Upper continuity bounds on the relative $q$-entropy for $q>1$

Details Upper continuity bounds on the relative $q$-entropy for $q>1$ Upper continuity bounds on the relative $q$-entropy for $q>1$

2010-10-07

arxiv.org/abs/1010.1335v3

J. Math. Phys. 52, 062203 (2011)

Physics

Mathematical Physics

7 pages, no figures. The statements and the proofs from Section III are corrected. The results of Section IV are improved. App

Scientific paper

10.1063/1.3600535

Generalized entropies and relative entropies are the subject of active research. Similar to the standard relative entropy, the relative $q$-entropy is generally unbounded for $q>1$. Upper bounds on the quantum relative $q$-entropy in terms of norm distances between its arguments are obtained in finite-dimensional context. These bounds characterize a continuity property in the sense of Fannes.

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