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.

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Cited by in corpus (5)

• Quantum conditional mutual information and approximate Markov chains
• Renyi generalizations of the conditional quantum mutual information
• Operational meaning of quantum measures of recovery
• Markov Gap and Bound Entanglement in Haar Random State
• Estimating Rényi's $\alpha$-Cross-Entropies in a Matrix-Based Way