The algebra of local unitary invariants of identical particles

We investigate the properties of the inverse limit of the algebras of local unitary invariant polynomials of quantum systems containing various types of fermionic and/or bosonic particles as the dimensions of the single particle state spaces tend to infinity. We show that the resulting algebras are free and present a combinatorial description of an algebraically independent generating set in terms of graphs. These generating sets can be interpreted as minimal sets of polynomial entanglement measures distinguishing between states showing different nonclassical behaviour.