Abstract
We further examine some properties of the conditional Renyi and Tsallis–Havrda–Charvat (THC) entropies. Such properties are interesting from the viewpoint of applications in studying protocols of quantum information science and foundations of quantum mechanics. In particular, we consider properties of the conditional Renyi and THC entropies with respect to conditioning on more. We also exemplify that the desired property can be violated with the conditional min-entropy. Applications of such results to the TCH entropy rate are considered. Connections between generalized conditional entropies and error probability are examined. Several relations between various conditional entropies are obtained. It is shown that such relations can be used for bounding the conditional Renyi and TCH entropies.
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