Analysing causal structures in generalised probabilistic theories

Abstract

Causal structures give us a way to understand the origin of observed correlations. These were developed for classical scenarios, but quantum mechanical experiments necessitate their generalisation. Here we study causal structures in a broad range of theories, which include both quantum and classical theory as special cases. We propose a method for analysing differences between such theories based on the so-called measurement entropy. We apply this method to several causal structures, deriving new relations that separate classical, quantum and more general theories within these causal structures. The constraints we derive for the most general theories are in a sense minimal requirements of any causal explanation in these scenarios. In addition, we make several technical contributions that give insight for the entropic analysis of quantum causal structures. In particular, we prove that for any causal structure and for any generalised probabilistic theory, the set of achievable entropy vectors form a convex cone.

11+13 pages, 5 figures, v2: new examples and additional discussion added, v3 (published version): presentation improved, v4: typos corrected, v5: error in equation (25) corrected

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Cited by in corpus (12)

• General probabilistic theories: An introduction
• Constraints on nonlocality in networks from no-signaling and independence
• A no-go theorem on the nature of the gravitational field beyond quantum theory
• Accessible fragments of generalized probabilistic theories, cone equivalence, and applications to witnessing nonclassicality
• Experimentally bounding deviations from quantum theory for a photonic three-level system using theory-agnostic tomography
• A mathematical framework for operational fine tunings
• Impossibility of superluminal signalling in Minkowski space-time does not rule out causal loops
• Relating Wigner's Friend Scenarios to Nonclassical Causal Compatibility, Monogamy Relations, and Fine Tuning
• Simulating all multipartite non-signalling channels via quasiprobabilistic mixtures of local channels in generalised probabilistic theories
• Symmetric observations without symmetric causal explanations
• Quantum causal inference in the presence of hidden common causes: An entropic approach
• Forward-backward stochastic simulations: Q-based model for measurement and Bell-nonlocality consistent with weak local realistic premises