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The Smooth Entropy Formalism on von Neumann Algebras | | Mario Berta
; Fabian Furrer
; Volkher B. Scholz
; | | Date: |
27 Jul 2011 | | Abstract: | We discuss quantum information theoretical concepts on von Neumann algebras
and lift the smooth entropy formalism to the most general quantum setting. For
the smooth min- and max-entropies 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 sketch possible
applications to continuous variable 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.
From this we generalize the formula of Renes and Renner characterizing the
optimal length of a distillable secure finite-key. We also elaborate on the
question when the formalism of von Neumann algebras is of advantage in the
description of quantum systems with an infinite number of degrees of freedom. | | Source: | arXiv, 1107.5460 | | Services: | Forum | Review | PDF | Favorites | |
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