Further results on generalized conditional entropies

Rastegin, Alexey E.

doi:10.1051/ita/2014029

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.

Résumé

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.

Reçu le : 2013-12-07
Accepté le : 2014-12-18

MR Zbl

DOI : 10.1051/ita/2014029

Classification : 94A17, 62B10, 39B62
Mots clés : Rényi entropy, Tsallis–Havrda–Charvát entropy, entropy rate, index of coincidence, error probability, Fano inequality

Affiliations des auteurs :

Rastegin, Alexey E. ¹

¹ Department of Theoretical Physics, Irkutsk State University, Gagarin Bv. 20, 664003 Irkutsk, Russia

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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. http://www.numdam.org/articles/10.1051/ita/2014029/

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