Privacy amplification and decoupling without smoothing

TL;DR

This paper extends privacy amplification and decoupling results to a broader range of sandwiched Rényi entropies, eliminating the need for smoothing and simplifying the analysis of quantum information tasks.

Contribution

It proves an achievability result for privacy amplification and decoupling using sandwiched Rényi entropy for α in (1,2], bypassing smoothing techniques.

Findings

Enables error exponent calculation for quantum tasks.

Simplifies proofs by replacing smoothing with Rényi entropy optimization.

Extends previous results limited to α=2.

Abstract

We prove an achievability result for privacy amplification and decoupling in terms of the sandwiched R\'enyi entropy of order $\alpha \in (1,2]$; this extends previous results which worked for $\alpha=2$. The fact that this proof works for $\alpha$ close to 1 means that we can bypass the smooth min-entropy in the many applications where the bound comes from the fully quantum AEP or entropy accumulation, and carry out the whole proof using the R\'enyi entropy, thereby easily obtaining an error exponent for the final task. This effectively replaces smoothing, which is a difficult high-dimensional optimization problem, by an optimization problem over a single real parameter $\alpha$.