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Entanglement is known to be a relative notion, defined with respect to thechoice of physical observables to be measured (i.e., the measurement setupused). This implies that, in general, the same state can be both separable andentangled for different measurement setups, but this does not exclude theexistence of states which are separable (or entangled) for all possible setups.We show that for systems of bosonic particles there indeed exist suchuniversally separable states: they are i.i.d. pure states. In contrast, thereis no such state for fermionic systems with a few exceptional cases. We alsofind that none of the fermionic and bosonic systems admits universallyentangled states.

Universal Separability and Entanglement in Identical Particle Systems