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We know that in classical information theory the Shannon Entropies follow such Venn-Diagram approach to summarize its' relations and inequalities between-marginal,joint and conditional entropies.

Is there such a Venn diagram approach for Von-Neumann entropies? Is there any research being performed in this direction?

Logical Entropy: Introduction to Classical and Quantum Logical Information Theory ( pdf ) by David Ellerman

Logical information theory explains this situation since all the Shannon definitions of simple, joint, conditional and mutual information can be obtained by a uniform requantifying transformation from the corresponding logical definitions, and the transformation preserves the Venn diagram relationships.

Yes I had seen this paper. Will check it out properly. Any idea behind the crux of this article?

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