Entanglement distance for an arbitrary state of M qubits

We propose a measure of entanglement that can be computed for any pure state of an $M$-qubit system. The entanglement measure has the form of a distance that we derive from an adapted application of the Fubini-Study metric. This measure is invariant under local unitary transformations and defined as trace of a suitable metric that we derive, the entanglement metric $tilde{g}$. Furthermore, the analysis of the eigenvalues of $tilde{g}$ gives information about the robustness of entanglement.