  In the last years, a relationship has been established between the quantum
Fisher information (QFI) and quantum entanglement. In the case of two-qubit
systems, all pure entangled states can be made useful for sub-shot-noise
interferometry while their QFI meets a necessary and sufficient condition [1].
In M-qubit systems, the QFI provides just a sufficient condition in the task of
detecting the degree of entanglement of a generic state [2]. In our work, we
show analytically that, for a large class of one-parameter non-optimal
two-qubit states, the maximally entangled states are associated with stationary
points of the QFI, as a function of such parameter. We show, via numerical
simulations, that this scenario is maintained for the generalisation of this
class of states to a generic M-qubit system. Furthermore, we suggest a scheme
for an interferometer able to detect the entanglement in a large class of
two-spin states.
