An m-fold superposition of typical sub-maximally entangled states gains a universal ln(m) entanglement enhancement, while maximally entangled states relax to the Haar limit via N-independent scaling laws.
(A4) collapse to the univer- sal cross-overlap2 −|A|: by independenceE[Tr(ρ A ψ ρA ϕ )] = Tr((¯ρA)2) = 2−|A|, fixed by the Hilbert-space dimension alone
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Typical Entanglement of Superpositions
An m-fold superposition of typical sub-maximally entangled states gains a universal ln(m) entanglement enhancement, while maximally entangled states relax to the Haar limit via N-independent scaling laws.