Entanglement robustness and geometry in systems of identical particles

The robustness properties of bipartite entanglement in systems of N bosons distributed in M different modes are analyzed using a definition of separability based on commuting algebras of observables, a natural choice when dealing with identical particles. Within this framework, expressions for the robustness and generalized robustness of entanglement can be explicitly given for large classes of boson states: Their entanglement content turns out to be, in general, much more stable than that of distinguishable particles states. Using these results, the geometrical structure of the space of N-boson states can be explicitly addressed.