Quasi-orthogonal packing capacity of a D-dimensional Hilbert space is exponential in D (doubly exponential in particle number), so typical environmental branch overlaps are exponentially small in entropy.
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Double-Exponential Quasi-Orthogonality: The Geometry of Decoherence
Quasi-orthogonal packing capacity of a D-dimensional Hilbert space is exponential in D (doubly exponential in particle number), so typical environmental branch overlaps are exponentially small in entropy.