Geodesic
Further results on generalized conditional entropies
Rastegin, Alexey E.1
1 Department of Theoretical Physics, Irkutsk State University, Gagarin Bv. 20, 664003 Irkutsk, Russia
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 49 (2015) no. 1, pp. 67-92

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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.

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DOI : 10.1051/ita/2014029
Classification : 94A17, 62B10, 39B62
Keywords: Rényi entropy, Tsallis–Havrda–Charvát entropy, entropy rate, index of coincidence, error probability, Fano inequality

Rastegin, Alexey E. 1

1 Department of Theoretical Physics, Irkutsk State University, Gagarin Bv. 20, 664003 Irkutsk, Russia 
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     title = {Further results on generalized conditional entropies},
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     pages = {67--92},
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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

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