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.

29 pages, 28 figs. New in v2: a section presenting in detail our characterization of Bell's theorem as a contradiction arising from (i) the framework of causal models, (ii) the principle of no fine-tuning, and (iii) certain operational features of quantum theory; a section explaining why a denial of hidden variables affords even fewer opportunities for causal explanations of quantum correlations

References in corpus (9)

• The Communication Cost of Simulating Bell Correlations
• Quantum-Bayesian Coherence: The No-Nonsense Version
• Beyond Bell's Theorem: Correlation Scenarios
• Causal Discovery with Continuous Additive Noise Models
• Quantum Graphical Models and Belief Propagation
• Against `Realism'
• A minimalist pilot-wave model for quantum electrodynamics
• Black Holes, Information Loss, and Hidden Variables
• New directions in Background Independent Quantum Gravity

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• Superdeterminism: A Guide for the Perplexed
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• A Unifying Framework for Spatial and Temporal Quantum Correlations
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• Quantifying causal influences in the presence of a quantum common cause
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• Causation does not explain contextuality
• Contextuality without incompatibility
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• Analysing causal structures with entropy
• Supermeasured: Violating Bell-Statistical Independence without violating physical statistical independence
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• Postquantum common-cause channels: the resource theory of local operations and shared entanglement
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• The device-independent outlook on quantum physics (lecture notes on the power of Bell's theorem)
• The Construction Interpretation: Conceptual Roads to Quantum Gravity
• The entropic approach to causal correlations
• Which causal structures might support a quantum-classical gap?
• Quantifying EPR: the resource theory of nonclassicality of common-cause assemblages
• Semidefinite tests for latent causal structures
• Measurement-dependence cost for Bell nonlocality: causal vs retrocausal models
• Indistinguishability of causal relations from limited marginals
• Quantum violation of local causality in urban network with hybrid photonic technologies
• Nonlocal quantum information transfer without superluminal signalling and communication
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• A general framework for cyclic and fine-tuned causal models and their compatibility with space-time
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• Embedding cyclic information-theoretic structures in acyclic spacetimes: no-go results for indefinite causality
• A local $\psi$-epistemic retrocausal hidden-variable model of Bell correlations with wavefunctions in physical space
• Testing quantum theory by generalizing noncontextuality
• Impossibility of superluminal signalling in Minkowski space-time does not rule out causal loops
• Quantum Nonlocality: how does Nature do it?
• Quantum Causal Unravelling
• The resource theory of nonclassicality of channel assemblages
• Superdeterministic hidden-variables models I: nonequilibrium and signalling
• Contextuality, Fine-Tuning, and Teleological Explanation
• Inability of the entropy vector method to certify nonclassicality in linelike causal structures
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• Causality - Complexity - Consistency: Can Space-Time Be Based on Logic and Computation?
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• Are Retrocausal Accounts of Entanglement Unnaturally Fine-Tuned?
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• Multistage games and Bell scenarios with communication
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• Extending the fair sampling assumption using causal diagrams
• A general quantum circuit framework for Extended Wigner's Friend Scenarios: logically and causally consistent reasoning without absolute measurement events
• $p$-adic Distance, Finite Precision and Emergent Superdeterminism: A Number-Theoretic Consistent-Histories Approach to Local Quantum Realism
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• Conservation of correlation in measurement underlying the violation of Bell inequalities and a game of joint mapping
• Counterfactual quantum measurements
• Fully quantum inflation: quantum marginal problem constraints in the service of causal inference
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• Forward-backward stochastic simulations: Q-based model for measurement and Bell-nonlocality consistent with weak local realistic premises
• The standard no-signalling constraints in Bell scenarios are neither sufficient nor necessary for preventing superluminal signalling with general interventions
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