Stellar representation of extremal Wignernegative spin states
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 Wignernegative 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 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 nonzero Wigner negativity. This offers evidence that all pure spin states also have nonzero Wigner negativity. The results can be applied to qubit ensembles exhibiting permutation invariance.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 June 2023
 DOI:
 10.1088/17518121/acd918
 arXiv:
 arXiv:2206.00195
 Bibcode:
 2023JPhA...56z5302D
 Keywords:

 Wigner negativity;
 stellar representation;
 spinj systems;
 symmetric state;
 entanglement;
 Quantum Physics
 EPrint:
 doi:10.1088/17518121/acd918