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.
The denominator, however, is barely above the floor: using the 2-replica method, the typical purity is (dA +d B)/(dAdB + 1)≈2 −|A| + 2−(N−|A|)
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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.