  We introduce the notion of an X-state on $n$-qubits. After taking the Zariski
closure of the set of X-states in the space of all mixed states, we obtain a
complex algebraic variety $\scr X$ that is equipped with the action of the Lie
group of local symmetries $G$. We show that the field of $G$-invariant rational
functions on $\scr X$ is purely transcendental over the complex numbers of
degree $2^{2n-1}-n-1$.
