Most symmetric separable states with conserved charge N are not symmetrically separable, with number entanglement showing Gaussian concentration around a strictly positive value.
BecauseD sep ˆN is a closed convex set 6, it has an (integer) purification dimension p-dimD sep ˆN =D, and a purifying manifoldχ 0, as defined in the previous section
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The typicality of symmetry-induced entanglement
Most symmetric separable states with conserved charge N are not symmetrically separable, with number entanglement showing Gaussian concentration around a strictly positive value.