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

Alexey E. Rastegin

Published 2010-10-07, updated 2011-06-27Version 3

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.