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

By Christopher J. Wood, Robert W. Spekkens. 2012

361 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Cognitive Neuroscience

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Citations in the corpus

Quantum machine learning (2016, neutral): “Furthermore, intuition of cause and eﬀect fails with quantum correlations, making causal discovery a challenge [98].”
Causal Inference via Algebraic Geometry: Feasibility Tests for Functional Causal Structures with Two Binary Observed Variables (2015, background): “6) without ﬁne-tuning [13].”
Theory-independent limits on correlations from generalized Bayesian networks (2014, methodology): “‘Leifer–Spekkens Markov’ for a GDAG and yet cannot be expressed using our tensor product form.”
Quantum common causes and quantum causal models (2016, background): “Several researchers recognized that the formalism of classical causal models could provide a unifying framework in which to pose the problem of deriving Bell-type constraints, and that this framework might be extended to address the problem of deriving constraints on the correlations that can be obt”
Rethinking Superdeterminism (2019, background): “(See [17] for an example of how this negates the problem of [15].”
The two Bellʼs theorems of John Bell (2014, background): “There is a similar argument deriving LC from signallocality, Reichenbach’s Principle 25, and “no fine-tuning” [58].”