2019/09/30 by Mark M. Wilde · 1 citation
Physics and Astronomy · Computer Science · Mathematics · #quant-ph #cs.IT #hep-th #math-ph #math.IT #math.MP
paper · pdf · doi:10.1007/s11128-019-2563-4
published as Quantum Information Processing vol. 19, Article no. 61, January 2020 · v2: 11 pages, accepted for publication in Quantum Information Processing
arxiv created 2020/01/22 · arxiv updated 2020/01/23
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.