Equivalence between contextuality and negativity of the Wigner function   for qudits
  Contextuality and negativity of the Wigner function are two notions of non-classicality for quantum systems. Howard, Wallman, Veitch and Emerson proved recently that these two notions coincide for qudits in odd prime dimension. This equivalence is particularly important since it promotes contextuality as a ressource that magic states must possess in order to allow for a quantum speed-up. We propose a simple proof of the equivalence between contextuality and negativity of the Wigner function based on character theory. This simplified approach allows us to generalize this equivalence to multiple qudits and to any qudit system of odd local dimension. 
Nicolas Delfosse, Cihan Okay, Juan Bermejo-Vega, Dan E. Browne and   Robert Raussendorf
quant-ph