Wigner negativity in spin-<i>j</i> systems

The nonclassicality of simple spin systems as measured by Wigner negativity is studied on a spherical phase space. Several SU(2)-covariant states with common qubit representations are addressed: spin coherent, spin cat (GHZ/N00N), and Dicke (W). We derive a bound on the Wigner negativity of spin cat states that rapidly approaches the true value as spin increases beyond j≈5. We find that spin cat states are not significantly Wigner-negative relative to their Dicke state counterparts of equal dimension. We also find, in contrast to several entanglement measures, that the most Wigner-negative Dicke basis element is spin-dependent, and is not the equatorial state │j,0〉 (or │j,±1/2〉for half-integer spins). These results underscore the influence that dynamical symmetry has on nonclassicality, and suggest a guiding perspective for finding novel quantum computational applications.