Proves integer Rényi QNEC by establishing log-convexity of Kosaki L^n norms under null-translation semigroups for σ-finite von Neumann algebras with half-sided modular inclusions, assuming only finite sandwiched Rényi divergence to the vacuum.
alpha-z-relative Renyi entropies
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abstract
We consider a two-parameter family of R\'enyi relative entropies $D_{\alpha,z}(\rho||\sigma)$ that are quantum generalisations of the classical R\'enyi divergence $D_{\alpha}(p||q)$. This family includes many known relative entropies (or divergences) such as the quantum relative entropy, the recently defined quantum R\'enyi divergences, as well as the quantum R\'enyi relative entropies. All its members satisfy the quantum generalizations of R\'enyi's axioms for a divergence. We consider the range of the parameters $\alpha,z$ for which the data processing inequality holds. We also investigate a variety of limiting cases for the two parameters, obtaining explicit formulas for each one of them.
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A general proof of integer R\'enyi QNEC
Proves integer Rényi QNEC by establishing log-convexity of Kosaki L^n norms under null-translation semigroups for σ-finite von Neumann algebras with half-sided modular inclusions, assuming only finite sandwiched Rényi divergence to the vacuum.