Bipartite entanglement in systems of identical particles: The partial transposition criterion

We study bipartite entanglement in systems of NN identical bosons distributed in MM different modes. For such systems, a definition of separability not related to any a priori Hilbert space tensor product structure is needed and can be given in terms of commuting subalgebras of observables. Using this generalized notion of separability, we classify the states for which partial transposition turns out to be a necessary and sufficient condition for entanglement detection.

► Mode-entanglement vs particle entanglement for identical particles.
► Negativity results an exhaustive entanglement witness for NN boson systems.
► Complete characterization of PPT states for NN boson systems.