On Strong Converse Theorems for Quantum Hypothesis Testing and Channel Coding
Abstract
Strong converse theorems refer to the study of impossibility results in information theory. In particular, Mosonyi and Ogawa established a one-shot strong converse bound for quantum hypothesis testing [Comm. Math. Phys, 334(3), 2014], which servers as a primitive tool for establishing a variety of tight strong converse theorems in quantum information theory. In this short note, we demonstrate an alternative one-line proof for this bound via the variational expression of measured R\'enyi divergences [Lett. Math. Phys, 107(12), 2017]. Then, we show that the variational expression is a direct consequence of H\"older's inequality.
Keywords
Cite
@article{arxiv.2403.13584,
title = {On Strong Converse Theorems for Quantum Hypothesis Testing and Channel Coding},
author = {Hao-Chung Cheng and Li Gao},
journal= {arXiv preprint arXiv:2403.13584},
year = {2024}
}
Comments
one-shot strong converse bound by Mosonyi and Ogawa [arXiv:1309.3228], variational expression by Berta, Fawzi, and Tomamichel [arXiv:1512.02615]