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arXiv · 1205.5231

Chain Rules for Smooth Min- and Max-Entropies

Alexander Vitanov·Frederic Dupuis·Marco Tomamichel·Renato Renner
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Abstract

The chain rule for the Shannon and von Neumann entropy, which relates the total entropy of a system to the entropies of its parts, is of central importance to information theory. Here we consider the chain rule for the more general smooth min- and max-entropy, used in one-shot information theory. For these entropy measures, the chain rule no longer holds as an equality, but manifests itself as a set of inequalities that reduce to the chain rule for the von Neumann entropy in the i.i.d. case.

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Alexander Vitanov, Frederic Dupuis, Marco Tomamichel, Renato Renner. 2013-10-24. Chain Rules for Smooth Min- and Max-Entropies. https://doi.org/10.1109/tit.2013.2238656

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