Wigner negativity in spin-$j$ systems

Abstract

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 ($\text{W}$). We derive a bound on the Wigner negativity of spin cat states that rapidly approaches the true value as spin increases beyond $j\gtrsim 5$. 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 not the equatorial state $|j,0⟩$ (or $|j,\pm 1/2⟩$ 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.

11 pages, 7 figures

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