Wigner negativity in spin-j 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 analyzed: spin coherent states, spin cat (Greenberger-Horne-Zeilinger or N00N) states, and Dicke (W) states. We derive a bound on the Wigner negativity of spin cat states that rapidly approaches the true value as spin increases beyond j greater than or similar to 5. We find that spin cat states are not significantlyWigner negative relative to their Dicke state counterparts of equal dimension. We also find, in contrast to several entanglement measures, that the mostWigner-negative Dicke basis element is spin dependent, and not the equatorial state vertical bar j, 0) (or vertical bar 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.