Preservation of a quantum Renyi relative entropy implies existence of a recovery map

Abstract

It is known that a necessary and sufficient condition for equality in the data processing inequality (DPI) for the quantum relative entropy is the existence of a recovery map. We show that equality in DPI for a sandwiched Rényi relative $\alpha$-entropy with $\alpha >1$ is also equivalent to this property. For the proof, we use an interpolating family of $L_p$-norms with respect to a state.

14 pages, no figures. Published version, minor changes. Comments welcome

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