Sharp Continuity Bounds for Entropy and Conditional Entropy
Quantum Physics
2017-01-11 v1
Abstract
The Renyi entropy plays an essential role in quantum information theory. We study the continuity estimation of the Renyi entropy. An inequality relating the Renyi entropy difference of two quantum states to their trace norm distance is derived. This inequality is shown to be tight in the sense that equality can be attained for every prescribed value of the trace norm distance. It includes the sharp Fannes inequality for von Neumann entropy as a special case.
Keywords
Cite
@article{arxiv.1701.02398,
title = {Sharp Continuity Bounds for Entropy and Conditional Entropy},
author = {Zhihua Chen and Zhihao Ma and Ismail Nikoufar and Shaoming Fei},
journal= {arXiv preprint arXiv:1701.02398},
year = {2017}
}