Classically, it is impossible to infer causal dependencies from the correlations between two variables alone, but in the quantum world causal relationships exist that can be completely characterized by observing the correlations between two systems.
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Chiribella, G. Good causes. Nature Phys 11, 379–380 (2015). https://doi.org/10.1038/nphys3295
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DOI: https://doi.org/10.1038/nphys3295