Critical points of the linear entropy for pure L-qubit states

We present a substantially improved version of the method proposed by Sawicki et al (2012 Phys. Rev. A 86 040304(R), 2014 Rev. Math. Phys. 26 1450004) for finding critical points of the linear entropy for an L-qubit system. The new approach is based on the correspondence between the momentum maps for abelian and non-abelian groups, as described in Kirwan (1984 Cohomology of Quotients in Symplectic and Algebraic Geometry (Mathematical Notes vol 31) (Princeton: Princeton Univ. Press)). The proposed method can be implemented numerically and is much easier than the previous method.