Hi all,
This Tuesday's talk will be by Fabian Furrer in HIT K52 at 5pm. Title and abstract below.
Cheers, Roger
--- The min- and max-entropies for infinite-dimensional quantum systems.
Since the introduction of the (smooth) min- and max-entropy, various results have affirmed their fundamental importance in quantum information theory. We have studied the behavior of these entropies for quantum systems with infinite-dimensional separable Hilbert spaces. As a main result, we show that the min- and max-entropy in infinite dimensions can be expressed in terms of convergent series of finite-dimensional min- and max-entropies. This allows us to generalize various known properties of the finite-dimensional (smooth) min- and max-entropy to the case of arbitrary quantum systems. As one important application we present the extension of the scope of the smooth min-entropy in privacy amplification, by showing that it can be used to bound the length of a secret key extractable from an only partially secure one, even if we allow the adversary's system to have an infinite-dimensional Hilbert space.