcomes of spin projection measurements performed in distant laboratories. In spite of these strong correlations marginal probability distributions should not depend on what was measured in the other laboratory what is called shortly: non-signalling. In several experiments, performed to test various Bell-type inequalities, some unexplained dependence of empirical marginal probability distributions on distant settings was observed. In this paper we demonstrate how a particular identification and selection procedure of paired distant outcomes is the most probable cause for this apparent violation of no-signalling principle. Thus this unexpected setting dependence does not prove the existence of superluminal influences and Einsteinian no-signalling principle has to be tested differently in dedicated experiments. We propose a detailed protocol telling how such experiments should be designed in order to be conclusive. We also explain how magical quantum correlations may be explained in a locally causal way.
An active area of research in the fields of machine learning and statistics is the development of causal discovery algorithms , the purpose of which is to infer the causal relations that hold among a set of variables from the correlations that these exhibit . We apply some of these algorithms to the correlations that arise for entangled quantum systems. We show that they cannot distinguish correlations that satisfy Bell inequalities from correlations that violate Bell inequalities, and consequently that they cannot do justice to the challenges of explaining certain quantum correlations causally. Nonetheless, by adapting the conceptual tools of causal inference, we can show that any attempt to provide a causal explanation of nonsignalling correlations that violate a Bell inequality must contradict a core principle of these algorithms, namely, that an observed statistical independence between variables should not be explained by fine-tuning of the causal parameters. In particular, we demonstrate the need for such fine-tuning for most of the causal mechanisms that have been proposed to underlie Bell correlations, including superluminal causal influences, superdeterminism (that is, a denial of freedom of choice of settings), and retrocausal influences which do not introduce causal cycles.
It is one of the most remarkable features of quantum physics that measurements on spatially separated systems cannot always be described by a locally causal theory. In such a theory, the outcomes of local measurements are determined in advance solely by some unknown (or hidden) variables and the choice of local measurements. Correlations that are allowed within the framework of a locally causal theory are termed classical. Typically, the fact that quantum mechanics does not always result in classical correlations is revealed by the violation of Bell inequalities, which are constraints that have to be satisfied by any classical correlations. It has been known for a long time that entanglement is necessary to demonstrate nonclassical correlations, and hence a Bell inequality violation. However, since some entangled quantum states are known to admit explicit locally causal models, the exact role of entanglement in Bell inequality violation has remained obscure. This thesis provides both a comprehensive review on these issues as well as a report on new discoveries made to clarify the relationship between entanglement and Bell inequality violation.
Since Bell's theorem, it is known that quantum correlations cannot be described by local variables (LV) alone: if one does not want to abandon classical mechanisms for correlations, a superluminal form of communication among the particles must be postulated. A natural question is whether such a postulate would imply the possibility of superluminal signaling. Here we show that the assumption of finite-speed superluminal communication indeed leads to signaling when no LV are present, and more generally when only LV derivable from quantum statistics are allowed. When the most general LV are allowed, we prove in a specific case that the model can be made again consistent with relativity, but the question remains open in general.