Tensor Fields on Orbits of Quantum States and Applications

On classical Lie groups, which act by means of a unitary representation on finite dimensional Hilbert spaces, quantum state dependent tensor field constructions are considered. While evading the traditional ambiguity on defining metrical structures on the convex set of mixed states, one can show that these tensor field constructions allow an alternative approach to the problem of deciding whether a given state in a n-level bi-partite quantum system is entangled or separable.