Super-quantum states in SU(2) invariant 3×N level systems

Nonclassicality of quantum states is expressed in many shades, one of the most stringent of them being a new standard introduced recently in Bharath and Ravishankar (2014), by expanding the notion of local hidden variables (LHV) to generalised local hidden variables (GLHV). Considering the family of SU(2) invariant 3×N level systems, we identify those states that do not admit a GLHV description, which we designate as super-quantum (called exceptional in Bharath and Ravishankar (2014). We show that all super-quantum states admit a universal geometrical description, and that they are most likely to lie on a line segment in the manifold, irrespective of the value of N. We also show that though a super-quantum state can be highly mixed, its relative rank with respect to the uniform state is always less than that of a state which admits a GLHV description.