Unsharp pointer observables and the structure of decoherence

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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 relations
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.