  Entanglement polytopes result in finitely many types of entanglement that can
be detected by only measuring single-particle spectra. With high probability,
however, the local spectra lie in more than one polytope, hence providing no
information about the entanglement type. To overcome this problem, we propose
to additionally use local filters. We experimentally demonstrate the detection
of entanglement polytopes in a four-qubit system. Using local filters we can
distinguish the entanglement type of states with the same single particle
spectra, but which belong to different polytopes.
