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arXiv · 1404.3628

How not to R\'enyi generalize the Quantum Conditional Mutual Information

Paul Erker
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Abstract

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 information does not imply that the state is close to a quantum Markov state.

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Paul Erker. 2014-04-14. How not to R\'enyi generalize the Quantum Conditional Mutual Information. https://doi.org/10.1088/1751-8113/48/27/275303

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