Universal separability and entanglement in identical-particle systems

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 independently and identically distributed (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.

Figure 1

Schematic diagram of spaces introduced for examination of entanglement. Given a pair $(\Gamma ,V)$, one can find in the total Hilbert space ${\mathcal{H}}_{\mathcal{X}}$ the subspace ${\mathcal{H}}_{\mathcal{X}}(\Gamma ,V),$ which is unitarily equivalent to the space ${\mathcal{H}}^{\mathrm{mes}}(\Gamma ,V)$ describing the measurement results under the map $\mathcal{X}$.