Complementarity, privacy, and entanglement

We develop a complementary information tradeoff which bounds the amount of information about complementary observables that can be simultaneously extracted from a quantum system. This leads directly to a simple characterization both private states (the quantum version of secret keys) and maximally-entangled states, revealing these to be a direct manifestation of the quantum mechanical phenomenon of complementarity. Furthermore, we conjecture a strengthened version of the tradeoff and show how these ideas can be adapted to create protocols for distilling secret keys or entangled states