Partially smoothed information measures

TL;DR

This paper introduces a new partial smoothing technique for information measures that better captures resource trade-offs in quantum information theory, leading to refined one-shot and asymptotic characterizations.

Contribution

It proposes a novel partial smoothing method for information measures, improving the analysis of quantum and classical information-theoretic tasks.

Findings

Provides asymptotic second-order characterizations for privacy amplification and state splitting.

Tightly characterizes resource trade-offs in quantum state merging.

Enhances understanding of one-shot information-theoretic problems.

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.