Some applications of matrix inequalities in R\'enyi entropy
Mathematical Physics
2016-09-26 v2 math.MP
Quantum Physics
Abstract
The R{\'e}nyi entropy is one of the important information measures that generalizes Shannon's entropy. The quantum R{\'e}nyi entropy has a fundamental role in quantum information theory, therefore, bounding this quantity is of vital importance. Another important quantity is R{\'e}nyi relative entropy on which R{\'e}nyi generalization of the conditional entropy, and mutual information are defined based. Thus, finding lower bound for R{\'e}nyi relative entropy is our goal in this paper. We use matrix inequalities to prove new bounds on the entropy of type , R{\'e}nyi entropy.
Keywords
Cite
@article{arxiv.1608.03362,
title = {Some applications of matrix inequalities in R\'enyi entropy},
author = {Hadi Reisizadeh and S. Mahmoud Manjegani},
journal= {arXiv preprint arXiv:1608.03362},
year = {2016}
}