Randomness extraction via a quantum generalization of the conditional collision entropy

Randomness extraction against side information is the art of distilling from a given source a key which is almost uniform conditioned on the side information. This paper provides randomness extraction against quantum side information whose extractable key length is given by a quantum generalization of the conditional collision entropy defined without the conventional smoothing. Based on the fact that the collision entropy is not subadditive, the quantum conditional collision entropy maximized with respect to additional side information is introduced, and is shown to be asymptotically optimal. The lower bound on it derived there ensures faster convergence to the conditional von Neumann entropy than that on the smooth min-entropy.