On the Concavity of Auxiliary Function in Classical-Quantum Channels
Quantum Physics
2016-10-26 v1 Information Theory
math.IT
Abstract
The auxiliary function of a classical channel appears in two fundamental quantities that upper and lower bound the error probability, respectively. A crucial property of the auxiliary function is its concavity, which leads to several important results in finite block length analysis. In this paper, we prove that the auxiliary function of a classical-quantum channel also enjoys the same concave property, extending an earlier partial result to its full generality. The key component in our proof is a beautiful result of geometric means of operators.
Cite
@article{arxiv.1602.03297,
title = {On the Concavity of Auxiliary Function in Classical-Quantum Channels},
author = {Hao-Chung Cheng and Min-Hsiu Hsieh},
journal= {arXiv preprint arXiv:1602.03297},
year = {2016}
}