The lesson of causal discovery algorithms for quantum correlations: causal explanations of Bell-inequality violations require fine-tuning

Abstract

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. 4 Other work in the field of machine learning has appealed to statistical features besides CI relations, but not the features of correlations that are relevant for Bellʼs theorem. Peters et al [8] demonstrate that if one is promised an additive noise model, then features of the joint distribution can often distinguish cause from effect in the case of a distribution on a pair of variables, where there are no CI relations to guide the analysis. Other approaches have appealed to the complexity of conditional distributions [3][4][5]. 5 A defining feature of a common cause is that if the statistical dependence between two variables is to be explained entirely by a common cause, then it must be the case that conditioning on the common cause makes the variables statistically independent. As we will see, this feature is built into the framework of causal models. Statements of Reichenbachʼs principle often assert it explicitly. New J. Phys. 17 (2015) 033002 C J Wood and R W Spekkens New J. Phys. 17 (2015) 033002 C J Wood and R W Spekkens

Entanglement is Necessary for Emergent Classicality in All Physical Theories

“…In particular, they create a tension with the other major theory of the twentieth century: relativity [1]. This is most clearly illustrated by Bell's theorem [2,3], in which certain entangled states are shown to violate local realism. In this paper we ask whether entanglement is a surprising feature of nature, or whether it should be expected in any nonclassical theory?…”

The two Bellʼs theorems of John Bell

“…that the causal structure of the theory should not change under small changes in the probability distribution for the hidden variables). There is a similar argument deriving LC from signallocality, Reichenbach's Principle 25, and "no fine-tuning" [58]. + With regard to the last clause, Axiom 3 implies that as long as an event (say f ) is in the past light cone of event e, it cannot be an effect of e. Moreover, if Principle 5 is also assumed, then unless f is within the future light cone of e, it cannot be an effect of e.…”

Explaining quantum correlations through evolution of causal models

“…The fundamental implications of quantum theory shed new light on this debate. It is thought these implications may lead to new insights into the foundations of quantum theory, and possibly even quantum theories of gravity [1][2][3][4][5][6][7][8][9][10].These realizations have their roots in the EinsteinPodolski-Rosen thought experiment [11] and the fundamental theorems of Bell [12] and of Kochen and Specker [13]. A cornerstone of modern physics, Bell's theorem, rigorously excludes classical concepts of causality.…”