English

Chain Rules for Smooth Min- and Max-Entropies

Quantum Physics 2013-10-25 v2 Mathematical Physics math.MP

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.

Keywords

Cite

@article{arxiv.1205.5231,
  title  = {Chain Rules for Smooth Min- and Max-Entropies},
  author = {Alexander Vitanov and Frederic Dupuis and Marco Tomamichel and Renato Renner},
  journal= {arXiv preprint arXiv:1205.5231},
  year   = {2013}
}
R2 v1 2026-06-21T21:08:36.118Z