A Tight Uniform Continuity Bound for Equivocation

Abstract

We prove a tight uniform continuity bound for the conditional Shannon entropy of discrete finitely supported random variables in terms of total variation distance.

arXiv comment4 pages, streamlined the proof in v2, minor changes + added a clarifying sentence in v3

References in corpus (8)

• A Sharp Fannes-type Inequality for the von Neumann Entropy
• Tight uniform continuity bounds for quantum entropies: conditional entropy, relative entropy distance and energy constraints
• Continuity of quantum conditional information
• Continuity of quantum channel capacities
• Approximate Degradable Quantum Channels
• Tight continuity bounds for the quantum conditional mutual information, for the Holevo quantity and for capacities of quantum channels
• Entropy Bounds for Discrete Random Variables via Maximal Coupling
• Maximum and minimum entropy states yielding local continuity bounds

Cited by in corpus (6)

• Optimal uniform continuity bound for conditional entropy of classical--quantum states
• Continuous majorization in quantum phase space
• A tight uniform continuity bound for the Arimoto-Rényi conditional entropy and its extension to classical-quantum states
• Close-to-optimal continuity bound for the von Neumann entropy and other quasi-classical applications of the Alicki-Fannes-Winter technique
• Continuity of entropies via integral representations
• Continuity bounds for quantum entropies arising from a fundamental entropic inequality