English

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 qq-entropy is generally unbounded for q>1q>1. Upper bounds on the quantum relative qq-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.

Keywords

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

R2 v1 2026-06-21T16:25:00.717Z