Barycentric measure of quantum entanglement

Majorana representation of quantum states by a constellation of n "stars" (points on the sphere) can be used to describe any pure state of a simple system of dimension n + 1 or a permutation symmetric pure state of a composite system consisting of n qubits. We analyze the variance of the distribution of the stars, which can serve as a measure of the degree of noncoherence for simple systems or an entanglement measure for composed systems. Dynamics of the Majorana points induced by a unitary dynamics of a pure state is investigated.