How not to Rényi generalize the Quantum Conditional Mutual Information

Abstract

We study the relation between the quantum conditional mutual information and the quantum $\alpha$-Rényi 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 $\alpha$-Rényi divergences over the set of all Markov states. The failure of the approach considered arises from the observation that a small quantum conditional mutual information does not imply that the state is close to a quantum Markov state.

7 pages, no figures

References in corpus (3)

• Structure of states which satisfy strong subadditivity of quantum entropy with equality
• Renyi generalizations of the conditional quantum mutual information
• On some entropy inequalities

Cited by in corpus (1)

• Renyi generalizations of the conditional quantum mutual information