How not to Rényi-generalize the quantum conditional mutual information
Journal of Physics A: Mathematical and Theoretical
We study the relation between the quantum conditional mutual information and the quantum $\alpha$-R\'enyi divergences. Considering the totally antisymmetric state we show that it is not possible to attain a proper generalization of the quantum conditional mutual information by optimizing the distance in terms of quantum $\alpha$-R\'enyi divergences over the set of all Markov states. The failure of the approach considered arises from the observation that a small quantum conditional mutual
... ional mutual information does not imply that the state is close to a quantum Markov state.