We lay a comprehensive foundation for the study of redundant information storage in decoherence processes. Redundancy has been proposed as a prerequisite for objectivity, the defining property of classical objects. We consider two ensembles of states for a model universe consisting of one system and many environments: the first consisting of arbitrary states, and the second consisting of “singly branching” states consistent with a simple decoherence model. Typical states from the random ensemble do not store information about the system redundantly, but information stored in branching states has a redundancy proportional to the environment’s size. We compute the specific redundancy for a wide range of model universes, and fit the results to a simple first-principles theory. Our results show that the presence of redundancy divides information about the system into three parts: classical (redundant); purely quantum; and the borderline, undifferentiated or “nonredundant,” information.

• Received 16 May 2005

DOI:https://doi.org/10.1103/PhysRevA.73.062310