Optimal uniform continuity bound for conditional entropy of classical--quantum states
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Publication:6324667
DOI10.1007/S11128-019-2563-4arXiv1909.01755WikidataQ126413851 ScholiaQ126413851MaRDI QIDQ6324667
Publication date: 4 September 2019
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.
Measures of information, entropy (94A17) Quantum information, communication, networks (quantum-theoretic aspects) (81P45)
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