Analysing causal structures with entropy.

Area of Science:

• Causal Inference
• Quantum Information Theory
• Information Theory

Background:

• Determining if correlations fit a causal structure is a core challenge in causal inference.
• This problem is generally computationally intractable, necessitating methods for compatibility certificates.

Purpose of the Study:

• To review and unify entropic approaches for causal inference.
• To explore the differences between classical, quantum, and post-quantum unobserved causes using entropic analysis.
• To highlight applications in quantum cryptography for eliminating classical causes.

Main Methods:

• Review of entropic techniques for causal structure compatibility.
• Unified terminology and conceptual framework for entropic methods.
• Analysis of unobserved causes considering classical, quantum, and post-quantum scenarios.

Main Results:

• Established new connections and filled gaps in entropic causal inference.
• Demonstrated the utility of entropic analysis in differentiating causal origins.
• Highlighted the importance of distinguishing classical from quantum causes.

Conclusions:

• Entropic approaches provide valuable certificates for causal compatibility.
• The distinction between classical and quantum causes has significant implications for quantum cryptography.
• Further research is needed to address the limitations of entropic methods and open problems.