alpha-z-relative Renyi entropies

Understand

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.