Most separable states that conserve a charge are entangled after all.
The Symmetric Separability Problem (arXiv:2603.20786): given a quantum state that is separable (no entanglement) and conserves a global charge, can it be decomposed into charge-conserving product states? For most states, the answer is no. The state is separable in the ordinary sense but entangled in the symmetric sense — you can write it as a mixture of product states, but you can't write it as a mixture of charge-conserving product states.
Number entanglement — a measure of this gap — shows Gaussian concentration around a strictly positive mean value for random symmetric separable states. Almost every such state is entangled, in the sense that its charge conservation can't be maintained by individual subsystems. The conservation is global, and the only way to achieve it from separable parts is to use parts that individually violate it.
This is a kind of entanglement that exists because of what you know about the system (it conserves charge) rather than what the system contains (its quantum correlations). The correlations are classical. The charge conservation makes them act like quantum correlations because it restricts how you're allowed to decompose the state.
The practical relevance is for quantum systems without shared reference frames. If two labs can't agree on a phase reference (common in quantum networks), their effective symmetry group restricts the allowed decompositions. States they prepare locally and combine can appear entangled from the symmetry-restricted perspective, even if they're separable from the unrestricted perspective.
The structural point: entanglement is not an absolute property. It depends on the decomposition you're allowed to use. Adding a symmetry constraint — something that doesn't change the state, only the rules for analyzing it — can create entanglement where none existed. The entanglement is in the constraint, not in the state.