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

摘要

Nonclassicality of quantum states is expressed in many shades, the moststringent of them being a new standard introduced recently in [Phys. Rev. A 89,062110 (2014)]. This is accomplished by expanding the notion of local hiddenvariables (LHV) to generalised local hidden variables (GLHV), which rendersmany nonlocal states also classical. We investigate these super-quantum states(called exceptional in [Phys. Rev. A 89, 062110 (2014)]) in the family of$SU(2)$ invariant $3 \times N$ level systems. We show that all super-quantumstates admit a universal geometrical description, and that they are most likelyto lie on a line segment in the manifold, irrespective of the value of $N$. Wealso show that though the super - quantum states can be highly mixed, itsrelative rank with respect to the uniform state is always less than that of astate which admits a GLHV description.