Further results on generalized conditional entropies
Department of Theoretical Physics, Irkutsk State
University, Gagarin Bv.
Received: 7 December 2013
Accepted: 18 December 2014
We further examine some properties of the conditional Rényi and Tsallis–Havrda–Charvát (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 Rényi 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 Rényi and TCH entropies.
Mathematics Subject Classification: 94A17 / 62B10 / 39B62
Key words: Rényi entropy / Tsallis–Havrda–Charvát entropy / entropy rate / index of coincidence / error probability / Fano inequality
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