A strengthened data processing inequality for the Belavkin-Staszewski relative entropy
Abstract
In this work, we provide a strengthening of the data processing inequality for the relative entropy introduced by Belavkin and Staszewski (BS-entropy). This extends previous results by Carlen and Vershynina for the relative entropy and other standard -divergences. To this end, we provide two new equivalent conditions for the equality case of the data processing inequality for the BS-entropy. Subsequently, we extend our result to a larger class of maximal -divergences. Here, we first focus on quantum channels which are conditional expectations onto subalgebras and use the Stinespring dilation to lift our results to arbitrary quantum channels.
Keywords
Cite
@article{arxiv.1904.10768,
title = {A strengthened data processing inequality for the Belavkin-Staszewski relative entropy},
author = {Andreas Bluhm and Angela Capel},
journal= {arXiv preprint arXiv:1904.10768},
year = {2020}
}
Comments
25 pages, no figures. We managed to extend the main result from conditional expectations to arbitrary quantum channels (see Section 4 and Section 7). Added one reference