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.
Accepté le :
DOI : 10.1051/ita/2014029
Mots-clés : Rényi entropy, Tsallis–Havrda–Charvát entropy, entropy rate, index of coincidence, error probability, Fano inequality
@article{ITA_2015__49_1_67_0,
author = {Rastegin, Alexey E.},
title = {Further results on generalized conditional entropies},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {67--92},
publisher = {EDP-Sciences},
volume = {49},
number = {1},
year = {2015},
doi = {10.1051/ita/2014029},
mrnumber = {3342174},
zbl = {1395.94219},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ita/2014029/}
}
TY - JOUR AU - Rastegin, Alexey E. TI - Further results on generalized conditional entropies JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2015 SP - 67 EP - 92 VL - 49 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ita/2014029/ DO - 10.1051/ita/2014029 LA - en ID - ITA_2015__49_1_67_0 ER -
%0 Journal Article %A Rastegin, Alexey E. %T Further results on generalized conditional entropies %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2015 %P 67-92 %V 49 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ita/2014029/ %R 10.1051/ita/2014029 %G en %F ITA_2015__49_1_67_0
Rastegin, Alexey E. Further results on generalized conditional entropies. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 49 (2015) no. 1, pp. 67-92. doi : 10.1051/ita/2014029. http://archive.numdam.org/articles/10.1051/ita/2014029/
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