For all alpha in [1/2, infinity], the regularized alpha-Renyi divergence from a bipartite state to the set of extensions of a fixed marginal equals the marginal divergence, and the measured version lies between the measured and standard marginal divergences.
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Uhlmann's theorem for relative entropies
For all alpha in [1/2, infinity], the regularized alpha-Renyi divergence from a bipartite state to the set of extensions of a fixed marginal equals the marginal divergence, and the measured version lies between the measured and standard marginal divergences.