A remainder term for H\"older's inequality for matrices and quantum entropy inequalities
Mathematical Physics
2016-05-17 v1 math.MP
Abstract
We prove a sharp remainder term for H\"older's inequality for traces as a consequence of the uniform convexity properties of the Schatten trace norms. We then show how this implies a novel family of Pinsker type bounds for the quantum Renyi entropy. Finally, we show how the sharp form of the usual quantum Pinsker inequality for relative entropy may be obtained as a fairly direct consequence of uniform convexity.
Keywords
Cite
@article{arxiv.1605.04581,
title = {A remainder term for H\"older's inequality for matrices and quantum entropy inequalities},
author = {Eric A. Carlen},
journal= {arXiv preprint arXiv:1605.04581},
year = {2016}
}