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