Wigner negativity on the sphere

Abstract

The rise of quantum information theory has largely vindicated the long-held belief that Wigner negativity is an indicator of genuine nonclassicality in quantum systems. This thesis explores its manifestation in spin-j systems using the spherical Wigner function. Common symmetric multi-qubit states are studied and compared. Spin coherent states are shown to never have vanishing Wigner negativity. Pure states that maximize negativity are determined and analyzed using the Majorana stellar representation. The relationship between negativity and state mixedness is discussed, and polytopes characterizing unitary orbits of lower-bounded Wigner functions are studied. Results throughout are contrasted with similar works on symmetric state entanglement and other forms of phase-space nonclassicality.