Upper continuity bounds on the relative $q$-entropy for $q>1$
Mathematical Physics
2011-06-28 v3 math.MP
Quantum Physics
Abstract
Generalized entropies and relative entropies are the subject of active research. Similar to the standard relative entropy, the relative -entropy is generally unbounded for . Upper bounds on the quantum relative -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.
Cite
@article{arxiv.1010.1335,
title = {Upper continuity bounds on the relative $q$-entropy for $q>1$},
author = {Alexey E. Rastegin},
journal= {arXiv preprint arXiv:1010.1335},
year = {2011}
}
Comments
7 pages, no figures. The statements and the proofs from Section III are corrected. The results of Section IV are improved. Appendix A has been excluded