  We show that three principle means of treating privacy amplification in
quantum key distribution, private state distillation, classical privacy
amplification, and via the uncertainty principle, are equivalent and
interchangeable. By adapting the security proof based on the uncertainty
principle, we construct a new protocol for private state distillation which we
prove is identical to standard classical privacy amplification. Underlying this
approach is a new characterization of private states, related to their standard
formulation by the uncertainty principle, which gives a more physical
understanding of security in quantum key distribution.
