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.
Cite
@article{arxiv.1909.01755,
title = {Optimal uniform continuity bound for conditional entropy of classical--quantum states},
author = {Mark M. Wilde},
journal= {arXiv preprint arXiv:1909.01755},
year = {2020}
}
Comments
v2: 11 pages, accepted for publication in Quantum Information Processing