The Smooth Entropy Formalism on von Neumann Algebras

Details The Smooth Entropy Formalism on von Neumann Algebras The Smooth Entropy Formalism on von Neumann Algebras

2011-07-27

arxiv.org/abs/1107.5460v1

Physics

Quantum Physics

Scientific paper

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.

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