Most symmetric separable states with conserved charge N are not symmetrically separable, with number entanglement showing Gaussian concentration around a strictly positive value.
Gurvits, inProceedings of the Thirty-Fifth Annual ACM Symposium on Theory of Computing, STOC ’03 (Association for Computing Machinery, New York, NY, USA, 2003) p
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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.