Universal framework for entanglement detection

We construct nonlinear multiparty entanglement measures for distinguishable particles, bosons, and fermions. In each case properties of an entanglement measure are related to the decomposition of the suitably chosen representation of the relevant symmetry group onto irreducible components. In the case of distinguishable particles considered entanglement measure reduces to the well-known many-particle concurrence. We prove that our entanglement criterion is sufficient and necessary for pure states living in both finite and infinite dimensional spaces. We generalize our entanglement measures to mixed states by the convex roof extension and give a nontrivial lower bound of thus obtained generalized concurrence.