Proves additivity of doubly minimized Petz Renyi mutual information for alpha in [1/2,2] and a novel duality plus additivity for the sandwiched version for alpha in [2/3, infinity] via Sion's minimax theorem.
Let X, Y, Z ∈ L(A) be positive semidefinite and such that X ≤ Y
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Doubly minimized Petz and sandwiched Renyi mutual information: Properties
Proves additivity of doubly minimized Petz Renyi mutual information for alpha in [1/2,2] and a novel duality plus additivity for the sandwiched version for alpha in [2/3, infinity] via Sion's minimax theorem.