Stellar representation of extremal Wigner-negative spin states

TL;DR

This paper uses the Majorana stellar representation to identify and analyze spin states with maximal Wigner negativity, revealing their unique configurations and rarity, and proving all coherent states have non-zero negativity.

Contribution

It characterizes extremal Wigner-negative spin states using Majorana representation and proves all coherent states have non-zero negativity, extending understanding of nonclassicality.

Findings

Maximal Wigner-negative states often lack high symmetry or Platonic solid configurations.

Random states up to spin 6 show high average negativity, but extremal states are rare.

All spin coherent states have non-zero Wigner negativity.

Abstract

The Majorana stellar representation is used to characterize spin states that have a maximally negative Wigner quasiprobability distribution on a spherical phase space. These maximally Wigner-negative spin states generally exhibit a partial but not high degree of symmetry within their star configurations. In particular, for spin $j > 2$, maximal constellations do not correspond to a Platonic solid when available and do not follow an obvious geometric pattern as dimension increases. In addition, they are generally different from spin states that maximize other measures of nonclassicality such as anticoherence or geometric entanglement. Random states ($j \leq 6$) display on average a relatively high amount of negativity, but the extremal states and those with similar negativity are statistically rare in Hilbert space. We also prove that all spin coherent states of arbitrary dimension have non-zero Wigner negativity. This offers evidence that all pure spin states also have non-zero Wigner negativity. The results can be applied to qubit ensembles exhibiting permutation invariance.