The entropic approach to causal correlations

Abstract

The existence of a global causal order between events places constraints on the correlations that parties may share. Such "causal correlations" have been the focus of recent attention, driven by the realization that some extensions of quantum mechanics may violate so-called causal inequalities. In this paper we study causal correlations from an entropic perspective, and we show how to use this framework to derive entropic causal inequalities. We consider two different ways to derive such inequalities. Firstly, we consider a method based on the causal Bayesian networks describing the causal relations between the parties. In contrast to the Bell-nonlocality scenario, where this method has previously been shown to be ineffective, we show that it leads to several interesting entropic causal inequalities. Secondly, we consider an alternative method based on counterfactual variables that has previously been used to derive entropic Bell inequalities. We compare the inequalities obtained via these two methods and discuss their violation by noncausal correlations. As an application of our approach, we derive bounds on the quantity of information - which is more naturally expressed in the entropic framework - that parties can communicate when operating in a definite causal order.

21 pages, 3 figures; updated to published version

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Cited by in corpus (13)

• Time-delocalized quantum subsystems and operations: on the existence of processes with indefinite causal structure in quantum mechanics
• Cyclic Quantum Causal Models
• On the definition and characterisation of multipartite causal (non)separability
• Experimental entanglement of temporal order
• Experimental Aspects of Indefinite Causal Order in Quantum Mechanics
• The Inflation Technique Completely Solves the Causal Compatibility Problem
• Analysing causal structures with entropy
• Genuinely Multipartite Noncausality
• Classical communication through quantum causal structures
• Composition rules for quantum processes: a no-go theorem
• Computational tools for solving a marginal problem with applications in Bell non-locality and causal modeling
• Quantum Causal Structure and Quantum Thermodynamics
• Classifying Causal Structures: Ascertaining when Classical Correlations are Constrained by Inequalities