Chain rules for quantum channels
Quantum Physics
2024-05-21 v2 Information Theory
Mathematical Physics
math.IT
math.MP
Abstract
Divergence chain rules for channels relate the divergence of a pair of channel inputs to the divergence of the corresponding channel outputs. An important special case of such a rule is the data-processing inequality, which tells us that if the same channel is applied to both inputs then the divergence cannot increase. Based on direct matrix analysis methods, we derive several R\'enyi divergence chain rules for channels in the quantum setting. Our results simplify and in some cases generalise previous derivations in the literature.
Keywords
Cite
@article{arxiv.2204.11153,
title = {Chain rules for quantum channels},
author = {Mario Berta and Marco Tomamichel},
journal= {arXiv preprint arXiv:2204.11153},
year = {2024}
}
Comments
v2: 6 pages, technical note, will appear at IEEE International Symposium on Information Theory 2022, final version with updated references