We present a method to construct entanglement measures for pure states of multipartite qubit systems. The key element of our approach is an antilinear operator that we call { \em comb} in reference to the { \em hairy-ball theorem}. For qubits (or spin 1/2) the combs are automatically invariant under $SL(2,\CC)$. This implies that the { \em filters} obtained from the combs are entanglement monotones by construction. We give alternative formulae for the concurrence and the 3-tangle as expectation values of certain antilinear operators. As an application we discuss inequivalent types of genuine four-, five- and six-qubit entanglement.
Categories: quant-ph