Analysing causal structures with entropy

Abstract

A central question for causal inference is to decide whether a set of correlations fit a given causal structure. In general, this decision problem is computationally infeasible and hence several approaches have emerged that look for certificates of compatibility. Here we review several such approaches based on entropy. We bring together the key aspects of these entropic techniques with unified terminology, filling several gaps and establishing new connections regarding their relation, all illustrated with examples. We consider cases where unobserved causes are classical, quantum and post-quantum and discuss what entropic analyses tell us about the difference. This has applications to quantum cryptography, where it can be crucial to eliminate the possibility of classical causes. We discuss the achievements and limitations of the entropic approach in comparison to other techniques and point out the main open problems.

19 (+3) pages, 5 (+1) figures. A few minor updates and corrections. There is a small error in the published version of this manuscript: the claim in the last sentence of Section 2(a)(ii) should be restricted to four variables. This is correct in the arXiv version

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• Proofs of network quantum nonlocality in continuous families of distributions
• Self-testing of physical theories, or, is quantum theory optimal with respect to some information-processing task?
• Non-Shannon inequalities in the entropy vector approach to causal structures
• Semidefinite tests for latent causal structures
• A mathematical framework for operational fine tunings
• Analysing causal structures in generalised probabilistic theories
• Impossibility of superluminal signalling in Minkowski space-time does not rule out causal loops
• Inferring Quantum Network Topology using Local Measurements
• Computational tools for solving a marginal problem with applications in Bell non-locality and causal modeling
• Analysing causal structures using Tsallis entropies
• Monogamy of Temporal Correlations: Witnessing non-Markovianity Beyond Data Processing
• On the insufficiency of entropic inequalities for detecting non-classicality in the Bell causal structure
• Classifying Causal Structures: Ascertaining when Classical Correlations are Constrained by Inequalities
• Memory attacks in network nonlocality and self-testing
• Distinguishing quantum causal scenarios with indistinguishable classical analogs: The significance of intermediate latents
• Guarantees on the structure of experimental quantum networks
• Quantum causal inference in the presence of hidden common causes: An entropic approach
• Monogamy relations for relativistically causal correlations