No Rényi-type divergence obeying DPI, tensor additivity and matched cq conditioning admits a universal off-diagonal quantum focusing inequality.
Preservation of a quantum Renyi relative entropy implies existence of a recovery map
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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 R\'enyi 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.
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No off-diagonal quantum focusing for R\'enyi divergences
No Rényi-type divergence obeying DPI, tensor additivity and matched cq conditioning admits a universal off-diagonal quantum focusing inequality.