Partially smoothed information measures
Abstract
Smooth entropies are a tool for quantifying resource trade-offs in (quantum) information theory and cryptography. In typical bi- and multi-partite problems, however, some of the sub-systems are often left unchanged and this is not reflected by the standard smoothing of information measures over a ball of close states. We propose to smooth instead only over a ball of close states which also have some of the reduced states on the relevant sub-systems fixed. This partial smoothing of information measures naturally allows to give more refined characterizations of various information-theoretic problems in the one-shot setting. In particular, we immediately get asymptotic second-order characterizations for tasks such as privacy amplification against classical side information or classical state splitting. For quantum problems like state merging the general resource trade-off is tightly characterized by partially smoothed information measures as well.
Cite
@article{arxiv.1807.05630,
title = {Partially smoothed information measures},
author = {Anurag Anshu and Mario Berta and Rahul Jain and Marco Tomamichel},
journal= {arXiv preprint arXiv:1807.05630},
year = {2020}
}
Comments
v2: slightly improved achievability bound for classical state splitting + fixed converse proof for privacy amplification, 25 pages