Uniform continuity bound for sandwiched R\'enyi conditional entropy

TL;DR

This paper establishes a simple, dimension-independent uniform continuity bound for the sandwiched Re9nyi conditional entropy across a range of b5 values, enhancing understanding of its stability.

Contribution

It introduces a novel uniform continuity bound for sandwiched Re9nyi conditional entropy valid for b5 in [1/2, 1) b7 (1, b5] that does not depend on the dimension of the conditioning system.

Findings

Bound is independent of system dimension

Applicable for b5 in [1/2, 1) b7 (1, b5]

Simplifies analysis of sandwiched Re9nyi entropy stability

Abstract

We prove a simple uniform continuity bound for the sandwiched R\'enyi conditional entropy for $\alpha \in [1/2, 1) \cup (1, \infty]$, which is independent of the dimension of the conditioning system.