On the rational invariants of quantum systems of n-qubits

For an n-qubit system, a rational function on the space of mixed states which is invariant with respect to the action of the group of local symmetries may be viewed as a detailed measure of entanglement. We show that the field of all such invariant rational functions is purely transcendental over the complex numbers and has transcendence degree 4^n - 2n-1. An explicit transcendence basis is also exhibited.