  In the case of two qubits, standard entanglement monotones like the linear
entropy fail to provide an efficient quantum estimation in the regime of weak
entanglement. In this paper, a more efficient entanglement estimation, by means
of a novel class of entanglement monotones, is proposed. Following an approach
based on the geometric formulation of quantum mechanics, these entanglement
monotones are defined by inner products on invariant tensor fields on bipartite
qubit orbits of the group SU(2)xSU(2).
