Wigner negativity in spin-$j$ systems

TL;DR

This paper investigates Wigner negativity as a measure of nonclassicality in spin-$j$ systems, deriving bounds and comparing different states to understand their quantum features and potential computational uses.

Contribution

It provides new bounds on Wigner negativity for spin cat states and reveals how dynamical symmetry influences nonclassicality in spin systems.

Findings

Spin cat states' negativity approaches true value for large spins

Spin cat states are not more Wigner-negative than Dicke states of same dimension

The most Wigner-negative Dicke basis element depends on spin, not just the equatorial state

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 ($\textsf{W}$). 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 $| j,0 \rangle$ (or $|j,\pm 1/2 \rangle$ 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.