The Smooth Entropy Formalism for von Neumann Algebras
Abstract
We discuss information-theoretic concepts on infinite-dimensional quantum systems. In particular, we lift the smooth entropy formalism as introduced by Renner and collaborators for finite-dimensional systems to von Neumann algebras. For the smooth conditional min- and max-entropy we recover similar characterizing properties and information-theoretic operational interpretations as in the finite-dimensional case. We generalize the entropic uncertainty relation with quantum side information of Tomamichel and Renner and discuss applications to quantum cryptography. In particular, we prove the possibility to perform privacy amplification and classical data compression with quantum side information modeled by a von Neumann algebra.
Keywords
Cite
@article{arxiv.1107.5460,
title = {The Smooth Entropy Formalism for von Neumann Algebras},
author = {Mario Berta and Fabian Furrer and Volkher B. Scholz},
journal= {arXiv preprint arXiv:1107.5460},
year = {2015}
}
Comments
v3: 28 pages, published version