Continuity estimates on the Tsallis relative entropy

Details Continuity estimates on the Tsallis relative entropy Continuity estimates on the Tsallis relative entropy

2011-02-25

arxiv.org/abs/1102.5154v2

Physics

Mathematical Physics

11 pages, no figures. New section, which presents a consequence of the monotonicity of the quantum f-divergence, is added. The

Scientific paper

Continuity properties of the Tsallis relative entropy are examined. The monotonicity of the quantum $f$-divergence leads to a consequence which is ready for estimating this measure from below. For order $\alpha\in(0;1)$, a family of lower continuity bounds of Pinsker type is obtained. For $\alpha>1$ and the commutative case, upper continuity bounds on the relative entropy in terms of the minimal probability in its second argument are derived. Both the lower and upper bounds presented are reformulated for the case of R\'{e}nyi's entropies. The Fano inequality is extended to Tsallis' entropies for all $\alpha>0$. The deduced bounds on the Tsallis conditional entropy are used for obtaining inequalities of Fannes type.

Affiliated with

Also associated with

No associations

Rating

Continuity estimates on the Tsallis relative entropy does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Continuity estimates on the Tsallis relative entropy, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Continuity estimates on the Tsallis relative entropy will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-709390