Duality of privacy amplification against quantum adversaries and data compression with quantum side information

Abstract

We show that the tasks of privacy amplification against quantum adversaries and data compression with quantum side information are dual in the sense that the ability to perform one implies the ability to perform the other. These are two of the most important primitives in classical information theory, and are shown to be connected by complementarity and the uncertainty principle in the quantum setting. Applications include a new uncertainty principle formulated in terms of smooth min- and max-entropies, as well as new conditions for approximate quantum error correction.Comment: v2: Includes a derivation of an entropic uncertainty principle for smooth min- and max-entropies. Discussion of the Holevo-Schumacher-Westmoreland theorem remove