  The theory of decoherence attempts to explain the emergent classical
behaviour of a quantum system interacting with its quantum environment. In
order to formalize this mechanism we introduce the idea that the information
preserved in an open quantum evolution (or channel) can be characterized in
terms of observables of the initial system. We use this approach to show that
information which is broadcast into many parts of the environment can be
encoded in a single observable. This supports a model of decoherence where the
pointer observable can be an arbitrary positive operator-valued measure (POVM).
This generalization makes it possible to characterize the emergence of a
realistic classical phase-space. In addition, this model clarifies the
relationships among the information preserved in the system, the information
flowing from the system to the environment (measurement), and the establishment
of correlations between the system and the environment.
