Optimal uniform continuity bound for conditional entropy of classical--quantum states

Abstract

In this short note, I show how a recent result of Alhejji and Smith [arXiv:1909.00787] regarding an optimal uniform continuity bound for classical conditional entropy leads to an optimal uniform continuity bound for quantum conditional entropy of classical--quantum states. The bound is optimal in the sense that there always exists a pair of classical--quantum states saturating the bound, and so no further improvements are possible. An immediate application is a uniform continuity bound for entanglement of formation that improves upon the one previously given by Winter in [arXiv:1507.07775]. Two intriguing open questions are raised regarding other possible uniform continuity bounds for conditional entropy, one about quantum--classical states and another about fully quantum bipartite states.

v2: 11 pages, accepted for publication in Quantum Information Processing

References in corpus (3)

• A Sharp Fannes-type Inequality for the von Neumann Entropy
• Continuity of quantum channel capacities
• A Tight Uniform Continuity Bound for Equivocation

Cited by in corpus (9)

• Bounding quantum capacities via partial orders and complementarity
• Continuity of characteristics of composite quantum systems
• 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
• Entanglement cost for infinite-dimensional physical systems
• Continuity bounds for quantum entropies arising from a fundamental entropic inequality
• Fundamental limitations to key distillation from Gaussian states with Gaussian operations
• Lipschitz continuity of quantum-classical conditional entropies with respect to angular distance and related properties