If record projectors commute with an apparatus-environment interaction, their populations are preserved while the corresponding environmental states can become distinguishable. Their conditional environment overlap then suppresses interference in the apparatus reduced density matrix. A nondegenerate record coupling can thereby select robust sectors; commutation alone does not select a unique basis in a degenerate or trivial interaction.[ref]
Pointer basis of quantum apparatus: Into what mixture does the wave packet collapse? by W. H. Zurek. 1981 abstract: recorded observables and the apparatus-environment interaction commutation condition
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